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Register a new userContinuous-variable nonlocality and contextuality
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Added by
Pierre-Emmanuel Emeriau
Publication date
2019
fields
Physics
and research's language is
English
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Contextuality is a non-classical behaviour that can be exhibited by quantum systems. It is increasingly studied for its relationship to quantum-over-classical advantages in informatic tasks. To date, it has largely been studied in discrete variable scenarios, where observables take values in discrete and usually finite sets. Practically, on the other hand, continuous-variable scenarios offer some of the most promising candidates for implementing quantum computations and informatic protocols. Here we set out a framework for treating contextuality in continuous-variable scenarios. It is shown that the Fine--Abramsky--Brandenburger theorem extends to this setting, an important consequence of which is that nonlocality can be viewed as a special case of contextuality, as in the discrete case. The contextual fraction, a quantifiable measure of contextuality that bears a precise relationship to Bell inequality violations and quantum advantages, can also be defined in this setting. It is shown to be a non-increasing monotone with respect to classical operations that include binning to discretise data. Finally, we consider how the contextual fraction can be formulated as an infinite linear program, and calculated with increasing accuracy using semi-definite programming approximations.
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Everyday experience supports the existence of physical properties independent of observation in strong contrast to the predictions of quantum theory. In particular, existence of physical properties that are independent of the measurement context is prohibited for certain quantum systems. This property is known as contextuality. This paper studies whether the process of decay in space-time generally destroys the ability of revealing contextuality. We find that in the most general situation the decay property does not diminish this ability. However, applying certain constraints due to the space-time structure either on the time evolution of the decaying system or on the measurement procedure, the criteria revealing contextuality become inherently dependent on the decay property or an impossibility. In particular, we derive how the context-revealing setup known as Bells nonlocality tests changes for decaying quantum systems. Our findings illustrate the interdependence between hidden and local hidden parameter theories and the role of time.
Contextuality and nonlocality are non-classical properties exhibited by quantum statistics whose implications profoundly impact both foundations and applications of quantum theory. In this paper we provide some insights into logical contextuality and inequality-free proofs. The former can be understood as the possibility version of contextuality, while the latter refers to proofs of quantum contextuality/nonlocality that are not based on violations of some noncontextuality (or Bell) inequality. The present work aims to build a bridge between these two concepts from what we call possibilistic paradoxes, which are sets of possibilistic conditions whose occurrence implies contextuality/nonlocality. As main result, we demonstrate the existence of possibilistic paradoxes whose occurrence is a necessary and sufficient condition for logical contextuality in a very important class of scenarios. Finally, we discuss some interesting consequences arising from the completeness of these possibilistic paradoxes.
The present paper is devoted to investigation of the classical capacity of infinite-dimensional quantum measurement channels. A number of usable conditions are introduced that enable us to apply previously obtained general results to specific models, in particular, to the multi-mode bosonic Gaussian measurement channels. An explicit formula for the classical capacity of the Gaussian measurement channel is obtained in this paper without assuming the global gauge symmetry, solely under certain threshold condition. The result is illustrated by the capacity computation for one-mode squeezed-noise heterodyne measurement channel.
In an abstract sense, quantum data hiding is the manifestation of the fact that two classes of quantum measurements can perform very differently in the task of binary quantum state discrimination. We investigate this phenomenon in the context of continuous variable quantum systems. First, we look at the celebrated case of data hiding against the set of local operations and classical communication. While previous studies have placed upper bounds on its maximum efficiency in terms of the local dimension and are thus not applicable to continuous variable systems, we tackle this latter case by establishing more general bounds that rely solely on the local mean photon number of the states employed. Along the way, we perform a quantitative analysis of the error introduced by the non-ideal Braunstein--Kimble quantum teleportation protocol, determining how much two-mode squeezing and local detection efficiency is needed in order to teleport an arbitrary local state of known mean energy with a prescribed accuracy. Finally, following a seminal proposal by Winter, we look at data hiding against the set of Gaussian operations and classical computation, providing the first example of a relatively simple scheme that works with a single mode only. The states employed can be generated from a two-mode squeezed vacuum by local photon counting; the larger the squeezing, the higher the efficiency of the scheme.
We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation rates in these settings. This removes the need for asymptotic continuity, which cannot be defined in the traditional sense for infinite-dimensional systems. We consider three applications, to the resource theories of (I) optical nonclassicality, (II) entanglement, and (III) quantum thermodynamics. In cases (II) and (III), the employed monotones are the (infinite-dimensional) squashed entanglement and the free energy, respectively. For case (I), we consider the measured relative entropy of nonclassicality and prove it to be lower semicontinuous and strongly superadditive. Our technique then yields computable upper bounds on asymptotic transformation rates including those achievable under linear optical elements. We also prove a number of results which ensure the measured relative entropy of nonclassicality to be bounded on any physically meaningful state, and to be easily computable for some class of states of interest, e.g., Fock diagonal states. We conclude by applying our findings to the problem of cat state manipulation and noisy Fock state purification.
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