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We investigate the long-time dynamics of generic time-dependent Lindblad master equations. In particular, we provide sufficient conditions such that asymptotically the dynamics is independent on the initial state preparation. These conditions represent a natural extension of Spohn's theorem to the case of a time-dependent generator. To illustrate our results, we analyse a quantum thermodynamics scenario and discuss the uniqueness of the limit cycle in a continuous Otto engine fuelled by a driven Ising chain, where the dissipation is described by non-local jump operators. As corollary of our main result, we show that any master equation which exhibits non-Markovianity in a finite time interval can be equally addressed by means of our approach. These findings pave the way for developing a more general theory of relaxation beyond the Markovian case., Comment: 11 pages, 1 figure

Thermodynamical systems at the nanoscale, such as single molecules interacting with highly structured vibrational environments, typically undergo non-equilibrium physical processes that lack precise microscopic descriptions. Photoisomerization is such an example which has emerged as a platform on which to study single-molecule ultrafast photochemical processes from a quantum resource theoretic perspective. However, upper bounds on its efficiency have only been obtained under significant simplifications that make the mathematics of the resource-theoretical treatment manageable. Here we generalize previous models for the photoisomers, while retaining the full vibrational structure, and still get analytical bounds on the efficiency of hotoisomerization. We quantify the impact of such vibrational structure on the optimal photoisomerization quantum yield both when the vibrational coordinate has no dynamics of its own and when we take into account the vibrational dynamics. This work serves as an example of how to bridge the gap between the abstract language of quantum resource theories and the open system formulation of nanoscale processes., Comment: 13 pages, 6 figures

Thermal machines are physical systems specifically designed to make thermal energy available for practical use through state transformations in a cyclic process. This concept relies on the presence of an additional element equipped with a clock, controlling which interaction Hamiltonian between the system and the reservoirs must act at a certain time and that remains unaffected during this process. In the domain of quantum dynamics, there is substantial evidence to suggest that fulfilling this final condition is, in fact, impossible, except in ideal and far-from-reality cases. In this study we start from one such idealized condition and proceed to relax the primary approximations to make the model more realistic and less ideal. The main result is a fully quantum description of the engine-clock dynamics within a realistic quantum framework. Furthermore, this approach offers the possibility to address the deeper and more fundamental challenge of defining meaningful time operators in the realm of quantum mechanics from a different standpoint., Comment: 9 pages, 2 figures

Currently envisaged tests for probing the quantum nature of the gravitational interaction in the low-energy regime typically focus either on the quantized center-of-mass degrees of freedom of two spherically-symmetric test masses or on the rotational degrees of freedom of non-symmetric masses under a gravitational interaction governed by the Newtonian potential. In contrast, here we investigate the interaction between the angular momenta of spherically-symmetric test masses considering a tree-level relativistic correction related to frame-dragging that leads to an effective dipolar interaction between the angular momenta. In this approach, the mass of the probes is not directly relevant; instead, their angular momentum plays the central role. We demonstrate that, while the optimal entangling rate is achieved with a maximally delocalized initial state, significant quantum correlations can still arise between two rotating systems even when each is initialized in an eigenstate of rotation. Additionally, we examine the robustness of the generated entanglement against typical sources of noise and observe that our combination of angular momentum and spherically-symmetric test-masses mitigates the impact of many common noise sources.

Hybrid quantum architectures that integrate matter and photonic degrees of freedom present a promising pathway toward scalable, fault-tolerant quantum computing. This approach needs to combine well-established entangling operations between distant registers using photonic degrees of freedom with direct interactions between matter qubits within a solid-state register. The high-fidelity control of such a register, however, poses significant challenges. In this work, we address these challenges with pulsed control sequences which modulate all inter-spin interactions to preserve the nearest-neighbor couplings while eliminating unwanted long-range interactions. We derive pulse sequences, including broadband and selective gates, using composite pulse and shaped pulse techniques as well as optimal control methods. This ensures robustness against uncertainties in spin positions, static offset detunings, and Rabi frequency fluctuations of the control fields. The control techniques developed here apply well beyond the present setting to a broad range of physical platforms. We demonstrate the efficacy of our methods for the resource state generation for fusion-based quantum computing in four- and six-spin systems encoded in the electronic ground states of nitrogen-vacancy centers. We also outline other elements of the proposed architecture, highlighting its potential for advancing quantum computing technology., Comment: 22 pages, 11 figures

The combination of chain-mapping and tensor-network techniques provides a powerful tool for the numerically exact simulation of open quantum systems interacting with structured environments. However, these methods suffer from a quadratic scaling with the physical simulation time, and therefore they become challenging in the presence of multiple environments. This is particularly true when fermionic environments, well-known to be highly correlated, are considered. In this work we first illustrate how a thermo-chemical modulation of the spectral density allows replacing the original fermionic environments with equivalent, but simpler, ones. Moreover, we show how this procedure reduces the number of chains needed to model multiple environments. We then provide a derivation of the fermionic Markovian closure construction, consisting of a small collection of damped fermionic modes undergoing a Lindblad-type dynamics and mimicking a continuum of bath modes. We describe, in particular, how the use of the Markovian closure allows for a polynomial reduction of the time complexity of chain-mapping based algorithms when long-time dynamics are needed., Comment: 20 pages, 9 figures. Submitted to the Journal of Chemical Physics

We introduce pentacene-doped naphthalene as a material for diamagnetic levitation, offering compelling applications in matter-wave interferometry and nuclear magnetic resonance. Pentacene-doped naphthalene offers remarkable polarizability of its nuclear spin ensemble, achieving polarization rates exceeding 80 % at cryogenic temperatures with polarization lifetimes extending weeks. We design a multi-spin Stern-Gerlach-type interferometry protocol which, thanks to the homogeneous spin distribution and the absence of a preferential nuclear-spin quantization axis, avoids many of the limitations associated with materials hosting electronic spin defects, such as nanodiamonds containing NV centers. We assess the potential of our interferometer to enhance existing bounds on the free parameters of objective collapse models. Beyond matter-wave interferometry, we analyze the prospects for implementing magic angle spinning at frequencies surpassing the current standard in NMR, capitalizing on the exceptional rotational capabilities offered by levitation. Additionally, we outline a novel protocol for measuring spin ensemble polarization via the position of the nanoparticle and conduct an analysis of dominant noise sources, benchmarking the required isolation levels for various applications., Comment: 27 pages, 10 figures

In a theoretical study, we investigate the spin dynamics of interacting nitrogen-vacancy (NV) centers and quadrupolar I = 3/2 nuclear spins, specifically 11B spins in hexagonal boron nitride (h-BN) nanosheets located near the microdiamond surface. We demonstrate the possibility of obtaining external spin-polarization by magnetic-field sweeps across the level anticrossings around zero-field. To achieve this, we leverage crystal strains to establish a polarization transfer mechanism that remains robust against variations in NV orientation, crystal strain inhomogeneity, and electron-nuclear effective couplings. These results pave the way for hyperpolarization of spins in nanomaterials near the diamond surface without experiencing polarization loss to intrinsic nuclear spin-1/2 species, such as 13C and 1H nuclear spins in diamond. The 11B spins in h-BN nanosheets, with their extended relaxation time and large surface area, present a promising alternative for relayed nuclear polarization to the liquid phase and for the development of quantum simulators based on surface nuclear spins., Comment: 15pages,11figures

Nuclear hyperpolarization is a known method to enhance the signal in nuclear magnetic resonance (NMR) by orders of magnitude. The present work addresses the $^{13}$C hyperpolarization in diamond micro- and nanoparticles, using the optically-pumped nitrogen-vacancy center (NV) to polarize $^{13}$C spins at room temperature. Consequences of the small particle size are mitigated by using a combination of surface treatment improving the $^{13}$C relaxation ($T_1$) time, as well as that of NV, and applying a technique for NV illumination based on a microphotonic structure. Monitoring the light-induced redistribution of the NV spin state populations with electron paramagnetic resonance, a strong polarization enhancement for the NV spin state is observed in a narrow spectral region corresponding to about 4\% of these defect centers. By combining adjustments to the `PulsePol' sequence and slow sample rotation, the NV-$^{13}$C polarization transfer rate is improved further. The hyperpolarized $^{13}$C NMR signal is observed in particles of 2 $\mu$m and 100 nm median sizes, with enhancements over the thermal signal (at 0.29 T magnetic field), of 1500 and 940, respectively. The present demonstration of room-temperature hyperpolarization anticipates the development of agents based on nanoparticles for sensitive magnetic resonance applications., Comment: 49 pages, 29 figures (main text: 15 pages, 5 figures and Supporting Information: 34 pages, 24 figures) Uploaded new version on March 24th, 2024: corrected affiliations, some typos/formatting

Noise in quantum devices is generally considered detrimental to computational accuracy. However, the recent proposal of noise-assisted simulation has demonstrated that noise can be an asset in digital quantum simulations of open systems on Noisy Intermediate-Scale Quantum (NISQ) devices. In this context, we introduce an optimized decoherence rate control scheme that can significantly reduce computational requirements by multiple orders of magnitude, in comparison to the original noise-assisted simulation. We further extend this approach to encompass Lindblad equations with time-dependent coefficients, using only quantum error characterization and mitigation techniques. This extension allows for the perturbative simulation of non-Markovian dynamics on NISQ devices, eliminating the need for ancilla qubits or mid-circuit measurements. Our contributions are validated through numerical experiments on an emulated IBMQ device. Overall, our work offers valuable optimizations that bring current quantum processors closer to effectively simulating realistic open systems.

Quantum heat engines are commonly believed to achieve their optimal efficiency when operated under quasi-static conditions. However, when running at finite power, they suffer effective friction due to the generation of coherences and transitions between energy eigenstates. It was noted that it is possible to increase the power of a quantum heat engine using external control schemes or suitable dephasing noise. Here, we investigate the thermodynamic cost associated with dephasing noise schemes using both numerical and analytical methods. Our findings unveil that the observed gain in power is generally not free of thermodynamic costs, as it involves heat flows from thermal baths into the dephasing bath. These contributions must be duly accounted for when determining the engine's overall efficiency. Interestingly, we identify a particular working regime where these costs become negligible, demonstrating that quantum heat engines can be operated at any power with an efficiency per cycle that approaches arbitrarily closely that under quasistatic operation., Comment: 27 + 5 pages, 11 figures

We investigate the nonequilibrium steady state of the anisotropic open quantum Rabi model, which exhibits first-order and second-order dissipative phase transitions upon varying the degree of anisotropy between the coupling strengths of rotating and counterrotating terms. Using both semiclassical and quantum approaches, we find a rich phase diagram resulting from the interplay between the anisotropy and the dissipation. First, there exists a bistable phase where both the normal and superradiant phases are stable. Second, there are multicritical points where the phase boundaries for the first- and second-order phase transitions meet. We show that a new set of critical exponents governs the scaling of the multicritical points. Finally, we discuss the feasibility of observing the multicritical transitions and bistability using a pair of trapped ions where the anisotropy can be tuned by controlling the intensity of the Raman transitions. Our study enlarges the scope of critical phenomena that may occur in finite-component quantum systems, which could be useful for applications in critical quantum sensing., Comment: 14 pages, 4+4 figures

The detection of the quantum nature of gravity in the low-energy limit hinges on achieving an unprecedented degree of force sensitivity with mechanical systems. Against this background, we explore the relationship between the sensitivity of mechanical systems to external forces and the properties of the quantum states they are prepared in. We establish that the main determinant of the force sensitivity in pure quantum states is their spatial delocalisation and we link the force sensitivity to the rate at which two mechanical systems become entangled under a quantum force. We exemplify this at the hand of two commonly considered configurations. One that involves gravitationally interacting objects prepared in non-Gaussian states such as Schr\"odinger-cat states, where the generation of entanglement is typically ascribed to the accumulation of a dynamical phase between components in superposition. The other prepares particles in Gaussian states that are strongly squeezed in momentum and delocalised in position where entanglement generation is attributed to accelerations. We offer a unified description of these two arrangements using the phase-space representation and link their entangling rate to their force sensitivity, showing that both configurations get entangled at the same rate provided that they are equally delocalised in space. Our description in phase space and the established relation between force sensitivity and entanglement sheds light on the intricacies of why the equivalence between these two configurations holds, something that is not always evident in the literature, due to the distinct physical and analytical methods employed to study each of them. Notably, we demonstrate that while the conventional computation of entanglement via the dynamical phase remains accurate for Schr\"odinger-cat states, it yields erroneous estimations for systems in squeezed cat states., Comment: Invited contribution to Contemporary Physics. 16 pages (+ bibliography), 6 figures

We present a quantum sensing technique that utilizes a sequence of $\pi$ pulses to cyclically drive the qubit dynamics along a geodesic path of adiabatic evolution. This approach effectively suppresses the effects of both decoherence noise and control errors while simultaneously removing unwanted resonance terms, such as higher harmonics and spurious responses commonly encountered in dynamical decoupling control. As a result, our technique offers robust, wide-band, unambiguous, and high-resolution quantum sensing capabilities for signal detection and individual addressing of quantum systems, including spins. To demonstrate its versatility, we showcase successful applications of our method in both low-frequency and high-frequency sensing scenarios. The significance of this quantum sensing technique extends to the detection of complex signals and the control of intricate quantum environments. By enhancing detection accuracy and enabling precise manipulation of quantum systems, our method holds considerable promise for a variety of practical applications.

Although the Schr{\"o}dinger and Heisenberg pictures are equivalent formulations of quantum mechanics, simulations performed choosing one over the other can greatly impact the computational resources required to solve a problem. Here we demonstrate that in Gaussian boson sampling, a central problem in quantum computing, a good choice of representation can shift the boundary between feasible and infeasible numerical simulability. To achieve this, we introduce a novel method for computing the probability distribution of boson sampling based on the time evolution of tensor networks in the Heisenberg picture. In addition, we overcome limitations of existing methods enabling simulations of realistic setups affected by non-uniform photon losses. Our results demonstrate the effectiveness of the method and its potential to advance quantum computing research., Comment: 6 pages, 2 figures

We develop a Markovian master equation that models the evolution of systems subject to arbitrary driving and control fields. Our approach combines time rescaling and weak-coupling limits for the system-environment interaction with a secular approximation. The derivation makes use of the adiabatic time evolution operator in a manner that allows for the efficient description of strong driving, while recovering the adiabatic master equation in the appropriate limit. To illustrate the effectiveness of our approach, we apply it to the paradigmatic case of a two-level (qubit) system subjected to a form of periodic driving that remains unsolvable using a Floquet representation. We demonstrate the reliability and broad scope of our approach by benchmarking the solutions of the derived reduced time evolution against numerically exact simulations using tensor networks. Our results provide rigorous conditions that must be satisfied by phenomenological master equations for driven systems that do not rely on first principles derivations., Comment: 20+8 pages, 5 figures. Comments are welcome

We propose and analyze a driven-dissipative quantum sensor that is continuously monitored close to a dissipative critical point. The sensor relies on the critical open Rabi model with the spin and phonon degrees of freedom of a single trapped ion to achieve criticality-enhanced sensitivity. Effective continuous monitoring of the sensor is realized via a co-trapped ancilla ion that switches between dark and bright internal states conditioned on a `jump' of the phonon population which, remarkably, achieves nearly perfect phonon counting despite a low photon collection efficiency. By exploiting both dissipative criticality and efficient continuous readout, the sensor device achieves highly precise sensing of oscillating electric field gradients at a criticality-enhanced precision scaling beyond the standard quantum limit, which we demonstrate is robust to the experimental imperfections in real-world applications., Comment: 9 pages, 5 figures, close to the published version

Conducting precise electronic-vibrational dynamics simulations of molecular systems poses significant challenges when dealing with realistic environments composed of numerous vibrational modes. Here, we introduce a technique for the construction of effective phonon spectral densities that capture accurately open system dynamics over a finite time interval of interest. When combined with existing non-perturbative simulation tools, our approach can reduce significantly the computational costs associated with many-body open system dynamics.

Nuclear spin hyperpolarization techniques, such as dynamic nuclear polarization (DNP) and parahydrogen-induced polarization (PHIP), have revolutionized nuclear magnetic resonance and magnetic resonance imaging. In these methods, a readily available source of high spin order, either electron spins in DNP or singlet states in hydrogen for PHIP, is brought into close proximity with nuclear spin targets, enabling efficient transfer of spin order under external quantum control. Despite vast disparities in energy scales and interaction mechanisms between electron spins in DNP and nuclear singlet states in PHIP, a pseudo-spin formalism allows us to establish an intriguing equivalence. As a result, the important low-field polarization transfer regime of PHIP can be mapped onto an analogous system equivalent to pulsed-DNP. This establishes a correspondence between key polarization transfer sequences in PHIP and DNP, facilitating the transfer of sequence development concepts. This promises fresh insights and significant cross-pollination between DNP and PHIP polarization sequence developers., Comment: 11+5 pages, 5 figures

Quantum systems are inherently open and susceptible to environmental noise, which can have both detrimental and beneficial effects on their dynamics. This phenomenon has been observed in bio-molecular systems, where noise enables novel functionalities, making the simulation of their dynamics a crucial target for digital and analog quantum simulation. Nevertheless, the computational capabilities of current quantum devices are often limited due to their inherent noise. In this work, we present a novel approach that capitalizes on the intrinsic noise of quantum devices to reduce the computational resources required for simulating open quantum systems. Our approach combines quantum noise characterization methods with quantum error mitigation techniques, enabling us to manipulate and control the intrinsic noise in a quantum circuit. Specifically, we selectively enhance or reduce decoherence rates in the quantum circuit to achieve the desired simulation of open system dynamics. We provide a detailed description of our methods and report on the results of noise characterization and quantum error mitigation experiments conducted on both real and emulated IBM Quantum computers. Additionally, we estimate the experimental resource requirements for our techniques. Our approach holds the potential to unlock new simulation techniques in Noisy Intermediate-Scale Quantum (NISQ) devices, harnessing their intrinsic noise to enhance quantum computations.

Given a unitary evolution $U$ on a multi-partite quantum system and an ensemble of initial states, how well can $U$ be simulated by local operations and classical communication (LOCC) on that ensemble? We answer this question by establishing a general, efficiently computable upper bound on the maximal LOCC simulation fidelity -- what we call an 'LOCC inequality'. We then apply our findings to the fundamental setting where $U$ implements a quantum Newtonian Hamiltonian over a gravitationally interacting system. Violation of our LOCC inequality can rule out the LOCCness of the underlying evolution, thereby establishing the non-classicality of the gravitational dynamics, which can no longer be explained by a local classical field. As a prominent application of this scheme we study systems of quantum harmonic oscillators initialised in coherent states following a normal distribution and interacting via Newtonian gravity, and discuss a possible physical implementation with torsion pendula. One of our main technical contributions is the analytical calculation of the above LOCC inequality for this family of systems. As opposed to existing tests based on the detection of gravitationally mediated entanglement, our proposal works with coherent states alone, and thus it does not require the generation of largely delocalised states of motion nor the detection of entanglement, which is never created at any point in the process., Comment: 26+20 pages, 7 figures. In v2 we improved the presentation considerably. v3 is close to the published version

When two particles interact primarily through gravity and follow the laws of quantum mechanics, the generation of entanglement is considered a hallmark of the quantum nature of the gravitational interaction. However, we demonstrate that entanglement dynamics can also occur in the presence of a weak quantum interaction and non-linear corrections to local quantum mechanics, even if the gravitational interaction is classical or absent at short distances. This highlights the importance of going beyond entanglement detection to conclusively test the quantum character of gravity, and it requires a thorough examination of the strength of other quantum forces and potential non-linear corrections to quantum mechanics in the realm of large masses., Comment: 16 pages, 4 figures

Continuous monitoring of driven-dissipative quantum optical systems is a crucial element in the implementation of quantum metrology, providing essential strategies for achieving highly precise measurements beyond the classical limit. In this context, the relevant figure of merit is the quantum Fisher information of the radiation field emitted by the driven-dissipative sensor. Saturation of the corresponding precision limit as defined by the quantum Cramer-Rao bound is typically not achieved by conventional, temporally local continuous measurement schemes such as counting or homodyning. To address the outstanding open challenge of efficient retrieval of the quantum Fisher information of the emission field, we design a novel continuous measurement strategy featuring temporally quasilocal measurement bases as captured by matrix product states. Such measurement can be implemented effectively by injecting the emission field of the sensor into an auxiliary open system, a `quantum decoder' module, which `decodes' specific input matrix product states into simple product states as its output field, and performing conventional continuous measurement at the output. We devise a universal recipe for the construction of the decoder by exploiting time reversal transformation of quantum optical input-output channels, thereby establishing a universal method to achieve the quantum Cramer-Rao precision limit for generic sensors based on continuous measurement. As a by-product, we establish an effective formula for the evaluation of the quantum Fisher information of the emission field of generic driven-dissipative open sensors. We illustrate the power of our scheme with paramagnetic open sensor designs including linear force sensors, fibre-interfaced nonlinear emitters, and driven-dissipative many-body sensors, and demonstrate that it can be robustly implemented under realistic experimental imperfections., Comment: published version

The elucidation of the mechanisms behind chiral-induced spin selectivity remains an outstanding scientific challenge. Here we consider the role of delocalised phonon modes in electron transport in chiral structures and demonstrate that spin selectivity can originate from spin-dependent energy and momentum conservation in electron-phonon scattering events. While this mechanism is robust to the specifical nature of the vibrational modes, the degree of spin polarization depends on environmental factors, such as external driving fields, temperatures and phonon relaxation rates. This dependence is used to present experimentally testable predictions of our model.

We exploit the properties of chain mapping transformations of bosonic environments to identify a finite collection of modes able to capture the characteristic features, or fingerprint, of the environment. Moreover we show that the countable infinity of residual bath modes can be replaced by a universal Markovian closure, namely a small collection of damped modes undergoing a Lindblad-type dynamics whose parametrization is independent of the spectral density under consideration. We show that the Markovian closure provides a quadratic speed-up with respect to standard chain mapping techniques and makes the memory requirement independent of the simulation time, while preserving all the information on the fingerprint modes. We illustrate the application of the Markovian closure to the computation of linear spectra but also to non-linear spectral response, a relevant experimentally accessible many body coherence witness for which efficient numerically exact calculations in realistic environments are currently lacking., Comment: 6+23 pages, 3+12 figures. Minor changes. Close to published version

We present the experimental implementation of a two-qubit phase gate, using a radio frequency (RF) controlled trapped-ion quantum processor. The RF-driven gate is generated by a pulsed dynamical decoupling sequence applied to the ions' carrier transitions only. It allows for a tunable phase shift with high-fidelity results, in particular a fringe contrast up to $99_{-2}^{+1}\%$ is observed in Ramsey-type measurements. We also prepare a Bell state using this laser-free gate. The phase gate is robust against common sources of error. We investigate the effect of the excitation of the center-of-mass (COM) mode, errors in the axial trap frequency, pulse area errors and errors in sequence timing. The contrast of the phase gate is not significantly reduced up to a COM mode excitation $<20$ phonons, trap frequency errors of +10%, and pulse area errors of -8%. The phase shift is not significantly affected up to $<10$ phonons and pulse area errors of -2%. Both, contrast and phase shift are robust to timing errors up to -30% and +15%. The gate implementation is resource efficient, since only a single driving field is required per ion. Furthermore, it holds the potential for fast gate speeds (gate times on the order of $100~\mu$s) by using two axial motional modes of a two-ion crystal through improved setups.

Electron-hole pairs in organic photovoltaics dissociate efficiently despite their Coulomb-binding energy exceeding thermal energy at room temperature. The electronic states involved in charge separation couple to structured vibrational environments containing multiple underdamped modes. The non-perturbative simulations of such large, spatially extended electronic-vibrational (vibronic) systems remains an outstanding challenge. Current methods bypass this difficulty by considering effective one-dimensional Coulomb potentials or unstructured environments. Here we extend and apply a recently developed method for the non-perturbative simulation of open quantum systems to the dynamics of charge separation in one, two and three-dimensional donor-acceptor networks. This allows us to identify the precise conditions in which underdamped vibrational motion induces efficient long-range charge separation. Our analysis provides a comprehensive picture of ultrafast charge separation by showing how different mechanisms driven either by electronic or vibronic couplings are well differentiated for a wide range of driving forces and how entropic effects become apparent in large vibronic systems. These results allow us to quantify the relative importance of electronic and vibronic contributions in organic photovoltaics and provide a toolbox for the design of efficient charge separation pathways in artificial nanostructures.

We show that the proof of the generalised quantum Stein's lemma [Brand\~ao & Plenio, Commun. Math. Phys. 295, 791 (2010)] is not correct due to a gap in the argument leading to Lemma III.9. Hence, the main achievability result of Brand\~ao & Plenio is not known to hold. This puts into question a number of established results in the literature, in particular the reversibility of quantum entanglement [Brand\~ao & Plenio, Commun. Math. Phys. 295, 829 (2010); Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brand\~ao & Gour, Phys. Rev. Lett. 115, 070503 (2015)] under asymptotically resource non-generating operations. We discuss potential ways to recover variants of the newly unsettled results using other approaches., Comment: 28 pages; in v2 we added Section V.D and Section VI, and corrected several small typos; v3 is close to the published version

Shor's factoring algorithm provides a super-polynomial speed-up over all known classical factoring algorithms. Here, we address the question of which quantum properties fuel this advantage. We investigate a sequential variant of Shor's algorithm with a fixed overall structure and identify the role of coherence for this algorithm quantitatively. We analyze this protocol in the framework of dynamical resource theories, which capture the resource character of operations that can create and detect coherence. This allows us to derive a lower and an upper bound on the success probability of the protocol, which depend on rigorously defined measures of coherence as a dynamical resource. We compare these bounds with the classical limit of the protocol and conclude that within the fixed structure that we consider, coherence is the quantum resource that determines its performance by bounding the success probability from below and above. Therefore, we shine new light on the fundamental role of coherence in quantum computation., Comment: 5+24 pages

Hyperpolarization of nuclear spins enhances nuclear magnetic resonance signals, which play a key role for imaging and spectroscopy in the natural and life sciences. This signal amplification unlocks previously inaccessible techniques, such as metabolic imaging of cancer cells. In this work, electron spins from the photoexcited triplet state of pentacene-doped naphthalene crystals are used to polarize surrounding protons. As existing strategies are rendered less effective by experimental constraints, they are replaced with optimal control pulses designed with RedCRAB. In contrast to previous optimal control approaches, which consider an average single nucleus, this closed-loop optimization is macroscopic. A 28% improvement in signal and 15% faster polarization rate is observed. Additionally, a strategy called Autonomously-optimized Repeated Linear Sweep (ARISE) is introduced to efficiently tailor existing hyperpolarization sequences in the presence of experimental uncertainty to enhance their performance. ARISE is expected to be broadly applicable in many experimental settings., Comment: 15 pages, 9 figures

We study the non-equilibrium dynamics of electron transmission from a straight waveguide to a helix with spin-orbit coupling. Transmission is found to be spin-selective and can lead to large spin polarizations of the itinerant electrons. The degree of spin selectivity depends on the width of the interface region, and no polarization is found for single-point couplings. We show that this is due to momentum conservation conditions arising from extended interfaces. We therefore identify interface structure and conservation of momentum as crucial ingredients for chiral-induced spin selectivity, and confirm that this mechanism is robust against static disorder.

We show that an interaction between a harmonic oscillator and a two-level test mass (TLTM) mediated by an LOCC channel produces a signature that in [D. Carney et al., PRX Quantum 2, 030330 (2021)] is claimed to be exclusively reserved for channels that can transmit quantum information. We provide an explicit example based on a measurement-and-feedback channel, explain where the proof of Carney et al. fails, discuss to what degree setups of this type can test the nature of the gravitational interaction and remark on some fundamental implications that an LOCC model of gravity may have in black hole physics., Comment: v2: matches published version

Present protocols of criticality-enhanced sensing with open quantum sensors assume direct measurement of the sensor and omit the radiation quanta emitted to the environment, thereby potentially missing valuable information. Here we propose a protocol for criticality-enhanced sensing via continuous observation of the emitted radiation quanta. Under general assumptions, we establish a scaling theory for the global quantum Fisher information of the joint system and environment state at dissipative critical points. We derive universal scaling laws featuring transient and long-time behavior governed by the underlying critical exponents. Importantly, such scaling laws exceed the standard quantum limit and can in principle saturate the Heisenberg limit. To harness such advantageous scaling, we propose a practical sensing scheme based on continuous detection of the emitted quanta as realized experimentally in various quantum-optical setups. In such a scheme a single interrogation corresponds to a (stochastic) quantum trajectory of the open system evolving under the nonunitary dynamics dependent on the parameter to be sensed and the backaction of the continuous measurement. Remarkably, we demonstrate that the associated precision scaling significantly exceeds that based on direct measurement of the critical steady state, thereby establishing the metrological value of the continuous detection of the emitted quanta at dissipative criticality. We illustrate our protocol via counting the photons emitted by the open Rabi model, a paradigmatic model for the study of dissipative phase transition with finite components. Our protocol is applicable to generic quantum-optical open sensors permitting continuous readout, and may find applications at the frontier of quantum sensing, such as the human-machine interface, magnetic diagnosis of heart disease, and zero-field nuclear magnetic resonance., Comment: 17 pages, 9 figures, published version

Nuclear spin hyperpolarization provides a promising route to overcome the challenges imposed by the limited sensitivity of nuclear magnetic resonance. Here we demonstrate that dissolution of spin-polarized pentacene-doped naphthalene crystals enables transfer of polarization to target molecules via intermolecular cross relaxation at room temperature and moderate magnetic fields (1.45$\,$T). This makes it possible to exploit the high spin polarization of optically polarized crystals while mitigating the challenges of its transfer to external nuclei, particularly of the large distances and prohibitively weak coupling between source and target nuclei across solid-solid or solid-liquid interfaces. With this method, here we inject the highly polarized mixture into a benchtop NMR spectrometer and observe the polarization dynamics for target $^1$H nuclei. Although the spectra are radiation damped due to the high naphthalene magnetization, we describe a procedure to process the data in order to obtain more conventional NMR spectra, and extract the target nuclei polarization. With the entire process occurring on a timescale of one minute, we observe NMR signals enhanced by factors between -200 and -1730 at 1.45$\,$T for a range of small molecules., Comment: 8 pages, 4 figures

The statistical mechanics characterization of a finite subsystem embedded in an infinite system is a fundamental question of quantum physics. Nevertheless, a full closed form { for all required entropic measures} does not exist in the general case even for free systems when the finite system in question is composed of several disjoint intervals. Here we develop a mathematical framework based on the Riemann-Hilbert approach to treat this problem in the one-dimensional case where the finite system is composed of two disjoint intervals and in the thermodynamic limit (both intervals and the space between them contains an infinite number of lattice sites and the result is given as a thermodynamic expansion). To demonstrate the usefulness of our method, we compute the change in the entanglement and negativity namely the spectrum of eigenvalues of the reduced density matrix with our without time reversal of one of the intervals. We do this in the case that the distance between the intervals is much larger than their size. The method we use can be easily applied to compute any power in an expansion in the ratio of the distance between the intervals to their size. {We expect these results to provide the necessary mathematical apparatus to address relevant questions in concrete physical scenarios, namely the structure and extent of quantum correlations in fermionic systems subject to local environment.

Matter-wave interferometry with solids is highly susceptible to minute fluctuations of environmental fields, including gravitational effects from distant sources. Hence, experiments require a degree of shielding that is extraordinarily challenging to achieve in realistic terrestrial or even space-based set-ups. Here, we design protocols that exploit the spatial correlations that are inherent in perturbations due to distant sources to reduce significantly their impact on the visibility of interference patterns. We show that interference patterns that are robust to such type of noise can be encoded in the joint probability distribution of two or more interferometers, provided that these are initialized in suitable states. We develop a general framework that makes use of N+1 interferometers that may differ in their masses to correct for environmental potential fields up to order N in their multipole expansion. Remarkably, our approach works for fields that fluctuate stochastically in any time scale and does not require the presence of quantum correlations among the different interferometers. Finally, we also show that the same ideas can be extended to the protection of entanglement between pairs of interferometers., Comment: 9 pages, 3 figures

Quantum error correcting codes (QECCs) are the means of choice whenever quantum systems suffer errors, e.g., due to imperfect devices, environments, or faulty channels. By now, a plethora of families of codes is known, but there is no universal approach to finding new or optimal codes for a certain task and subject to specific experimental constraints. In particular, once found, a QECC is typically used in very diverse contexts, while its resilience against errors is captured in a single figure of merit, the distance of the code. This does not necessarily give rise to the most efficient protection possible given a certain known error or a particular application for which the code is employed. In this paper, we investigate the loss channel, which plays a key role in quantum communication, and in particular in quantum key distribution over long distances. We develop a numerical set of tools that allows to optimize an encoding specifically for recovering lost particles both deterministically and probabilistically, where some knowledge about what was lost is available, and demonstrate its capabilities. This allows us to arrive at new codes ideal for the distribution of entangled states in this particular setting, and also to investigate if encoding in qudits or allowing for non-deterministic correction proves advantageous compared to known QECCs. While we here focus on the case of losses, our methodology is applicable whenever the errors in a system can be characterized by a known linear map., Comment: 28 pages, 14 figures, changed title; version accepted in Quantum

In 1957 Feynman suggested that the quantum/classical character of gravity may be assessed by testing the gravitational interaction due to source masses in superposition. However, in all proposed experimental realisations using matter-wave interferometry the extreme weakness of this interaction requires pure initial states with extreme squeezing to achieve measurable effects of non-classical interaction for reasonable experiment durations. In practice, the systems that can be prepared in such nonclassical states are limited to small masses, which in turn limits the strength of their interaction. Here we address this key challenge--the weakness of gravitational interaction--by using a massive body as an amplifying mediator of gravitational interaction between two test systems. Our analysis shows that this results in an effective interaction between the two test-systems that grows with the mass of the mediator, is independent of its initial state and, therefore, its temperature. This greatly reduces the requirement on the mass and degree of delocalization of the test systems and, while still highly challenging, brings experiments on gravitational source masses a step closer to reality., Comment: 6 + 4(supplemental) pages, 2 figures, matches published version

Quantum resource theory formulations of thermodynamics offer a versatile tool for the study of fundamental limitations to the efficiency of physical processes, independently of the microscopic details governing their dynamics. Despite the ubiquitous presence of non-Markovian dynamics in open quantum systems at the nanoscale, rigorous proofs of their beneficial effects on the efficiency of quantum dynamical processes at the bio-molecular level have not been reported yet. Here we combine the resource theory of athermality with concepts from the theory of divisibility classes for quantum channels, to prove that memory effects can increase the efficiency of photoisomerization to levels that are not achievable under a purely thermal Markovian (i.e. memoryless) evolution. This provides rigorous evidence that memory effects can provide a resource in biological quantum dynamics, and, more generally, quantum thermodynamics at the nanoscale., Comment: v2: Added authors email addresses, corrected mistake in first line of Appendix D, by replacing "Markovian" with "embeddable"; v3: Presentation improved

Quantum coherence is one of the key features that fuels applications for which quantum mechanics exceeds the power of classical physics. This explains the considerable efforts that were undertaken to quantify coherence via quantum resource theories. An application of the resulting framework to concrete technological tasks is however largely missing. Here, we address this problem and connect the ability of an operation to detect or create coherence to the performance of interferometric experiments., Comment: 5+15 pages, matches published version

We present a ground-state cooling scheme for the mechanical degrees of freedom of mesoscopic magnetic particles levitated in low-frequency traps. Our method makes use of a binary sensor and suitably shaped pulses to perform weak, adaptive measurements on the position of the magnet. This allows us to precisely determine the position and momentum of the particle, transforming the initial high-entropy thermal state into a pure coherent state. The energy is then extracted by shifting the trap center. By delegating the task of energy extraction to a coherent displacement operation we overcome the limitations associated with cooling schemes that rely on the dissipation of a two-level system coupled to the oscillator. We numerically benchmark our protocol in realistic experimental conditions, including heating rates and imperfect readout fidelities, showing that it is well suited for magnetogravitational traps operating at cryogenic temperatures. Our results pave the way for ground-state cooling of micron-scale particles., Comment: 6+10 pages, 3+8 figures, matches published version

We show that the dynamic resource theory of quantum entanglement can be formulated using the superchannel theory. In this formulation, we identify the separable channels and the class of free superchannels that preserve channel separability as free resources, and choose the swap channels as dynamic entanglement golden units. Our first result is that the one-shot dynamic entanglement cost of a bipartite quantum channel under the free superchannels is bounded by the standard log-robustness of channels. The one-shot distillable dynamic entanglement of a bipartite quantum channel under the free superchannels is found to be bounded by a resource monotone that we construct from the hypothesis-testing relative entropy of channels with minimization over separable channels. We also address the one-shot catalytic dynamic entanglement cost of a bipartite quantum channel under a larger class of free superchannels that could generate the dynamic entanglement which is asymptotically negligible; it is bounded by the generalized log-robustness of channels., Comment: 19 pages, 5 figures. See two independent related works by B. Regula and R. Takagi, and by X. Yuan et al

Biocompatible nanoscale probes for sensitive detection of paramagnetic species and molecules associated with their (bio)chemical transformations would provide a desirable tool for a better understanding of cellular redox processes. Here, we describe an analytical tool based on quantum sensing techniques. We magnetically coupled negatively charged nitrogen-vacancy (NV) centers in nanodiamonds (NDs) with nitroxide radicals present in a bioinert polymer coating of the NDs. We demonstrated that the T1 spin relaxation time of NV centers is very sensitive to the number of nitroxide radicals, with a resolution down to ~10 spins per ND (detection of approximately $ 10^-23 $ mol in a localized volume). The detection is based on T1 shortening upon the radical attachment and we propose a theoretical model describing this phenomenon. We further show this colloidally stable, water-soluble system can be used dynamically for spatiotemporal readout of a redox chemical process (oxidation of ascorbic acid) occurring near the ND surface in an aqueous environment under ambient conditions., Comment: 26 pages (plus 18 pages of supporting information), 3 figures (plus 8 figures in supporting information)

We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation rates in these settings. This removes the need for asymptotic continuity, which cannot be defined in the traditional sense for infinite-dimensional systems. We consider three applications, to the resource theories of (I) optical nonclassicality, (II) entanglement, and (III) quantum thermodynamics. In cases (II) and (III), the employed monotones are the (infinite-dimensional) squashed entanglement and the free energy, respectively. For case (I), we consider the measured relative entropy of nonclassicality and prove it to be lower semicontinuous and strongly superadditive. One of our main technical contributions, and a key tool to establish these results, is a handy variational expression for the measured relative entropy of nonclassicality. Our technique then yields computable upper bounds on asymptotic transformation rates, including those achievable under linear optical elements. We also prove a number of results which guarantee that the measured relative entropy of nonclassicality is bounded on any physically meaningful state and easily computable for some classes of states of interest, e.g., Fock diagonal states. We conclude by applying our findings to the problem of cat state manipulation and noisy Fock state purification., Comment: 46 pages, 5 figures. v3 is closed to the published version

Precise spectroscopy of oscillating fields plays significant roles in many fields. Here, we propose an experimentally feasible scheme to measure the frequency of a fast-oscillating field using a single-qubit sensor. By invoking a stable classical clock, the signal phase correlations between successive measurements enable us to extract the target frequency with extremely high precision. In addition, we integrate dynamical decoupling technique into the framework to suppress the influence of slow environmental noise. Our framework is feasible with a variety of atomic and single solid-state-spin systems within the state-of-the-art experimental capabilities as a versatile tool for quantum spectroscopy.