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.
Related papers
- Nonlocality activation in a photonic quantum network [0.44270590458998854]
Bell nonlocality is crucial for device-independent technologies like quantum key distribution and randomness generation.
We show that single copies of Bell-local states can give rise to nonlocality after being embedded into a quantum network of multiple parties.
Our findings have fundamental implications for nonlocality and enable the practical use of nonlocal correlations in real-world applications.
arXiv Detail & Related papers (2023-09-12T18:14:49Z) - Overlapping qubits from non-isometric maps and de Sitter tensor networks [41.94295877935867]
We show that processes in local effective theories can be spoofed with a quantum system with fewer degrees of freedom.
We highlight how approximate overlapping qubits are conceptually connected to Hilbert space dimension verification, degree-of-freedom counting in black holes and holography.
arXiv Detail & Related papers (2023-04-05T18:08:30Z) - Entanglement and localization in long-range quadratic Lindbladians [49.1574468325115]
Signatures of localization have been observed in condensed matter and cold atomic systems.
We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths.
We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping.
arXiv Detail & Related papers (2023-03-13T12:45:25Z) - Detection of Beyond-Quantum Non-locality based on Standard Local Quantum
Observables [46.03321798937856]
We show that device independent detection cannot distinguish beyond-quantum non-local states from standard quantum states.
This paper gives a device dependent detection based on local observables to distinguish any beyond-quantum non-local state from all standard quantum states.
arXiv Detail & Related papers (2023-01-10T20:19:34Z) - Quantum theories with local information flow [0.0]
Bell non-locality is a term that applies to specific modifications and interpretations of quantum mechanics.
Motivated by Bell's original inequality, we identify four viable categories of quantum theories.
arXiv Detail & Related papers (2022-11-23T22:06:03Z) - Genuine Bell locality and nonlocality in the networks [0.0]
Local hidden variables are strictly distributed in the specific observers rather than the whole ones.
Moreors are involved in the proposed linear and non-linear Bell-type inequalities.
How entanglement swapping replaces the joint measurements in the Bell tests is demonstrated.
arXiv Detail & Related papers (2022-09-23T04:23:16Z) - Non-standard entanglement structure of local unitary self-dual models as
a saturated situation of repeatability in general probabilistic theories [61.12008553173672]
We show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry.
We also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable.
arXiv Detail & Related papers (2021-11-29T23:37:58Z) - Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
An important problem in any quantum resource theory is to determine how quantum states can be converted into each other.
Very few results have been presented on the intermediate regime between probabilistic and approximate transformations.
We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations.
We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
arXiv Detail & Related papers (2021-11-24T17:29:43Z) - Quantum Bell Nonlocality is Entanglement [10.628932392896374]
Bell nonlocality describes a manifestation of quantum mechanics that cannot be explained by any local hidden variable model.
We develop a dynamical framework in which quantum Bell nonlocality emerges as special form of entanglement.
arXiv Detail & Related papers (2020-12-12T23:02:06Z) - Localizable quantum coherence [0.0]
Coherence is a fundamental notion in quantum mechanics, defined relative to a reference basis.
We put forward a notion of localizable coherence as the coherence that can be stored in a particular subsystem.
We show that it can be applied to reveal the real-space structure of states of interest in quantum many-body theory.
arXiv Detail & Related papers (2020-05-06T17:44:05Z) - Quantum Mechanical description of Bell's experiment assumes Locality [91.3755431537592]
Bell's experiment description assumes the (Quantum Mechanics-language equivalent of the classical) condition of Locality.
This result is complementary to a recently published one demonstrating that non-Locality is necessary to describe said experiment.
It is concluded that, within the framework of Quantum Mechanics, there is absolutely no reason to believe in the existence of non-Local effects.
arXiv Detail & Related papers (2020-02-27T15:04:08Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.