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arXiv:2407.16035 · Physics Letters A

Controlling nonlocality of bipartite qubit states via quantum channels

A. Rutkowski, Katarzyna Siudzińska

Published Jan 30, 2025• 0 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2025.130313

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Sequential sharing of quantum nonlocality (SSQN) is crucial for device-independent tasks in quantum information processing, wherein relaying the post-measurement qubit through a local quantum channel to a subsequent observer constitutes an essential operational step. Here we present a theoretical analysis of noise robustness of sequential sharing for bipartite Bell and tripartite Mermin nonlocality under the influence of local phase-flip, bit-flip, and depolarizing quantum channels. It is proved that arbitrarily many independent observers can sequentially share the quantum nonlocality of Bell, Greenberger-Horne-Zeilinger, and W states via respective noise-immune channels, whereas such unbound feature of SSQN is lost under other local noisy quantum channels. Furthermore, we demonstrate that the noise-immune channel enabling unbounded SSQN can be switched by employing our newly designed measurement strategies assisted by local unitary operations on the initial entangled states. Moreover, as illustrative examples of noise robustness, we propose two concrete schemes for sharing Bell and Mermin nonlocality with two sequential local observers on one side subject to local noisy channels. Our work establishes a practical framework for realizing the SSQN under noisy quantum channels, and reveals the connection between noise robustness and measurement strategies.
Entanglement breaking channels play a significant role in quantum information theory. In this work we investigate qubit channels through their property of `non-locality breaking', defined in a natural way but within the purview of CHSH nonlocality. This also provides a different perspective on the relationship between entanglement and nonlocality through the dual picture of quantum channels instead of through states. For a channel to be entanglement breaking it is sufficient to `break' the entanglement of maximally entangled states. We provide examples to show that for CHSH nonlocality breaking such a property does not hold in general, though for certain channels and for a restricted class of states for all channels this holds.We also consider channels whose output remains local under SLOCC and call them `strongly non-locality breaking'. We provide a closed form necessary-sufficient condition for any two-qubit state to show hidden CHSH nonlocality, which is likely to be useful for other purposes as well. This in turn allows us to characterize all strongly non-locality breaking qubit channels. It turns out that unital qubit channels breaking nonlocality of maximally entangled states are strongly non-locality breaking while extremal qubit channels cannot be so unless they are entanglement breaking.
Quantum mechanics is a highly nonlocal theory of nature. Quantum systems exhibit correlations which cannot be described by any classical theory of locality. We develop the resource theory of dynamical Bell nonlocality, which includes bipartite states, classical channels, quantum channels and measurements. In the state scenario, all separable states are Bell local. However, there exist mixed bipartite entangled states which also admit Bell local behaviour. To address this anomaly, we introduce the notion of fully Bell locality and show that all entangled states are Bell nonlocal, in the sense that they can be used to simulate at least one nonlocal bipartite Positive Operator Valued Measure (POVM) channel. We take a step further and generalise this result to bipartite entangled quantum channels. We then generalize the CHSH inequality from bipartite classical channels to bipartite POVM channels and devise a technique to check if a given bipartite POVM channel is nonlocal or not. Finally we provide a systematic method to quantify Bell nonlocality of bipartite quantum channels by extending any monotone for Bell nonlocality of classical channels to quantum channels and also introduce the precise definition of relative entropy of Bell nonlocality. We leave some open problems in the way.