Entanglement without hidden nonlocality

Flavien Hirsch,Tamás Vértesi,Joseph Bowles,Nicolas Brunner,Marco Túlio Quintino

doi:10.1088/1367-2630/18/11/113019

Flavien Hirsch, Tamás Vértesi + Show 3 more

Open Access

https://doi.org/10.1088/1367-2630/18/11/113019

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Abstract

We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.

Highlights

We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality
We prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state
We proved that there exist entangled quantum states which do not display hidden nonlocality, i.e. which remain local after any local filtering on a single copy of the state

Summary

Bell nonlocality and quantum steering

Say Alice and Bob, sharing an entangled quantum state ρ. The quantum statistics can be reproduced by a so-called local hidden state model (LHS), where σλ denotes the local quantum state and pA(a|x, λ) is Alice’s response function If such a decomposition cannot be found, ρ is said to be ‘steerable’ for the set {Ma|x}; note that one would usually consider here a set of measurements Mb|y that is tomographically complete, and focus the analysis on the set of conditional states of Bob’s system σa|x = TrA(Ma|x ⊗ 1 ρ),. Werner showed that some entangled quantum states admit a LHS model (3) for all projective measurements [13] This result was later extended to general POVMs [14]. Certain steerable states were shown to admit a LHV model for projective measurements [28], and the same hold considering general POVMs [30]. LHV and LHS models for different classes of entangled states were constructed, see e.g. [31, 32, 19, 33, 34, 35, 36, 37]

Hidden nonlocality

Main result

Conclusion