Search

Quantum sensors are now universally acknowledged as one of the most promising near-term quantum technologies. The traditional formulation of quantum sensing introduces a concrete bound on ultimate precision through the so-called local sensing framework, in which a significant knowledge of prior information about the unknown parameter value is implicitly assumed. Moreover, the framework provides a systematic approach for optimizing the sensing protocol. In contrast, the paradigm of global sensing aims to find a precision bound for parameter estimation in the absence of such prior information. In recent years, vigorous research has been pursued to describe the contours of global quantum estimation. Here, we review some of these emerging developments. These developments are both in the realm of finding ultimate precision bounds with respect to appropriate figures of merit in the global sensing paradigm, as well as in the search for algorithms that achieve these bounds. We categorize these developments into two largely mutually exclusive camps; one employing Bayesian updating and the other seeking to generalize the frequentist picture of local sensing towards the global paradigm. In the first approach, in order to achieve the best performance, one has to optimize the measurement settings adaptively. In the second approach, the measurement setting is fixed, however the challenge is to identify this fixed measurement optimally., Comment: Topical Review, Close to published version

Conventional formulation of quantum sensing has been mostly developed in the context of local estimation, where the unknown parameter is roughly known. In contrast, global sensing, where the prior information is incomplete and the unknown parameter is only known to lie within a broad interval, is practically more engaging but has received far less theoretical attention. Available formulations of global sensing rely on adaptive Bayesian strategies or minimizing average uncertainty. These methods either rely on challenging adaptive measurements or provide unsaturable bounds. Here, we provide an operationally motivated approach to global sensing in the frequentist picture. Our scheme yields a saturable bound on average uncertainty and allows for optimizing the measurement as well as the probe preparation simultaneously. We illustrate the implications for Gaussian single-mode sensing tasks like thermometry and phase estimation by showing that the optimal measurement indeed changes from homodyne, for local sensing, towards heterodyne, for global sensing. Depending on the task, this transformation can be gradual or sudden., Comment: 4.5 pages + 3 figs, Comments/suggestions welcome

The main power of quantum sensors is achieved when the probe is composed of several particles. In this situation, quantum features such as entanglement contribute in enhancing the precision of quantum sensors beyond the capacity of classical sensors. Originally, quantum sensing was formulated for non-interacting particles which are prepared in a special form of maximally entangled states. These probes are extremely sensitive to decoherence and any interaction between particles is detrimental to their performance. An alternative framework for quantum sensing has been developed exploiting quantum many-body systems, where the interaction between particles plays a crucial role. In this review, we investigate different aspects of the latter approach for quantum metrology and sensing. Many-body probes have been used in both equilibrium and non-equilibrium scenarios. Quantum criticality has been identified as a resource for achieving quantum enhanced sensitivity in both scenarios. In equilibrium, various types of criticalities, such as first order, second order, topological, and localization phase transitions have been exploited for sensing purposes. In non-equilibrium scenarios, quantum enhanced sensitivity has been discovered for Floquet, dissipative, and time crystal phase transitions. While each type of these criticalities has its own characteristics, the presence of one feature is crucial for achieving quantum enhanced sensitivity: the energy/quasi-energy gap closing. In non-equilibrium quantum sensing, time is another parameter which can affect the sensitivity of the probe. Typically, the sensitivity enhances as the probe evolves in time. In general, a more complete understanding of resources for non-equilibrium quantum sensors is now rapidly evolving. In this review, we provide an overview of recent progress in quantum metrology and sensing using many-body systems., Comment: Review article. Newly added Section in v2: Optimal control and machine learning strategies for quantum sensing. Several new references added. Feedback is highly appreciated!

Quantum many-body systems undergoing phase transitions have been proposed as probes enabling beyond-classical enhancement of sensing precision. However, this enhancement is usually limited to a very narrow region around the critical point. Here, we systematically develop a modular approach for introducing multiple phase transitions in a many-body system. This naturally allows us to enlarge the region of quantum-enhanced precision by encompassing the newly created phase boundaries. Our approach is general and can be applied to both symmetry-breaking and topological quantum sensors. In symmetry-breaking sensors, we show that the newly created critical points inherit the original universality class and a simple total magnetization measurement already suffices to locate them. In topological sensors, our modular construction creates multiple bands which leads to a rich phase diagram. In both cases, Heisenberg scaling for Hamiltonian parameter estimation is achieved at all the phase boundaries. This can be exploited to create a global sensor which significantly outperforms a uniform probe., Comment: 4+6 pages, 6+4 figures, accepted for publication in Physical Review Letters

Near-term quantum simulators are mostly based on qubit-based architectures. However, their imperfect nature significantly limits their practical application. The situation is even worse for simulating fermionic systems, which underlie most of material science and chemistry, as one has to adopt fermion-to-qubit encodings which create significant additional resource overhead and trainability issues. Thanks to recent advances in trapping and manipulation of neutral atoms in optical tweezers, digital fermionic quantum simulators are becoming viable. A key question is whether these emerging fermionic simulators can outperform qubit-based simulators for characterizing strongly correlated electronic systems. Here, we perform a comprehensive comparison of resource efficiency between qubit and fermionic simulators for variational ground-state emulation of fermionic systems in both condensed matter systems and quantum chemistry problems. We show that the fermionic simulators indeed outperform their qubit counterparts with respect to resources for quantum evolution (circuit depth), as well as classical optimization (number of required parameters and iterations). In addition, they show less sensitivity to the random initialization of the circuit. The relative advantage of fermionic simulators becomes even more pronounced as interaction becomes stronger, or tunneling is allowed in more than one dimension, as well as for spinful fermions. Importantly, this improvement is scalable, i.e., the performance gap between fermionic and qubit simulators only grows for bigger system sizes., Comment: Accepted in Physical Review Research, 13 pages, 8 Figures, Close to published version

Second order quantum phase transitions, with well-known features such as long-range entanglement, symmetry breaking, and gap closing, exhibit quantum enhancement for sensing at criticality. However, it is unclear which of these features are responsible for this enhancement. To address this issue, we investigate phase transitions in free-fermionic topological systems that exhibit neither symmetry-breaking nor long-range entanglement. We analytically demonstrate that quantum enhanced sensing is possible using topological edge states near the phase boundary. Remarkably, such enhancement also endures for ground states of such models that are accessible in solid state experiments. We illustrate the results with 1D Su-Schrieffer-Heeger chain and a 2D Chern insulator which are both experimentally accessible. While neither symmetry-breaking nor long-range entanglement are essential, gap closing remains as the major candidate for the ultimate source of quantum enhanced sensing. In addition, we also provide a fixed and simple measurement strategy that achieves near-optimal precision for sensing using generic edge states irrespective of the parameter value. This paves the way for development of topological quantum sensors which are expected to also be robust against local perturbations., Comment: 6+6 pages, 2 figures (close to published version)

Quantum many-body systems have been extensively studied from the perspective of quantum technology, and conversely, critical phenomena in such systems have been characterized by operationally relevant resources like entanglement. In this paper, we investigate robustness of magic (RoM), the resource in magic state injection based quantum computation schemes in the context of the transverse field anisotropic XY model. We show that the the factorizable ground state in the symmetry broken configuration is composed of an enormous number of highly magical $H$ states. We find the existence of a point very near the quantum critical point where magic contained explicitly in the correlation between two distant qubits attains a sharp maxima. Unlike bipartite entanglement, this persists over very long distances, capturing the presence of long range correlation near the phase transition. We derive scaling laws and extract corresponding exponents around criticality. Finally, we study the effect of temperature on two-qubit RoM and show that it reveals a crossover between dominance of quantum and thermal fluctuations., Comment: 22 pages, 7+1 figures

We introduce a quantity called the coherence of purification which can be a measure of total quantumness for a single system. We prove that coherence of purification is always more than the coherence of the system. For a pure state, the coherence of purification is same as the relative entropy of coherence. Furthermore, we show that the difference in the coherence of purification of a quantum state before and after the dephasing can capture residual quantumness. In addition, we show that the entanglement of purification that can be created by incoherent operation between two subsystems is upper bounded by the coherence of purification of the original system. We show that the coherence of purification is a resource in quantum state discrimination process. In the absence of coherence, entanglement and quantum correlations, the coherence of purification may play an important role in quantum information processing tasks., Comment: 8 pages, 1 fig, comments welcome

We show that the fidelity of the standard quantum teleportation protocol, which utilizes an impure resource state, applied successively, can be significantly improved, when used in conjunction with a quantum switch. In particular, we find that for two such teleportation channels conjugated with the superposition of causal order, teleportation fidelity beyond the classical threshold is achieved for significantly larger noise than would be possible conventionally. One can even make the effective teleportation channel perfectly faithful for very large noise. We also discuss the generalization of our scheme for more than two pathways, and define a figure of merit in that context., Comment: 4+ pages, 8 figs, Comments Welcome

As the minituarization of electronic devices, which are sensitive to temperature, grows apace, sensing of temperature with ever smaller probes is more important than ever. Genuinely quantum mechanical schemes of thermometry are thus expected to be crucial to future technological progress. We propose a new method to measure the temperature of a bath using the weak measurement scheme with a finite dimensional probe. The precision offered by the present scheme not only shows similar qualitative features as the usual Quantum Fisher Information based thermometric protocols, but also allows for flexibility over setting the optimal thermometric window through judicious choice of post selection measurements., Comment: Additional analysis, one new figure, accepted for publication in Physical Review A

We propose a novel approach to qubit thermometry using a quantum switch, that introduces an indefinite causal order in the probe-bath interaction, to significantly enhance the thermometric precision. The resulting qubit probe shows improved precision in both low and high temperature regimes when compared to optimal qubit probes studied previously. It even performs better than a Harmonic oscillator probe, in spite of having only two energy levels rather than an infinite number of energy levels as that in a harmonic oscillator. We thereby show unambiguously that quantum resources such as the quantum switch can significantly improve equilibrium thermometry. We also derive a new form of thermodynamic uncertainty relation that is tighter and depends on the energy gap of the probe. The present work may pave the way for using indefinite causal order as a metrological resource., Comment: 4 pages, 5 figures, comments are welcome

Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations in both forward and reverse directions for arbitrary quantum states, i.e., mixed as well as pure, and arbitrary incompatible quantum observables, none of which suffer from the problem of triviality. Besides the tightness, the interpretations of terms in these uncertainty relations may be of independent inter- est. We provide the possible generalization of stronger uncertainty relations to sum of variances of more than two observables. We also demonstrate applications of techniques used here to, firstly, obtain a simple reverse quantum speed limit for quantum states undergoing Markovian dynamical evolution, and secondly, to provide a lower bound for fidelity between two quantum states., Comment: 4.5 + 3.5 pages, 2+1 figures, comments welcome

Generation of steady quantumness in the presence of an environment is of utmost importance if we are to build practical quantum devices. We propose a scheme of generating steady coherence and magic in a qubit system attached to a heat bath at a certain temperature through its interaction with another qubit system attached to a spin bath. Coherence generation in the reduced qubit is always possible in this model. The steady coherence in the reduced qubit attached to the heat bath may be used to enhance the subsequent transient performance of a quantum absorption refrigerator. For the case of generation of magic, which is the quantum resource responsible for implementation of gates which are not simulable via stabilizer computation, we show that there exists a critical temperature of the heat bath beyond which it is not possible to create magic in the reduced qubit attached to the heat bath. Below the critical temperature, the strength of interaction between the qubits must lie within a certain region for creation of magic. We further note that by increasing the strength of coupling of the second qubit to the spin bath, typified by the reset probability, keeping the coupling strength of the first qubit to the heat bath fixed, it is possible to increase the critical temperature of the heat bath for creation of magic., Comment: 7 pages, 7 figures, accepted for publication in Physical Review A

Quantum addition channels have been recently introduced in the context of deriving entropic power inequalities for finite dimensional quantum systems. We prove a reverse entropy power equality which can be used to analytically prove an inequality conjectured recently for arbitrary dimension and arbitrary addition weight. We show that the relative entropic difference between the output of such a quantum additon channel and the corresponding classical mixture quantitatively captures the amount of coherence present in a quantum system. This new coherence measure admits an upper bound in terms of the relative entropy of coherence and is utilized to formulate a state-dependent uncertainty relation for two observables. Our results may provide deep insights to the origin of quantum coherence for mixed states that truly come from the discrepancy between quantum addition and the classical mixture., Comment: 6 pages + references, comments/suggestions most welcome

Two primary facets of quantum technological advancement that hold great promise are quantum communication and quantum computation. For quantum communication, the canonical resource is entanglement. For quantum gate implementation, the resource is 'magic' in an auxiliary system. It has already been shown that quantum coherence is the fundamental resource for the creation of entanglement. We argue on the similar spirit that quantum coherence is the fundamental resource when it comes to the creation of magic. This unifies the two strands of modern development in quantum technology under the common underpinning of existence of quantum superposition, quantified by the coherence in quantum theory. We also attempt to obtain magic monotones inspired from coherence monotones and vice versa. We further study the interplay between quantum coherence and magic in a qutrit system and that between quantum entanglement and magic in a qutrit-qubit setting., Comment: 14 pages, 4 figures, version accepted by J. Phys. A for a special issue on quantum coherence

Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present alternative forms of uncertainty relations, in both state dependent and state independent forms, based on the mean deviation. We illustrate the robustness of this formulation in situations where the standard deviation based uncertainty relation is inapplicable. We apply the mean deviation based uncertainty relation to detect EPR violation in a lossy scenario for a higher inefficiency threshold than that allowed by the standard deviation based approach. We demonstrate that the mean deviation based uncertainty relation can perform equally well as the standard deviation based uncertainty relation as non-linear witness for entanglement detection., Comment: Close to published version, open to further comments

Quantum speed limit, furnishing a lower bound on the required time for the evolution of a quantum system through the state space, imposes an ultimate natural limitation to the dynamics of physical devices. Quantum absorption refrigerators, on the other hand, have attracted a great deal of attention in the last few years. In this article, we discuss the effects of quantum speed limit on the performance of a quantum absorption refrigerator. In particular, we show that there exists a trade-off relation between the steady cooling rate of the refrigerator and the minimum time taken to reach the steady state. Based on this, we define a figure of merit called "bounding second order cooling rate" and show that this scales linearly with the unitary interaction strength among the constituent qubits. We also study the increase of bounding second order cooling rate with the thermalization strength. We subsequently demonstrate that coherence in the initial three qubit system can significantly increase the bounding second order cooling rate. We study the efficiency of the refrigerator at maximum bounding second order cooling rate and, in a limiting case, we show that the efficiency at maximum bounding second order cooling rate is given by a simple formula reminiscent of the Curzon-Ahlborn relation., Comment: Accepted in Physical Review E

In this brief report, we prove that robustness of coherence (ROC), in contrast to many popular quantitative measures of quantum coherence derived from the resource theoretic framework of coherence, may be sub-additive for a specific class of multipartite quantum states. We investigate how the sub-additivity is affected by admixture with other classes of states for which ROC is super-additive. We show that pairs of quantum states may have different orderings with respect to relative entropy of coherence, $l_{1}$-norm of coherence and ROC and numerically study the difference in ordering for coherence measures chosen pairwise., Comment: 4 pages + 3 figures, comments welcome

We propose the notion of quantum coherence for superpositions over states which are not necessarily mutually orthogonal. This anticipatedly leads to a resource theory of non-orthogonal coherence. We characterize free states and free operations in this theory, and connect the latter with free operations in the resource theory of quantum coherence for orthogonal bases. We show that the concept of non-orthogonal coherence naturally furnishes us with a wave-particle duality in quantum double-slit experiments where the channels beyond the slits are leaky between them. Furthermore, we demonstrate existence of a unique maximally coherent qubit state corresponding to any given purity. In addition, and in contradistinction with the case of orthogonal bases, there appears a non-trivial minimally coherent qubit state for a given purity. We also study the behavior of quantum coherence for some typical configurations of non-orthogonal bases which have no analogs for orthogonal bases. We further investigate the problem of determining the energy cost of creating non-orthogonal coherence, and find that it scales linearly with the non-orthogonal coherence created., Comment: 13 pages, 8 figures, close to the published version

An exact reduced dynamical map along with its operator sum representation is derived for a central spin interacting with a thermal spin environment. The dynamics of the central spin shows high sustainability of quantum traits such as coherence and entanglement in the low-temperature regime. However, for sufficiently high temperature and when the number of bath particles approaches the thermodynamic limit, this feature vanishes and the dynamics closely mimics Markovian evolution. The properties of the long-time-averaged state and the trapped information of the initial state for the central qubit are also investigated in detail, confirming that the nonergodicity of the dynamics can be attributed to the finite temperature and finite size of the bath. It is shown that if a certain stringent resonance condition is satisfied, the long-time-averaged state retains quantum coherence, which can have far reaching technological implications in engineering quantum devices. An exact time-local master equation of the canonical form is derived. With the help of this master equation, the nonequilibrium properties of the central spin system are studied by investigating the detailed balance condition and irreversible entropy production rate. The result reveals that the central qubit thermalizes only in the limit of very high temperature and large number of bath spins., Comment: Close to published version

An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins. The Kraus operators for the dynamical map are also derived. The non-Markovianity of the dynamics in terms of the divisibility breaking of the dynamical map and increase of the trace distance fidelity between quantum states is shown. Moreover, it is observed that the irreversible entropy production rate is always negative (for a fixed initial state) whenever the dynamics exhibits non-Markovian behavior. In continuation with the study of witnessing non-Markovianity, it is shown that the positive rate of change of the purity of the central qubit is a faithful indicator of the non-Markovian information back flow. Given the experimental feasibility of measuring the purity of a quantum state, a possibility of experimental demonstration of non-Markovianity and the negative irreversible entropy production rate is addressed. This gives the present work considerable practical importance for detecting the non-Markovianity and the negative irreversible entropy production rate., Comment: Figures modified, minor changes in the manuscript. Accepted for publication in Physical Review A

The interplay between steering and quantum coherence is studied in a scenario, where two atoms move through an external massless scalar field. We show that just like entanglement, the steering induced coherence of the equilibrium state may increase or decrease with acceleration depending on the initial condition of the state. We also investigate the condition for coherence steerability - as opposed to simple state steerability. Interestingly, we find that the quantum coherence of the equilibrium state cannot be steered, even when the steering induced coherence is non-zero. We argue that under any condition, gravity prohibits the coherence steering of the equilibrium state., Comment: (6+\epsilon) pages, 3 figures

We formulate a new error-disturbance relation, which is free from explicit dependence upon variances in observables. This error-disturbance relation shows improvement over the one provided by the Branciard inequality and the Ozawa inequality for some initial states and for particular class of joint measurements under consideration. We also prove a modified form of Ozawa's error-disturbance relation. The later relation provides a tighter bound compared to the Ozawa and the Branciard inequalities for a small number of states., Comment: 5+pages, 3 figures