Non-locality breaking qubit channels: the case for CHSH inequality

Pal, Rajarshi; Ghosh, Sibasish

doi:10.1088/1751-8113/48/15/155302

Cited by 19 publications

(54 citation statements)

References 28 publications

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“…As a result of Chois theorem [31], a quantum channel acting on a density matrix r A can be expressed as follows: [28]. Nonlocality-breaking channels are a generalization of the well-studied entanglement-breaking channels [29].…”

Section: Nonlocality and Chsh-breaking Channelsmentioning

confidence: 99%

“…For a general nonunital channel, we know of no analytical criteria for determining whether or not it is CHSH-breaking, and one typically obtains results by numerically searching over all input states and measurement settings [28]. Nevertheless, in appendices B and C, we provide analytical conditions for when special classes of nonunital channels are CHSH-breaking.…”

Section: Nonlocality and Chsh-breaking Channelsmentioning

confidence: 99%

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Channel activation of CHSH nonlocality

et al. 2020

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Quantum channels that break CHSH nonlocality on all input states are known as CHSH-breaking channels. In quantum networks, such channels are useless for distributing correlations that can violate the CHSH Inequality. Motivated by previous work on activation of nonlocality in quantum states, here we demonstrate an analogous activation of CHSH-breaking channels. That is, we show that certain pairs of CHSH-breaking channels are no longer CHSH-breaking when used in combination. We find that this type of activation can emerge in both uni-directional and bi-directional communication scenarios.

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Section: Nonlocality and Chsh-breaking Channelsmentioning

confidence: 99%

Section: Nonlocality and Chsh-breaking Channelsmentioning

confidence: 99%

Channel activation of CHSH nonlocality

et al. 2020

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“…In this work, we begin by briefly reviewing the aforementioned activation scenarios and pay particular attention to the following: (1) the complete characterisation of hidden nonlocality (or activation through local filtering) for two-qubit systems recently derived in [10], (2) a case of the activation through tensoring called k-copy nonlocality (or superactivation of nonlocality) [11], and (3) activation through the combination of arXiv:1609.08025v1 [quant-ph] 26 Sep 2016 tensoring and local filtering [12,13]. Moreover, we have focused (though not restricted) on the study of these three scenarios over two-qubit systems.…”

Section: Introductionmentioning

confidence: 99%

On the Activation of Quantum Nonlocality

2016

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We report on some quantum properties of physical systems, namely, entanglement, nonlocality, k-copy nonlocality (superactivation of nonlocality), hidden nonlocality (activation of nonlocality through local filtering) and the activation of nonlocality through tensoring and local filtering. The aim of this work is two-fold. First, we provide a review of the numerical procedures that must be followed in order to calculate the aforementioned properties, in particular, for any two-qubit system, and reproduce the bounds for two-qudit Werner states. Second, we use such numerical tools to calculate new bounds of these properties for two-qudit Isotropic states and two-qubit Hirsch states.

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“…The violation of a Bell inequality is a sufficient condition for quantum entanglement, but it is known not to be necessary, as there exist entangled states that do not violate any Bell inequality [30,31]. In our framework, this is equivalent to saying that there exist genuinely quantum channels that would never pass this test [32].4. Bell tests are very fragile with respect to losses (during storage or detection) [18,33].Experimental violations of the Clauser-Horne-Shimony-Holt inequality (CHSH) [34] have been reported for quantum memories [35][36][37], but without closing all loopholes (in particular the detection and locality loopholes).…”

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confidence: 96%

Resource Theory of Quantum Memories and Their Faithful Verification with Minimal Assumptions

2018

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We provide a complete set of game-theoretic conditions equivalent to the existence of a transformation from one quantum channel into another one, by means of classically correlated pre/post processing maps only. Such conditions naturally induce tests to certify that a quantum memory is capable of storing quantum information, as opposed to memories that can be simulated by measurement and state preparation (corresponding to entanglement-breaking channels). These results are formulated as a resource theory of genuine quantum memories (correlated in time), mirroring the resource theory of entanglement in quantum states (correlated spatially). As the set of conditions is complete, the corresponding tests are faithful, in the sense that any non entanglement-breaking channel can be certified. Moreover, they only require the assumption of trusted inputs, known to be unavoidable for quantum channel verification. As such, the tests we propose are intrinsically different from the usual process tomography, for which the probes of both the input and the output of the channel must be trusted. An explicit construction is provided and shown to be experimentally realizable, even in the presence of arbitrarily strong losses in the memory or detectors.Consider a vendor selling quantum devices purportedly able of storing quantum information for a period of time. However, during their operation, the devices always break the entanglement between the stored subsystem and any other subsystem. Such devices are arguably useless as quantum memories; for example, they would not be able to establish entangled links in a quantum repeater scheme [1,2]. In the terminology of quantum channels [3][4][5], those devices correspond to entanglementbreaking (EB) channels [6,7], which are exactly equivalent to the measure-and-prepare channels depicted in Fig. 1. Measure-and-prepare channels are implemented by measuring the input state, storing the classical information corresponding to the measurement outcome for the required duration, and then using that information to prepare a quantum state. Even though strictly speaking, such channels are quantum channels (since they act upon an input quantum system), they actually transmit only classical information from the input to the output. Thus, in constructing a quantum memory, one aims to produce a device that could retain some correlations between the stored system and remote systems.Due to its relevance in quantum information science, the benchmarking of quantum memories has been extensively considered in the literature [8][9][10][11][12]. An obvious way to verify whether a channel is EB or not is by performing process tomography [13][14][15], that is, by feeding through the channel a tomographically complete set of states and performing a tomographically complete measurement at the output. By collecting sufficient statistics, it is possible to reconstruct the process matrix corresponding to the channel up to any desired level of accuracy, and check whether the channel is EB or not. This scheme, however...

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Non-locality breaking qubit channels: the case for CHSH inequality

Cited by 19 publications

References 28 publications

Channel activation of CHSH nonlocality

Channel activation of CHSH nonlocality

On the Activation of Quantum Nonlocality

Resource Theory of Quantum Memories and Their Faithful Verification with Minimal Assumptions

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