Quantum resource theory of Bell nonlocality in Hilbert space
- URL: http://arxiv.org/abs/2311.01941v2
- Date: Fri, 17 Nov 2023 19:25:54 GMT
- Title: Quantum resource theory of Bell nonlocality in Hilbert space
- Authors: Gennaro Zanfardino, Wojciech Roga, Masahiro Takeoka and Fabrizio
Illuminati
- Abstract summary: We introduce a Hilbert space based resource theory of Bell nonlocality with the aim of providing bona fide measures of quantum nonlocality.
We construct our theory by defining the set of local (or free) states, i.e., the states that do not violate the Clauser-Horne-Shimony-Holt inequality.
We illustrate the general resource theory so developed by applying it to specific classes of quantum states, including two-qubit Werner states, Bell-diagonal states, and Bell-diagonal states at fixed convexity.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We introduce a Hilbert space based resource theory of Bell nonlocality with
the aim of providing bona fide measures of quantum nonlocality depending only
on the intrinsic properties of the quantum states being considered. We
construct our theory by defining the set of local (or free) states, i.e., the
states that do not violate the Clauser-Horne-Shimony-Holt inequality; the set
of free operations, i.e., the transformations that do not create the
nonlocality resource, which includes local operations and shared randomness;
and suitable measures of nonlocality based either on geometric distances or
relative entropies with respect to the set of local states. We discuss the
basic axiomatic structure that is needed for a meaningful characterization and
quantification of Bell nonlocality and we illustrate the general resource
theory so developed by applying it to specific classes of quantum states,
including two-qubit Werner states, Bell-diagonal states, and Bell-diagonal
states at fixed convexity.
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