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The article provides a continuous time description of correlated quantum channels in terms of a joint master equation (ME) for the quantum system S in order to identify the structure of the Lindblad generators responsible for the arising specific correlations among the carriers. A pragmatic approach is adopted in the analysis, deriving interaction between subsystems and subenvironments in terms of a collision model.

We investigate the coherent mixing of copropagating edge channels in a quantum Hall bar produced by step potentials. In the case of two edge channels it is found that, although a single step induces only a few percent mixing, a series of steps could yield 50% mixing. In addition, a strong mixing is found when the potential height of a single step allows a different number of edge channels on the two sides of the step. Charge density probability has been also calculated even for the case where the step is smoothened. [ABSTRACT FROM AUTHOR]

We present a theory of the cavity quantum electrodynamics of the graphene cyclotron resonance. By employing a canonical transformation, we derive an effective Hamiltonian for the system comprising two neighboring Landau levels dressed by the cavity electromagnetic field (integer quantum Hall polaritons). This generalized Dicke Hamiltonian, which contains terms that are quadratic in the electromagnetic field and respects gauge invariance, is then used to calculate thermodynamic properties of the quantum Hall polariton system. Finally, we demonstrate that the generalized Dicke description fails when the graphene sheet is heavily doped, i.e., when the Landau level spectrum of two-dimensional massless Dirac fermions is approximately harmonic. In this case we "integrate out" the Landau levels in valence band and obtain an effective Hamiltonian for the entire stack of Landau levels in conduction band, as dressed by strong light-matter interactions. [ABSTRACT FROM AUTHOR]

We introduce and characterize two different measures which quantify the level of synchronization of coupled continuous variable quantum systems. The two measures allow us to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is, in principle, unbounded; however, in the absence of quantum resources (e.g., squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronization and, finally, discuss an application based on quantum optomechanical systems. [ABSTRACT FROM AUTHOR]

We study the estimation of the overlap between two unknown pure quantum states of a finite-dimensional system, given M and N copies of each type. This is a fundamental primitive in quantum information processing that is commonly accomplished from the outcomes of N swap tests, a joint measurement on one copy of each type whose outcome probability is a linear function of the squared overlap. We show that a more precise estimate can be obtained by allowing for general collective measurements on all copies. We derive the statistics of the optimal measurement and compute the optimal mean square error in the asymptotic pointwise and finite Bayesian estimation settings. Besides, we consider two strategies relying on the estimation of one or both states and show that, although they are suboptimal, they outperform the swap test. In particular, the swap test is extremely inefficient for small values of the overlap, which become exponentially more likely as the dimension increases. Finally, we show that the optimal measurement is less invasive than the swap test and study the robustness to depolarizing noise for qubit states. [ABSTRACT FROM AUTHOR]

Quantum batteries are energy-storing devices, governed by quantum mechanics, that promise high charging performance thanks to collective effects. Because of its experimental feasibility, the Dicke battery-which comprises N two-level systems coupled to a common photon mode-is one of the most promising designs for quantum batteries. However, the chaotic nature of the model severely hinders the extractable energy (ergotropy). Here, we use reinforcement learning to optimize the charging process of a Dicke battery either by modulating the coupling strength, or the system-cavity detuning. We find that the ergotropy and quantum mechanical energy fluctuations (charging precision) can be greatly improved with respect to standard charging strategies by countering the detrimental effect of quantum chaos. Notably, the collective speedup of the charging time can be preserved even when nearly fully charging the battery.

A fundamental problem in quantum thermodynamics is to properly quantify the work extractable from out-of-equilibrium systems. While for closed systems, maximum quantum work extraction is defined in terms of the ergotropy functional, this question is unclear in open systems interacting with an environment. The concept of local ergotropy has been proposed, but it presents several problems, such as it is not guaranteed to be nonincreasing in time. Here, we introduce the concept of extended local ergotropy by exploiting the free evolution of the system-environment compound. At variance with the local ergotropy, the extended local ergotropy is greater, is nonincreasing in time, and activates the potential of work extraction in many cases. We then concentrate on specific schemes in which we alternate repeated local unitaries and free system-environment evolution. We provide examples based on the Jaynes-Cummings model, presenting practical protocols and analytic results that serve as proof of principle for the aforementioned advantages.

We demonstrate an asymmetry between the beneficial effects one can obtain using nonlocal operations and nonlocal states to mitigate the detrimental effects of environmental noise in the work extraction process from quantum battery models. Specifically, we show that using nonlocal recovery operations after the noise action can, in general, increase the amount of work one can recover from the battery even with separable (i.e., nonentangled) input states. On the contrary, employing entangled input states with local recovery operations will generally not improve the battery performance.

In the absence of quantum repeaters, quantum communication proved to be nearly impossible across optical fibers longer than ≳20  km due to the drop of transmissivity below the critical threshold of 1/2. However, if the signals fed into the fiber are separated by a sufficiently short time interval, memory effects must be taken into account. In this Letter, we show that by properly accounting for these effects it is possible to devise schemes that enable unassisted quantum communication across arbitrarily long optical fibers at a fixed positive qubit transmission rate. We also demonstrate how to achieve entanglement-assisted communication over arbitrarily long distances at a rate of the same order of the maximum achievable in the unassisted noiseless case.

We present upper bounds on the quantum and private capacity of single-mode, phase-insensitive bosonic Gaussian channels based on degradable extensions. Our findings are state of the art in the following parameter regions: low temperature and high transmissivity for the thermal attenuator, low temperature for additive Gaussian noise, high temperature and intermediate amplification for the thermal amplifier.

We study the transferring of useful energy (work) along a transmission line that allows for partial preservation of quantum coherence. As a figure of merit we adopt the maximum values that ergotropy, total ergotropy, and nonequilibrium free energy attain at the output of the line for an assigned input energy threshold. For phase-invariant bosonic Gaussian channel (BGC) models, we show that coherent inputs are optimal. For (one-mode) not phase-invariant BGCs we solve the optimization problem under the extra restriction of Gaussian input signals.

A general attenuator Φ_{λ,σ} is a bosonic quantum channel that acts by combining the input with a fixed environment state σ in a beam splitter of transmissivity λ. If σ is a thermal state, the resulting channel is a thermal attenuator, whose quantum capacity vanishes for λ≤1/2. We study the quantum capacity of these objects for generic σ, proving a number of unexpected results. Most notably, we show that for any arbitrary value of λ>0 there exists a suitable single-mode state σ(λ) such that the quantum capacity of Φ_{λ,σ(λ)} is larger than a universal constant c>0. Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity, provided that the environment state is appropriately controlled. We also find examples of states σ such that the quantum capacity of Φ_{λ,σ} is not monotonic in λ. These findings may have implications for the study of communication lines running across integrated optical circuits, of which general attenuators provide natural models.

A new upper bound for the quantum capacity of the d-dimensional depolarizing channels is presented. Our derivation makes use of a flagged extension of the map where the receiver obtains a copy of a state σ_{0} whenever the messages are transmitted without errors, and a copy of a state σ_{1}, when instead the original state gets fully depolarized. By varying the overlap between the flag states, the resulting transformation nicely interpolates between the depolarizing map (when σ_{0}=σ_{1}), and the d-dimensional erasure channel (when σ_{0} and σ_{1} have orthogonal support). We find sufficient conditions for degradability of the flagged channel, which let us calculate its quantum capacity in a suitable parameter region. From this last result we get the upper bound for the depolarizing channel, which by a direct comparison appears to be tighter than previous available results for d>2, and for d=2 it is tighter in an intermediate regime of noise. In particular, in the limit of large d values, our findings present a previously unnoticed O(1) correction.

We propose a spatial analog of the Berry's phase mechanism for the coherent manipulation of states of nonrelativistic massive particles moving in a two-dimensional landscape. In our construction the temporal modulation of the system Hamiltonian is replaced by a modulation of the confining potential along the transverse direction of the particle propagation. By properly tuning the model parameters the resulting scattering input-output relations exhibit a Wilczek-Zee non-Abelian phase shift contribution that is intrinsically geometrical, hence insensitive to the specific details of the potential landscape. A theoretical derivation of the effect is provided together with practical examples.

We experimentally realize protocols that allow us to extract work beyond the free energy difference from a single-electron transistor at the single thermodynamic trajectory level. With two carefully designed out-of-equilibrium driving cycles featuring kicks of the control parameter, we demonstrate work extraction up to large fractions of k_{B}T or with probabilities substantially greater than 1/2, despite the zero free energy difference over the cycle. Our results are explained in the framework of nonequilibrium fluctuation relations. We thus show that irreversibility can be used as a resource for optimal work extraction even in the absence of feedback from an external operator.

We investigate a quantum battery made of N two-level systems, which is charged by an optical mode via an energy-conserving interaction. We quantify the fraction of energy stored in the battery that can be extracted in order to perform thermodynamic work. We first demonstrate that this quantity is highly reduced by the presence of correlations between the charger and the battery or between the subsystems composing the battery. We then show that the correlation-induced suppression of extractable energy, however, can be mitigated by preparing the charger in a coherent optical state. We conclude by proving that the charger-battery system is asymptotically free of such locking correlations in the N→∞ limit.

The Clausius inequality has deep implications for reversibility and the arrow of time. Quantum theory is able to extend this result for closed systems by inspecting the trajectory of the density matrix on its manifold. Here we show that this approach can provide an upper and lower bound to the irreversible entropy production for open quantum systems as well. These provide insights on how the information on the initial state is forgotten through a thermalization process. Limits of the applicability of our bounds are discussed and demonstrated in a quantum photonic simulator.

This corrects the article DOI: 10.1103/PhysRevLett.119.120503.

Given a certain amount of entanglement available as a resource, what is the most efficient way to accomplish a quantum task? We address this question in the relevant case of continuous variable quantum teleportation protocols implemented using two-mode Gaussian states with a limited degree of entanglement and energy. We first characterize the class of single-mode phase-insensitive Gaussian channels that can be simulated via a Braunstein-Kimble protocol with nonunit gain and minimum shared entanglement, showing that infinite energy is not necessary apart from the special case of the quantum limited attenuator. We also find that apart from the identity, all phase-insensitive Gaussian channels can be simulated through a two-mode squeezed state with finite energy, albeit with a larger entanglement. We then consider the problem of teleporting single-mode coherent states with Gaussian-distributed displacement in phase space. Performing a geometrical optimization over phase-insensitive Gaussian channels, we determine the maximum average teleportation fidelity achievable with any finite entanglement and for any realistically finite variance of the input distribution.

We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We apply this technique to the analysis of finite-time isothermal processes in which, differently from quasistatic transformations, the state of the system is not able to continuously relax to the equilibrium ensemble. Our approach allows one to formally evaluate perturbations up to arbitrary order to the work and heat exchange associated with an arbitrary process. Within first order in the perturbation expansion, we identify a general formula for the efficiency at maximum power of a finite-time Carnot engine. We also clarify under which assumptions and in which limit one can recover previous phenomenological results as, for example, the Curzon-Ahlborn efficiency.

We prove the long-standing conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the entropy power inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p→q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.

Under the eigenstate thermalization hypothesis (ETH), quantum-quenched systems equilibrate towards canonical, thermal ensembles. While at first glance the ETH might seem a very strong hypothesis, we show that it is indeed not only sufficient but also necessary for thermalization. More specifically, we consider systems coupled to baths with well-defined macroscopic temperature and show that whenever all product states thermalize then the ETH must hold. Our result definitively settles the question of determining whether a quantum system has a thermal behavior, reducing it to checking whether its Hamiltonian satisfies the ETH.

We give a cheat sensitive protocol for blind universal quantum computation that is efficient in terms of computational and communication resources: it allows one party to perform an arbitrary computation on a second party's quantum computer without revealing either which computation is performed, or its input and output. The first party's computational capabilities can be extremely limited: she must only be able to create and measure single-qubit superposition states. The second party is not required to use measurement-based quantum computation. The protocol requires the (optimal) exchange of O(Jlog2(N)) single-qubit states, where J is the computational depth and N is the number of qubits needed for the computation.

We study Coulomb interactions in the finite bias response of Mach-Zehnder interferometers, which exploit copropagating edge states in the integer quantum Hall effect. Here, interactions are particularly important since the coherent coupling of edge channels is due to a resonant mechanism that is spoiled by inelastic processes. We find that interactions yield a saturation, as a function of bias voltage, of the period-averaged interferometer current, which gives rise to unusual features, such as negative differential conductance, enhancement of the visibility of the current, and nonbounded or even diverging visibility of the differential conductance.

We present a theoretical study of an electronic quantum refrigerator based on four quantum dots arranged in a square configuration, in contact with as many thermal reservoirs. We show that the system implements the minimal mechanism for acting as a self-contained quantum refrigerator, by demonstrating heat extraction from the coldest reservoir and the cooling of the nearby quantum dot.

The unique optoelectronic properties of graphene make this two-dimensional material an ideal platform for fundamental studies of cavity quantum electrodynamics in the strong-coupling regime. The celebrated Dicke model of cavity quantum electrodynamics can be approximately realized in this material when the cyclotron transition of its 2D massless Dirac fermion carriers is nearly resonant with a cavity photon mode. We develop the theory of strong matter-photon coupling in this circumstance, emphasizing the essential role of a dynamically generated matter energy term that is quadratic in the photon field and absent in graphene's low-energy Dirac model.

In quantum mechanics, the Heisenberg uncertainty relations and the Cramér-Rao inequalities typically limit the precision in the estimation of a parameter through the standard deviation of a conjugate observable. Here we extend these relations by giving a bound to the precision of a parameter in terms of the expectation value of the conjugate observable. This has both foundational and practical consequences: in quantum optics it resolves a controversy over which is the ultimate precision in interferometry.

The sensitivity in optical interferometry is strongly affected by losses during the signal propagation or at the detection stage. The optimal quantum states of the probing signals in the presence of loss were recently found. However, in many cases of practical interest, their associated accuracy is worse than the one obtainable without employing quantum resources (e.g., entanglement and squeezing) but neglecting the detector's loss. Here, we detail an experiment that can reach the latter even in the presence of imperfect detectors: it employs a phase-sensitive amplification of the signals after the phase sensing, before the detection. We experimentally demonstrated the feasibility of a phase estimation experiment able to reach its optimal working regime. Since our method uses coherent states as input signals, it is a practical technique that can be used for high-sensitivity interferometry and, in contrast to the optimal strategies, does not require one to have an exact characterization of the loss beforehand.

In interferometry, sub-Heisenberg strategies claim to achieve a phase estimation error smaller than the inverse of the mean number of photons employed (Heisenberg bound). Here we show that one can achieve a comparable precision without performing any measurement, just using the large prior information that sub-Heisenberg strategies require. For uniform prior (i.e., no prior information), we prove that these strategies cannot achieve more than a fixed gain of about 1.73 over Heisenberg-limited interferometry. Analogous results hold for arbitrary single-mode prior distributions. These results extend also beyond interferometry: the effective error in estimating any parameter is lower bounded by a quantity proportional to the inverse expectation value (above a ground state) of the generator of translations of the parameter.

We introduce and experimentally demonstrate a new method that allows us to controllably couple copropagating spin-resolved edge states of a two-dimensional electron gas (2DEG) in the integer quantum Hall regime. The scheme exploits a spatially periodic in-plane magnetic field that is created by an array of Cobalt nanomagnets placed at the boundary of the 2DEG. A maximum charge or spin transfer of 28±1% is achieved at 250 mK., (© 2011 American Physical Society)

We study the transmission of classical information in quantum channels. We present a decoding procedure that is very simple but still achieves the channel capacity. It is used to give an alternative straightforward proof that the classical capacity is given by the regularized Holevo bound. This procedure uses only projective measurements and is based on successive "yes-no" tests only.

Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can interact with its former self in the past. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we analyze an alternative quantum formulation of CTCs based on teleportation and postselection, and show that it is inequivalent to Deutsch's. The predictions or retrodictions of our theory can be simulated experimentally: we report the results of an experiment illustrating how in our particular theory the "grandfather paradox" is resolved.

We show that an Aharonov-Bohm ring with asymmetric electron injection can act as a coherent detector of electron dephasing. The presence of a dephasing source in one of the two arms of a moderately-to-highly asymmetric ring changes the response of the system from total reflection to complete transmission while preserving the coherence of the electrons propagating from the ring, even for strong dephasing. We interpret this phenomenon as an implementation of an interaction-free measurement.

We introduce a general model describing correlated noise effects in quantum optical communication via attenuating media. The memory effects account for the environment finite relaxation times, which are unavoidable in any realistic model. The use of a proper set of collective field variables allows us to unravel the memory, showing that the n-fold concatenation of the memory channel is unitarily equivalent to the direct product of n single-mode lossy bosonic channels. We then compute the ultimate (classical and quantum) transmission rates, showing their enhancement with respect to the memoryless case and proving that coherent state encoding is optimal.

Quantum teleportation of an n-qubit state performed using as an entangled resource a general bipartite state of 2n qubits instead of n Bell states is equivalent to a correlated Pauli channel. This yields a new characterization of such channels in terms of many-body correlation functions of the teleporting media. It provides a relatively simple method for determining whether a correlated quantum channel is able to reliably convey quantum messages by studying the entanglement properties of the teleportation mediating system. Our model is then generalized to the continuous-variable case.

Optimal control theory is a promising candidate for a drastic improvement of the performance of quantum information tasks. We explore its ultimate limit in paradigmatic cases, and demonstrate that it coincides with the maximum speed limit allowed by quantum evolution.

An optical transmitter irradiates a target region containing a bright thermal-noise bath in which a low-reflectivity object might be embedded. The light received from this region is used to decide whether the object is present or absent. The performance achieved using a coherent-state transmitter is compared with that of a quantum-illumination transmitter, i.e., one that employs the signal beam obtained from spontaneous parametric down-conversion. By making the optimum joint measurement on the light received from the target region together with the retained spontaneous parametric down-conversion idler beam, the quantum-illumination system realizes a 6 dB advantage in the error-probability exponent over the optimum reception coherent-state system. This advantage accrues despite there being no entanglement between the light collected from the target region and the retained idler beam.

Tensor network representations of many-body quantum systems can be described in terms of quantum channels. We focus on channels associated with the multiscale entanglement renormalization ansatz tensor network that has been recently introduced to efficiently describe critical systems. Our approach allows us to compute the multiscale entanglement renormalization ansatz correspondent to the thermodynamical limit of a critical system introducing a transfer matrix formalism, and to relate the system critical exponents to the convergence rates of the associated channels.

We propose a cheat sensitive quantum protocol to perform a private search on a classical database which is efficient in terms of communication complexity. It allows a user to retrieve an item from the database provider without revealing which item he or she retrieved: if the provider tries to obtain information on the query, the person querying the database can find it out. The protocol ensures also perfect data privacy of the database: the information that the user can retrieve in a single query is bounded and does not depend on the size of the database. With respect to the known (quantum and classical) strategies for private information retrieval, our protocol displays an exponential reduction in communication complexity and in running-time computational complexity.

A random access memory (RAM) uses n bits to randomly address N=2(n) distinct memory cells. A quantum random access memory (QRAM) uses n qubits to address any quantum superposition of N memory cells. We present an architecture that exponentially reduces the requirements for a memory call: O(logN) switches need be thrown instead of the N used in conventional (classical or quantum) RAM designs. This yields a more robust QRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing. A quantum optical implementation is presented.