arXiv subjects

Nicolas Brunner

Publications and source records attributed to Nicolas Brunner.

At least 73 records · Page 4Linked to original sources

arXiv2021

Quantum measurement incompatibility in subspaces

We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is incompatible, one considers the set of measurements obtained by projection onto any strict subspace of fixed dimension. We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility: measurements that become compatible in every subspace, (ii) fully compressible incompatibility: measurements that remain incompatible in every subspace, and (iii) partly compressible incompatibility: measurements that are compatible in some subspace and incompatible in another. For each class we discuss explicit examples. Finally, we present some applications of these ideas. First we show that joint measurability and coexistence are two inequivalent notions of incompatibility in the simplest case of qubit systems. Second we highlight the implications of our results for tests of quantum steering.

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arXiv2021

Quantum entanglement in the triangle network

Beyond future applications, quantum networks open interesting fundamental perspectives, notably novel forms of quantum correlations. In this work we discuss quantum correlations in networks from the perspective of the underlying quantum states and their entanglement. We address the questions of which states can be prepared in the so-called triangle network, consisting of three nodes connected pairwise by three sources. We derive necessary criteria for a state to be preparable in such a network, considering both the cases where the sources are statistically independent and classically correlated. This shows that the network structure imposes strong and non-trivial constraints on the set of preparable states, fundamentally different from the standard characterization of multipartite quantum entanglement.

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arXiv2020

Hybrid Thermal Machines: Generalized Thermodynamic Resources for Multitasking

Thermal machines perform useful tasks--such as producing work, cooling, or heating--by exchanging energy, and possibly additional conserved quantities such as particles, with reservoirs. Here we consider thermal machines that perform more than one useful task simultaneously, terming these "hybrid thermal machines". We outline their restrictions imposed by the laws of thermodynamics and we quantify their performance in terms of efficiencies. To illustrate their full potential, reservoirs that feature multiple conserved quantities, described by generalized Gibbs ensembles, are considered. A minimal model for a hybrid thermal machine is introduced, featuring three reservoirs and two conserved quantities, e.g., energy and particle number. This model can be readily implemented in a thermoelectric setup based on quantum dots, and hybrid regimes are accessible considering realistic parameters.

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arXiv2020

Fast semidefinite programming with feedforward neural networks

Semidefinite programming is an important optimization task, often used in time-sensitive applications. Though they are solvable in polynomial time, in practice they can be too slow to be used in online, i.e. real-time applications. Here we propose to solve feasibility semidefinite programs using artificial neural networks. Given the optimization constraints as an input, a neural network outputs values for the optimization parameters such that the constraints are satisfied, both for the primal and the dual formulations of the task. We train the network without having to exactly solve the semidefinite program even once, thus avoiding the possibly time-consuming task of having to generate many training samples with conventional solvers. The neural network method is only inconclusive if both the primal and dual models fail to provide feasible solutions. Otherwise we always obtain a certificate, which guarantees false positives to be excluded. We examine the performance of the method on a hierarchy of quantum information tasks, the Navascués-Pironio-Acín hierarchy applied to the Bell scenario. We demonstrate that the trained neural network gives decent accuracy, while showing orders of magnitude increase in speed compared to a traditional solver.

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arXiv2020

Entanglement for any definition of two subsystems

The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a set of states. In this work we define the notion of an "absolutely entangled set" of quantum states: for any possible choice of global basis, at least one of the states in the set is entangled. Hence, for all bipartitions, i.e. any possible definition of the subsystems, the set features entanglement. We present a minimum example of this phenomenon, with a set of four states in $\mathbb{C}^4 = \mathbb{C}^2 \otimes \mathbb{C}^2$. Moreover, we propose a quantitative measure for absolute set entanglement. To lower-bound this quantity, we develop a method based on polynomial optimization to perform convex optimization over unitaries, which is of independent interest.

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arXiv2020

Informationally restricted quantum correlations

Quantum communication leads to strong correlations, that can outperform classical ones. Complementary to previous works in this area, we investigate correlations in prepare-and-measure scenarios assuming a bound on the information content of the quantum communication, rather than on its Hilbert-space dimension. Specifically, we explore the extent of classical and quantum correlations given an upper bound on the one-shot accessible information. We provide a characterisation of the set of classical correlations and show that quantum correlations are stronger than classical ones. We also show that limiting information rather than dimension leads to stronger quantum correlations. Moreover, we present device-independent tests for placing lower bounds on the information given observed correlations. Finally, we show that quantum communication carrying $\log d$ bits of information is at least as strong a resource as $d$-dimensional classical communication assisted by pre-shared entanglement.

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arXiv2020

A neural network oracle for quantum nonlocality problems in networks

Characterizing quantum nonlocality in networks is a challenging, but important problem. Using quantum sources one can achieve distributions which are unattainable classically. A key point in investigations is to decide whether an observed probability distribution can be reproduced using only classical resources. This causal inference task is challenging even for simple networks, both analytically and using standard numerical techniques. We propose to use neural networks as numerical tools to overcome these challenges, by learning the classical strategies required to reproduce a distribution. As such, the neural network acts as an oracle, demonstrating that a behavior is classical if it can be learned. We apply our method to several examples in the triangle configuration. After demonstrating that the method is consistent with previously known results, we give solid evidence that the distribution presented in [N. Gisin, Entropy 21(3), 325 (2019)] is indeed nonlocal as conjectured. Finally we examine the genuinely nonlocal distribution presented in [M.-O. Renou et al., PRL 123, 140401 (2019)], and, guided by the findings of the neural network, conjecture nonlocality in a new range of parameters in these distributions. The method allows us to get an estimate on the noise robustness of all examined distributions.

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arXiv2020

Quantum nonlocality in networks can be demonstrated with an arbitrarily small level of independence between the sources

Quantum nonlocality can be observed in networks even in the case where every party can only perform a single measurement, i.e. does not receive any input. So far, this effect has been demonstrated under the assumption that all sources in the network are fully independent from each other. Here we investigate to what extent this independence assumption can be relaxed. After formalizing the question, we show that, in the triangle network without inputs, quantum nonlocality can be observed, even when assuming only an arbitrarily small level of independence between the sources. This means that quantum predictions cannot be reproduced by a local model unless the three sources can be perfectly correlated.

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arXiv2020

Critical heat current for operating an entanglement engine

Autonomous entanglement engines have recently been proposed to generate steady-state bipartite and multipartite entanglement exploiting only incoherent interactions with thermal baths at different temperatures. In this work, we investigate the interplay between heat current and entanglement in a two-qubit entanglement engine, deriving a critical heat current for successful operation of the engine, i.e. a cut-off above which entanglement is present. The heat current can thus be seen as a witness to the presence of entanglement. In the regime of weak-inter qubit coupling, we also investigate the effect of two experimentally relevant parameters for the qubits, the energy detuning and tunnelling, on the entanglement production. Finally, we show that the regime of strong inter-qubit coupling provides no clear advantage over the weak regime, in the context of out-of-equilibrium entanglement engines.

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arXiv2020

Constraints on nonlocality in networks from no-signaling and independence

Generalising the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is however challenging. Here we investigate constraints on correlations in networks under the two natural assumptions of no-signaling and independence of the sources. We consider the ``triangle network'', and derive strong constraints on correlations even though the parties receive no input, i.e. each party performs a fixed measurement. We show that some of these constraints are tight, by constructing explicit local models (i.e. where sources distribute classical variables) that can saturate them. However, we also observe that other constraints can apparently not be saturated by local models, which opens the possibility of having nonlocal (but non-signaling) correlations in the triangle network.

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arXiv2020

Quantum teleportation of single-electron states

We consider a scheme for on-demand teleportation of a dual-rail electron qubit state, based on single-electron sources and detectors. The scheme has a maximal efficiency of 25%, which is limited both by the shared entangled state as well as the Bell-state measurement. We consider two experimental implementations, realizable with current technology. The first relies on surface acoustic waves, where all the ingredients are readily available. The second is based on Lorentzian voltage pulses in quantum Hall edge channels. As single-electron detection is not yet experimentally established in these systems, we consider a tomographic detection of teleportation using current correlators up to (and including) third order. For both implementations we take into account environmental effects.

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arXiv2020

Quantifying measurement incompatibility of mutually unbiased bases

Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of $k$ MUB in dimension $d$, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of $k=d+1$ MUB (given $d$ is a prime power). On the way, we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements. Moreover, we prove the existence of sets of $k$ MUB that are operationally inequivalent, as they feature different noise robustness, and we provide a lower bound on the number of such inequivalent sets up to dimension 32. Finally, we discuss applications of our results for Einstein-Podolsky-Rosen steering.

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arXiv2019

Exploring the limits of no backward in time signalling

We present an operational and model-independent framework to investigate the concept of no-backwards-in-time signaling. We define no-backwards-in-time signaling conditions, closely related to the spatial no-signaling conditions. These allow for theoretical possibilities in which the future affects the past, nevertheless without signaling backwards in time. This is analogous to non-local but no-signaling spatial correlations. Furthermore, our results shed new light on situations with indefinite causal structure and their connection to quantum theory.

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arXiv2019

Semi-device-independent characterization of quantum measurements under a minimum overlap assumption

Recently, a novel framework for semi-device-independent quantum prepare-and-measure protocols has been proposed, based on the assumption of a limited distinguishability between the prepared quantum states. Here, we discuss the problem of characterizing an unknown quantum measurement device in this setting. We present several methods to attack this problem. Considering the simplest scenario of two preparations with lower bounded overlap, we show that genuine 3-outcome POVMs can be certified, even in the presence of noise. Moreover, we show that the optimal POVM for performing unambiguous state discrimination can be self-tested.

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arXiv2019

Unifying paradigms of quantum refrigeration: A universal and attainable bound on cooling

Cooling quantum systems is arguably one of the most important thermodynamic tasks connected to modern quantum technologies and an interesting question from a foundational perspective. It is thus of no surprise that many different theoretical cooling schemes have been proposed, differing in the assumed control paradigm and complexity, and operating either in a single cycle or in steady state limits. Working out bounds on quantum cooling has since been a highly context dependent task with multiple answers, with no general result that holds independent of assumptions. In this letter we derive a universal bound for cooling quantum systems in the limit of infinite cycles (or steady state regimes) that is valid for any control paradigm and machine size. The bound only depends on a single parameter of the refrigerator and is theoretically attainable in all control paradigms. For qubit targets we prove that this bound is achievable in a single cycle and by autonomous machines.

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arXiv2019

All quantum resources provide an advantage in exclusion tasks

A key ingredient in quantum resource theories is a notion of measure. Such as a measure should have a number of fundamental properties, and desirably also a clear operational meaning. Here we show that a natural measure known as the convex weight, which quantifies the resource cost of a quantum device, has all the desired properties. In particular, the convex weight of any quantum resource corresponds exactly to the relative advantage it offers in an exclusion task. After presenting the general result, we show how the construction works for state assemblages, sets of measurements and sets of transformations. Moreover, in order to bound the convex weight analytically, we give a complete characterisation of the convex components and corresponding weights of such devices.

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arXiv2019

Anomalous Weak Values Without Post-Selection

A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an "anomalous weak value", is generally believed to be possible only when a non-trivial post-selection is performed, i.e., when only a particular subset of the data is considered. Here we show, however, that this is not the case in general: in scenarios in which several weak measurements are sequentially performed, an anomalous weak value can be obtained without post-selection, i.e., without discarding any data. We discuss several questions that this raises about the subtle relation between weak values and pointer positions for sequential weak measurements. Finally, we consider some implications of our results for the problem of distinguishing different causal structures.

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arXiv2019

Sequential random access codes and self-testing of quantum measurement instruments

Quantum Random Access Codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.

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