Thermodynamic work from operational principles

In recent years we have witnessed a concentrated effort to make sense of thermodynamics for small-scale systems. One of the main difficulties is to capture a suitable notion of work that models realistically the purpose of quantum machines, in an analogous way to the role played, for macroscopic machines, by the energy stored in the idealisation of a lifted weight. Despite of several attempts to resolve this issue by putting forward specific models, these are far from capturing realistically the transitions that a quantum machine is expected to perform. In this work, we adopt a novel strategy by considering arbitrary kinds of systems that one can attach to a quantum thermal machine and seeking for work quantifiers. These are functions that measure the value of a transition and generalise the concept of work beyond the model of a lifted weight. We do so by imposing simple operational axioms that any reasonable work quantifier must fulfil and by deriving from them stringent mathematical condition with a clear physical interpretation. Our approach allows us to derive much of the structure of the theory of thermodynamics without taking as a primitive the definition of work. We can derive, for any work quantifier, a quantitative second law in the sense of bounding the work that can be performed using some non-equilibrium resource by the work that is needed to create it. We also discuss in detail the role of reversibility and correlations in connection with the second law. Furthermore, we recover the usual identification of work with energy in degrees of freedom with vanishing entropy as a particular case of our formalism. Our mathematical results can be formulated abstractly and are general enough to carry over to other resource theories than quantum thermodynamics.Comment: 22 pages, 4 figures, axioms significantly simplified, more comprehensive discussion of relationship to previous approache

Classical Rules in Quantum Games

We consider two aspects of quantum game theory: the extent to which the quantum solution solves the original classical game, and to what extent the new solution can be obtained in a classical model.Comment: The previous title, "Quantum games are no fun (yet)", was too whimsical for Physical Review. This is a comment on most, but not all, papers on quantum game theor

Continuous matrix product state tomography of quantum transport experiments

In recent years, a close connection between the description of open quantum systems, the input-output formalism of quantum optics, and continuous matrix product states in quantum field theory has been established. So far, however, this connection has not been extended to the condensed-matter context. In this work, we substantially develop further and apply a machinery of continuous matrix product states (cMPS) to perform tomography of transport experiments. We first present an extension of the tomographic possibilities of cMPS by showing that reconstruction schemes do not need to be based on low-order correlation functions only, but also on low-order counting probabilities. We show that fermionic quantum transport settings can be formulated within the cMPS framework. This allows us to present a reconstruction scheme based on the measurement of low-order correlation functions that provides access to quantities that are not directly measurable with present technology. Emblematic examples are high-order correlations functions and waiting times distributions (WTD). The latter are of particular interest since they offer insights into short-time scale physics. We demonstrate the functioning of the method with actual data, opening up the way to accessing WTD within the quantum regime.Comment: 11 pages, 4 figure

Quantum field tomography

We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states, a complete set of variational states grasping states in quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on low-order correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomised continuous matrix product states from their correlation data and study the robustness of the reconstruction for different noise models. We also apply the method to data generated by simulations based on continuous matrix product states and using the time-dependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as encountered in experiments with ultra-cold atoms on top of atom chips. By virtue of the analogy with the input-output formalism in quantum optics, it also allows for studying open quantum systems.Comment: 31 pages, 5 figures, minor change

Optimal entanglement witnesses for continuous-variable systems

This paper is concerned with all tests for continuous-variable entanglement that arise from linear combinations of second moments or variances of canonical coordinates, as they are commonly used in experiments to detect entanglement. All such tests for bi-partite and multi-partite entanglement correspond to hyperplanes in the set of second moments. It is shown that all optimal tests, those that are most robust against imperfections with respect to some figure of merit for a given state, can be constructed from solutions to semi-definite optimization problems. Moreover, we show that for each such test, referred to as entanglement witness based on second moments, there is a one-to-one correspondence between the witness and a stronger product criterion, which amounts to a non-linear witness, based on the same measurements. This generalizes the known product criteria. The presented tests are all applicable also to non-Gaussian states. To provide a service to the community, we present the documentation of two numerical routines, FULLYWIT and MULTIWIT, which have been made publicly available.Comment: 14 pages LaTeX, 1 figure, presentation improved, references update

Equilibration in low-dimensional quantum matrix models

Matrix models play an important role in studies of quantum gravity, being candidates for a formulation of M-theory, but are notoriously difficult to solve. In this work, we present a fresh approach by introducing a novel exact model provably equivalent with low-dimensional bosonic matrix models. In this equivalent model significant local structure becomes apparent and it can serve as a simple toy model for analytical and precise numerical study. We derive a substantial part of the low energy spectrum, find a conserved charge, and are able to derive numerically the Regge trajectories. To exemplify the usefulness of the approach, we address questions of equilibration starting from a non-equilibrium situation, building upon an intuition from quantum information. We finally discuss possible generalizations of the approach.Comment: 5+2 pages, 2 figures; v2: published versio

Continuity bounds on the quantum relative entropy

The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose, including the trace norm distance. More precisely, we derive lower and upper bounds on the relative entropy in terms of various distance measures for the difference of the states based on unitarily invariant norms. The upper bounds can be considered as statements of continuity of the relative entropy distance in the sense of Fannes. We employ methods from optimisation theory to obtain bounds that are as sharp as possible.Comment: 13 pages (ReVTeX), 3 figures, replaced with published versio