Gauge-Invariant Quantum Thermodynamics: Consequences for the First Law.

The universality of classical thermodynamics rests on the central limit theorem, due to which, measurements of thermal fluctuations are unable to reveal detailed information regarding the microscopic structure of a macroscopic body. When small systems are considered and fluctuations become important, thermodynamic quantities can be understood in the context of classical stochastic mechanics. A fundamental assumption behind thermodynamics is therefore that of coarse graining, which stems from a substantial lack of control over all degrees of freedom. However, when quantum systems are concerned, one claims a high level of control. As a consequence, information theory plays a major role in the identification of thermodynamic functions. Here, drawing from the concept of gauge symmetry-essential in all modern physical theories-we put forward a new possible intermediate route. Working within the realm of quantum thermodynamics, we explicitly construct physically motivated gauge transformations which encode a gentle variant of coarse graining behind thermodynamics. As a first application of this new framework, we reinterpret quantum work and heat, as well as the role of quantum coherence.

Quantum Switch as a Thermodynamic Resource in the Context of Passive States.

In recent years, many works have explored possible advantages of indefinite causal order, with the main focus on its controlled implementation known as quantum switch. In this paper, we tackle advantages in quantum thermodynamics, studying whether quantum switch is capable of activating a passive state, either alone or with extra resources (active control state) and/or operations (measurement of the control system). By disproving the first possibility and confirming the second one, we show that quantum switch is not a thermodynamic resource in the discussed context, though it can facilitate work extraction given external resources. We discuss our findings by considering specific examples: a qubit system subject to rotations around the x and y axes in the Bloch sphere, as well as general unitaries from the U(2) group; and the system as a quantum harmonic oscillator with displacement operators, as well as with a combination of displacement and squeeze operators.

Thermodynamics of Reduced State of the Field.

Recent years have seen the flourishing of research devoted to quantum effects on mesoscopic and macroscopic scales. In this context, in Entropy 2019, 21, 705, a formalism aiming at describing macroscopic quantum fields, dubbed Reduced State of the Field (RSF), was envisaged. While, in the original work, a proper notion of entropy for macroscopic fields, together with their dynamical equations, was derived, here, we expand thermodynamic analysis of the RSF, discussing the notion of heat, solving dynamical equations in various regimes of interest, and showing the thermodynamic implications of these solutions.

Comment on "Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries".

In the abstract of [Phys. Rev. Lett. 125, 040601 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.040601] one can read that "[…] to have a nonzero rate of change of the extractable work, the state ρ_{W} of the battery cannot be an eigenstate of a 'free energy operator,' defined by F≡H_{W}+ß^{-1}log(ρ_{W}), where H_{W} is the Hamiltonian of the battery and ß is the inverse temperature […]." Contrarily to what is presented below Eq. (17) of the Letter, we observe that the above conclusion does not hold when the battery is subject to nonunitary dynamics.

Bounding the Sets of Classical and Quantum Correlations in Networks.

We present a method that allows the study of classical and quantum correlations in networks with causally independent parties, such as the scenario underlying entanglement swapping. By imposing relaxations of factorization constraints in a form compatible with semidefinite programing, it enables the use of the Navascués-Pironio-Acín hierarchy in complex quantum networks. We first show how the technique successfully identifies correlations not attainable in the entanglement-swapping scenario. Then we use it to show how the nonlocal power of measurements can be activated in a network: there exist measuring devices that, despite being unable to generate nonlocal correlations in the standard Bell scenario, provide a classical-quantum separation in an entanglement swapping configuration.

Mutual Unbiasedness in Coarse-Grained Continuous Variables.

The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.

Uncertainty Relations for Coarse-Grained Measurements: An Overview.

Uncertainty relations involving incompatible observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, several uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90th anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing.

Optimal control of effective Hamiltonians.

We present a systematic scheme for the optimization of quantum simulations. Specifically, we show how polychromatic driving can be used to significantly improve the driving of Raman transitions in the Lambda system, which opens new possibilities for controlled driving-induced effective dynamics.

Reliable entanglement detection under coarse-grained measurements.

We derive reliable entanglement witnesses for coarse-grained measurements on continuous variable systems. These witnesses never return a "false positive" for identification of entanglement, under any degree of coarse graining. We show that even in the case of Gaussian states, entanglement witnesses based on the Shannon entropy can outperform those based on variances. We apply our results to experimental identification of spatial entanglement of photon pairs.

Collective uncertainty entanglement test.

For a given pure state of a composite quantum system we analyze the product of its projections onto a set of locally orthogonal separable pure states. We derive a bound for this product analogous to the entropic uncertainty relations. For bipartite systems the bound is saturated for maximally entangled states and it allows us to construct a family of entanglement measures, we shall call collectibility. As these quantities are experimentally accessible, the approach advocated contributes to the task of experimental quantification of quantum entanglement, while for a three-qubit system it is capable to identify the genuine three-party entanglement.