arXiv subjects

Rodrigo Gallego

Publications and source records attributed to Rodrigo Gallego.

At least 19 recordsLinked to original sources

arXiv2020

By-passing fluctuation theorems

Fluctuation theorems impose constraints on possible work extraction probabilities in thermodynamical processes. These constraints are stronger than the usual second law, which is concerned only with average values. Here, we show that such constraints, expressed in the form of the Jarzysnki equality, can be bypassed if one allows for the use of catalysts - additional degrees of freedom that may become correlated with the system from which work is extracted, but whose reduced state remains unchanged so that they can be re-used. This violation can be achieved both for small systems but also for macroscopic many-body systems and leads to positive work extraction per particle with finite probability from macroscopic states in equilibrium. In addition to studying such violations for a single system, we also discuss the scenario in which many parties use the same catalyst to induce local transitions. We show that there exist catalytic processes that lead to highly correlated work distributions, expected to have implications for stochastic and quantum thermodynamics.

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arXiv2019

Cooling to absolute zero: The unattainability principle

The unattainability principle (UP) is an operational formulation of the third law of thermodynamics stating the impossibility to bring a system to its ground state in finite time. In this work, several recent derivations of the UP are presented, with a focus on the set of assumptions and allowed sets of operations under which the UP can be formally derived. First, we discuss derivations allowing for arbitrary unitary evolutions as the set of operations. There the aim is to provide fundamental bounds on the minimal achievable temperature, which are applicable with almost full generality. These bounds show that perfect cooling requires an infinite amount of a given resource -- worst-case work, heat bath's size and dimensionality or non-equilibrium states among others -- which can in turn be argued to imply that an infinite amount of time is required to access those resources. Secondly, we present derivations within a less general set of operations conceived to capture a broad class of currently available experimental settings. In particular, the UP is here derived within a model of linear and driven quantum refrigerators consisting on a network of harmonic oscillators coupled to several reservoirs at different temperatures.

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arXiv2017

Third Law of Thermodynamics as a Single Inequality

The third law of thermodynamics in the form of the unattainability principle states that exact ground-state cooling requires infinite resources. Here we investigate the amount of non-equilibrium resources needed for approximate cooling. We consider as resource any system out of equilibrium, allowing for resources beyond the i.i.d. assumption and including the input of work as a particular case. We establish in full generality a sufficient and a necessary condition for cooling and show that for a vast class of non-equilibrium resources these two conditions coincide, providing a single necessary and sufficient criterion. Such conditions are expressed in terms of a single function playing a similar role for the third law to the one of the free energy for the second law. From a technical point of view we provide new results about concavity/convexity of certain Renyi-divergences, which might be of independent interest.

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arXiv2017

Statistical ensembles without typicality

Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of these ensembles in statistical descriptions. However, there is still no full consensus on the precise reasoning justifying the use of such ensembles. In this work, we provide a new approach to derive maximum-entropy ensembles taking a strictly operational perspective. We investigate the set of possible transitions that a system can undergo together with an environment, when one only has partial information about both the system and its environment. The set of all these allowed transitions encodes thermodynamic laws and limitations on thermodynamic tasks as particular cases. Our main result is that the set of allowed transitions coincides with the one possible if both system and environment were assigned the maximum entropy state compatible with the partial information. This justifies the overwhelming success of such ensembles and provides a derivation without relying on considerations of typicality or information-theoretic measures.

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arXiv2017

Axiomatic characterization of the quantum relative entropy and free energy

Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: i) Continuity in the first argument, ii) the validity of the data-processing inequality, iii) additivity under tensor products, and iv) super-additivity. This observation has immediate implications for quantum thermodynamics, which we discuss. Specifically, we demonstrate that, under reasonable restrictions, the free energy is singled out as a measure of athermality. In particular, we consider an extended class of Gibbs-preserving maps as free operations in a resource-theoretic framework, in which a catalyst is allowed to build up correlations with the system at hand. The free energy is the only extensive and continuous function that is monotonic under such free operations.

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arXiv2017

Nonlocality free wirings and the distinguishability between Bell boxes

Bell nonlocality can be formulated in terms of a resource theory with local-hidden variable models as resourceless objects. Two such theories are known, one built upon local operations assisted by shared randomness (LOSRs) and the other one allowing, in addition, for prior-to-input classical communication. We show that prior communication, although unable to create nonlocality, leads to wirings not only beyond LOSRs but also not contained in a much broader class of (nonlocality-generating) global wirings. Technically, this is shown by proving that it can improve the statistical distinguishability between Bell correlations optimised over all fixed measurement choices. This has implications in nonlocality quantification, and leads us to a natural universal definition of Bell nonlocality measures. To end up with, we also consider the statistical strength of nonlocality proofs. We point out some issues of its standard definition in the resource-theoretic operational framework, and suggest simple fixes for them. Our findings reveal non-trivial features of the geometry of the set of wirings and may have implications in the operational distinguishability of nonlocal behaviors.

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arXiv2016

Classical communication cost of quantum steering

Quantum steering is observed when performing appropriate local measurements on an entangled state. Here we discuss the possibility of simulating classically this effect, using classical communication instead of entanglement. We show that infinite communication is necessary for exactly simulating steering for any pure entangled state, as well as for a class of mixed entangled states. Moreover, we discuss the communication cost of steering for general entangled states, as well as approximate simulation. Our findings reveal striking differences between Bell nonlocality and steering, and provide a natural way of measuring the strength of the latter.

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arXiv2015

The resource theory of steering

We present an operational framework for Einstein-Podolsky-Rosen steering as a physical resource. To begin with, we characterize the set of steering non-increasing operations (SNIOs) --i.e., those that do not create steering-- on arbitrary-dimensional bipartite systems composed of a quantum subsystem and a black-box device. Next, we introduce the notion of convex steering monotones as the fundamental axiomatic quantifiers of steering. As a convenient example thereof, we present the relative entropy of steering. In addition, we prove that two previously proposed quantifiers, the steerable weight and the robustness of steering, are also convex steering monotones. To end up with, for minimal-dimensional systems, we establish, on the one hand, necessary and sufficient conditions for pure-state steering conversions under stochastic SNIOs and prove, on the other hand, the non-existence of steering bits, i.e., measure-independent maximally steerable states from which all states can be obtained by means of the free operations. Our findings reveal unexpected aspects of steering and lay foundations for further resource-theory approaches, with potential implications in Bell non-locality.

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arXiv2015

Robust amplification of Santha-Vazirani sources with three devices

We demonstrate that amplification of arbitrarily weak randomness is possible using quantum resources. We present a randomness amplification protocol that involves Bell experiments. We find a Bell inequality which can amplify arbitrarily weak randomness and give a detailed analysis of the protocol involving it. Our analysis includes finding a sufficient violation of Bell inequality as a function of the initial quality of randomness. It has a very important property that for any quality the required violation is strictly lower than possible to obtain using quantum resources. Among other things, it means that the protocol takes a finite amount of time to amplify arbitrarily weak randomness.

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arXiv2015

Detection loophole attacks on semi-device-independent quantum and classical protocols

Semi-device-independent quantum protocols realize information tasks - e.g. secure key distribution, random access coding, and randomness generation - in a scenario where no assumption on the internal working of the devices used in the protocol is made, except their dimension. These protocols offer two main advantages: first, their implementation is often less demanding than fully-device-independent protocols. Second, they are more secure than their device-dependent counterparts. Their classical analogous is represented by random access codes, which provide a general framework for describing one-sided classical communication tasks. We discuss conditions under which detection inefficiencies can be exploited by a malicious provider to fake the performance of semi-device-independent quantum and classical protocols - and how to prevent it.

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arXiv2014

Nonlocality in sequential correlation scenarios

As first shown by Popescu [S. Popescu, Phys. Rev. Lett. 74, 2619 (1995)], some quantum states only reveal their nonlocality when subjected to a sequence of measurements while giving rise to local correlations in standard Bell tests. Motivated by this manifestation of "hidden nonlocality" we set out to develop a general framework for the study of nonlocality when sequences of measurements are performed. Similar to [R. Gallego et al., Phys. Rev. Lett. 109, 070401 (2013)] our approach is operational, i.e. the task is to identify the set of allowed operations in sequential correlation scenarios and define nonlocality as the resource that cannot be created by these operations. This leads to a characterisation of sequential nonlocality that contains as particular cases standard nonlocality and hidden nonlocality.

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arXiv2012

Full randomness from arbitrarily deterministic events

Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact that a theory makes prediction only in probabilistic terms does not imply the existence of any form of randomness in nature. The question then remains whether one can certify randomness independent of the physical framework used. While standard Bell tests approach this question from this perspective, they require prior perfect randomness, which renders the approach circular. Recently, it has been shown that it is possible to certify full randomness using almost perfect random bits. Here, we prove that full randomness can indeed be certified using quantum non-locality under the minimal possible assumptions: the existence of a source of arbitrarily weak (but non-zero) randomness and the impossibility of instantaneous signalling. Thus we are left with a strict dichotomic choice: either our world is fully deterministic or there exist in nature events that are fully random. Apart from the foundational implications, our results represent a quantum protocol for full randomness amplification, an information task known to be impossible classically. Finally, they open a new path for device-independent protocols under minimal assumptions.

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arXiv2012

Robustness of Device Independent Dimension Witnesses

Device independent dimension witnesses provide a lower bound on the dimensionality of classical and quantum systems in a "black box" scenario where only correlations between preparations, measurements and outcomes are considered. We address the problem of the robustness of dimension witnesses, namely that to witness the dimension of a system or to discriminate between its quantum or classical nature, even in the presence of loss. We consider the case when shared randomness is allowed between preparations and measurements and we provide a threshold in the detection efficiency such that dimension witnessing can still be performed.

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arXiv2012

Fully nonlocal quantum correlations

Quantum mechanics is a nonlocal theory, but not as nonlocal as the no-signalling principle allows. However, there exist quantum correlations that exhibit maximal nonlocality: they are as nonlocal as any non-signalling correlations and thus have a local content, quantified by the fraction $p_L$ of events admitting a local description, equal to zero. Exploiting the link between the Kochen-Specker and Bell's theorems, we derive, from every Kochen-Specker proof, Bell inequalities maximally violated by quantum correlations. We then show that these Bell inequalities lead to experimental bounds on the local content of quantum correlations which are significantly better than those based on other constructions. We perform the experimental demonstration of a Bell test originating from the Peres-Mermin Kochen-Specker proof, providing an upper bound on the local content $p_L\lesssim 0.22$.

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arXiv2012

Fully nonlocal, monogamous, and random genuinely multipartite quantum correlations

Local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal, monogamous, and associated to fully random outcomes. This makes these states ideal for bipartite cryptographic tasks. Genuine-multipartite nonlocality constitutes a stronger notion of nonlocality that appears in the multipartite case. Maximal genuine-multipartite nonlocality, monogamy and full random outcomes are thus highly desired properties for multipartite correlations in intrinsically genuine-multipartite cryptographic scenarios. We prove that local measurements on Greenberger-Horne-Zeilinger states, for all local dimension and number of parts, can produce correlations that are fully genuine-multipartite nonlocal, monogamous and with fully random outcomes. A key ingredient in our proof is a multipartite chained Bell inequality detecting genuine-multipartite nonlocality, which we introduce. Finally, we discuss the applications of our results for intrinsically genuine-multipartite cryptographic protocols such as device-independent secret sharing.

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arXiv2012

Quantum correlations require multipartite information principles

Identifying which correlations among distant observers are possible within our current description of Nature, based on quantum mechanics, is a fundamental problem in Physics. Recently, information concepts have been proposed as the key ingredient to characterize the set of quantum correlations. Novel information principles, such as, information causality or non-trivial communication complexity, have been introduced in this context and successfully applied to some concrete scenarios. We show in this work a fundamental limitation of this approach: no principle based on bipartite information concepts is able to single out the set of quantum correlations for an arbitrary number of parties. Our results reflect the intricate structure of quantum correlations and imply that new and intrinsically multipartite information concepts are needed for their full understanding.

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arXiv2011

An operational framework for nonlocality

Due to the importance of entanglement for quantum information purposes, a framework has been developed for its characterization and quantification as a resource based on the following operational principle: entanglement among $N$ parties cannot be created by local operations and classical communication, even when $N-1$ parties collaborate. More recently, nonlocality has been identified as another resource, alternative to entanglement and necessary for device-independent quantum information protocols. We introduce an operational framework for nonlocality based on a similar principle: nonlocality among $N$ parties cannot be created by local operations and allowed classical communication even when $N-1$ parties collaborate. We then show that the standard definition of multipartite nonlocality, due to Svetlichny, is inconsistent with this operational approach: according to it, genuine tripartite nonlocality could be created by two collaborating parties. We finally discuss alternative definitions for which consistency is recovered.

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arXiv2011

Experimental estimation of the dimension of classical and quantum systems

An overwhelming majority of experiments in classical and quantum physics make a priori assumptions about the dimension of the system under consideration. However, would it be possible to assess the dimension of a completely unknown system only from the results of measurements performed on it, without any extra assumption? The concept of a dimension witness answers this question, as it allows one to bound the dimension of an unknown classical or quantum system in a device-independent manner, that is, only from the statistics of measurements performed on it. Here, we report on the experimental demonstration of dimension witnesses in a prepare and measure scenario. We use pairs of photons entangled in both polarization and orbital angular momentum to generate ensembles of classical and quantum states of dimensions up to 4. We then use a dimension witness to certify their dimensionality as well as their quantum nature. Our results open new avenues for the device-independent estimation of unknown quantum systems and for applications in quantum information science.

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