Extended Local Ergotropy.

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.

Work Extraction Processes from Noisy Quantum Batteries: The Role of Nonlocal Resources.

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.

Restoring Quantum Communication Efficiency over High Loss Optical Fibers.

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.

Estimating Quantum and Private Capacities of Gaussian Channels via Degradable Extensions.

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.

Quantum Energy Lines and the Optimal Output Ergotropy Problem.

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.

Bosonic Quantum Communication across Arbitrarily High Loss Channels.

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.

Quantum Flags and New Bounds on the Quantum Capacity of the Depolarizing Channel.

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.

Geometric Phase through Spatial Potential Engineering.

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.

Author Correction: All-optical implementation of collision-based evolutions of open quantum systems.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Two-parameter Hong-Ou-Mandel dip.

A modification of the standard Hong-Ou-Mandel interferometer is proposed which allows one to replicate the celebrated coincidence dip in the case of two-independent delay parameters. In the ideal case where such delays are sufficiently stable with respect to the mean wavelength of the pump source, properly symmetrized input bi-photon states allow one to pinpoint their values through the identification of a zero in the coincidence counts, a feature that cannot be simulated by semiclassical inputs having the same spectral properties. Besides, in the presence of fluctuating parameters the zero in the coincidences is washed away: still the bi-photon state permits to recover the values of parameters with a visibility which is higher than the one allowed by semiclassical sources. The detrimental role of loss and dispersion is also analyzed and an application in the context of quantum positioning is presented.

Optimal Probabilistic Work Extraction beyond the Free Energy Difference with a Single-Electron Device.

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.

All-optical implementation of collision-based evolutions of open quantum systems.

We present a new optical scheme enabling the implementation of highly stable and configurable non-Markovian dynamics. Here one photon qubit can circulate in a multipass bulk geometry consisting of two concatenated Sagnac interferometers to simulate the so called collisional model, where the system interacts at discrete times with a vacuum environment. We show the optical features of our apparatus and three different implementations of it, replicating a pure Markovian scenario and two non-Markovian ones, where we quantify the information backflow by tracking the evolution of the initial entanglement between the system photon and an ancillary one.

Extractable Work, the Role of Correlations, and Asymptotic Freedom in Quantum Batteries.

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.

Author Correction: Narrow bounds for the quantum capacity of thermal attenuators.

The original version of this Article contained an error in Equation (40). The numerator of the fraction inside the logarithm was missing an overall minus sign. This has been corrected in the PDF and HTML versions of the Article.

Geometrical Bounds on Irreversibility in Open Quantum Systems.

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.

Narrow bounds for the quantum capacity of thermal attenuators.

Thermal attenuator channels model the decoherence of quantum systems interacting with a thermal bath, e.g., a two-level system subject to thermal noise and an electromagnetic signal traveling through a fiber or in free-space. Hence determining the quantum capacity of these channels is an outstanding open problem for quantum computation and communication. Here we derive several upper bounds on the quantum capacity of qubit and bosonic thermal attenuators. We introduce an extended version of such channels which is degradable and hence has a single-letter quantum capacity, bounding that of the original thermal attenuators. Another bound for bosonic attenuators is given by the bottleneck inequality applied to a particular channel decomposition. With respect to previously known bounds we report better results in a broad range of attenuation and noise: we can now approximate the quantum capacity up to a negligible uncertainty for most practical applications, e.g., for low thermal noise.

Erratum: Optimal Continuous Variable Quantum Teleportation with Limited Resources [Phys. Rev. Lett. 119, 120503 (2017)].

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

Slow Dynamics and Thermodynamics of Open Quantum Systems.

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.

Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels.

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.

Optimal Continuous Variable Quantum Teleportation with Limited Resources.

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.