Recycling qubits for the generation of Bell nonlocality between independent sequential observers

Abstract

There is currently much interest in the recycling of entangled systems, for use in quantum information protocols by sequential observers. In this work, we study the sequential generation of Bell nonlocality via recycling one or both components of two-qubit states. We first give a description of two-valued qubit measurements in terms of measurement bias, strength, and reversibility, and derive useful tradeoff relations between them. Then, we derive one-sided monogamy relations for unbiased observables, that strengthen the recent Conjecture in [S. Cheng et al., Phys. Rev. A 104, L060201 (2021) ] that if the first pair of observers violate Bell nonlocality then a subsequent independent pair cannot, and give semi-analytic results for the best possible monogamy relation. We also extend the construction in [P. J. Brown and R. Colbeck, Phys. Rev. Lett. 125, 090401 (2020)] to obtain (i) a broader class of two-qubit states that allow the recycling of one qubit by a given number of observers on one side, and (ii) a scheme for generating Bell nonlocality between arbitrarily many independent observers on each side, via the two-sided recycling of multiqubit states. Our results are based on a formalism that is applicable to more general problems in recycling entanglement, and hence is expected to aid progress in this field.

Mermin and Svetlichny inequalities for non-projective measurement observables

“…To deal with such situations, Hall and Cheng have provided the necessary and sufficient conditions to violate the Bell-CHSH inequalities for nonprojective measurements on arbitrary two qubits [5], by improving the Horodecki bound (of sharp observables) [6]. The generalization of the bound is also useful for the task of 'resource recycling' where bonafide parties use the noisy detector to implement the task [7,8]. Here, by resource, we mean any quantum correlations which can be shared by two or more parties, eg., quantum entanglement, nonlocality, steering, etc [9,10].…”

“…Our results are particularly useful in the cases where there are apparatus limitations such as detector noise. Also, these bounds are useful for the task where the preservation of entanglement is paramount, such as recycling resources [7,8,18,19,20], randomness generations [21] and state discriminations [22].…”

Quantum Bell nonlocality cannot be shared under a special kind of bilateral measurements for high-dimensional quantum states

“…Moreover, in Ref. [32], they have studied the sequential generation of Bell nonlocality between independent observers via recycling the components of entangled systems. They obtained the stronger one-sided monogamy relations than [31].…”

Sharing Quantum Nonlocality in Star Network Scenarios

“…1). Recently, Cheng et al [28,29] explored the Bell nonlocality sharing in bilateral sequential measurements (see FIG. 2), in which a pair of entangled states is distributed to multiple Alices and Bobs.…”