New concise upper bounds on quantum violation of general multipartite Bell inequalities

Loubenets, Elena R.

doi:10.1063/1.4982961

Cited by 8 publications

(18 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since, for every source operator, tr[T From (20) and our results in [6,8,28] it follows that the quantum nonlocality parameters Υ ρ d,N and Υ…”

Section: Quantum Nonlocalitymentioning

confidence: 68%

“…It is also well known that the maximal quantum violation of bipartite Bell inequalities on correlation functions cannot exceed the real Grothendieck's constant K (R) G ∈ [1.676, 1.783] independently of a dimension of a bipartite state and numbers of measurement settings and outcomes per site. But the latter is not already the case for quantum violation of bipartite Bell inequalities on joint probabilities and last years bounds on the maximal quantum violation of general 2 Bell inequalities were intensively discussed in the literature, see [6,8,23,24,25,26,27,28] and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…×···×S N ] = 1, from(28) it follows that ||T (ρ)S 1 ×···×S N || cov ≥ 1, ∀T (ρ) S 1 ×···×S N , and ||T (ρ) S 1 ×···×S N || cov = 1 if T (ρ)S 1 ×···×S N is tensor positive. This and the analytical upper bounds(27) imply.If, for an N -partite quantum state ρ and arbitrary integers S 1 , ..., S N ≥ 1, there exists a tensor positive source operator T(ρ) S 1 ×···×1 ↑ n ×···×S N for some n = 1, ..., N , then Υ (ρ)S 1 ×···×S N = 1 and this N -partite state is the S 1 × · · · × S N -setting local, that is, satisfies all general S ′ 1 × · · · × S ′ Nsetting Bell inequalities with S ′ 1 ≤ S 1 , ..., S ′ N ≤ S N measurement settings at N sites.If, for an N -partite quantum state ρ, tensor positive source operators T (ρ) S 1 ×···×1 ↑ n ×···×S N for some arbitrary n = 1, ..., N , exist for all integers S 1 , ..., S N ≥ 1, then Υ ρ = 1 and this N -partite state ρ is (fully) local, that is, satisfies all general Bell inequalities.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Bell’s Nonlocality in a General Nonsignaling Case: Quantitatively and Conceptually

Loubenets

2017

Found Phys

Self Cite

View full text Add to dashboard Cite

Quantum violation of Bell inequalities is now used in many quantum information applications and it is important to analyze it both quantitatively and conceptually. In the present paper, we analyze violation of multipartite Bell inequalities via the local probability model -the LqHV (local quasi hidden variable) model [Loubenets, J. Math. Phys. 53, 022201 (2012)], incorporating the LHV model only as a particular case and correctly reproducing the probabilistic description of every quantum correlation scenario, more generally, every nonsignaling scenario. The LqHV probability framework allows us to construct nonsignaling analogs of Bell inequalities and to specify parameters quantifying violation of Bell inequalities -Bell's nonlocality -in a general nonsignaling case. For quantum correlation scenarios on an N-qudit state, we evaluate these nonlocality parameters analytically in terms of dilation characteristics of an N-qudit state and also, numerically -in d and N. In view of our rigorous mathematical description of Bell's nonlocality in a general nonsignaling case via the local probability model, we argue that violation of Bell inequalities in a quantum case is not due to violation of the Einstein-Podolsky-Rosen (EPR) locality conjectured by Bell but due to the improper HV modelling of "quantum realism".

show abstract

“…Since, for every source operator, tr[T From (20) and our results in [6,8,28] it follows that the quantum nonlocality parameters Υ ρ d,N and Υ…”

Section: Quantum Nonlocalitymentioning

confidence: 68%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Bell’s Nonlocality in a General Nonsignaling Case: Quantitatively and Conceptually

Loubenets

2017

Found Phys

Self Cite

View full text Add to dashboard Cite

show abstract

“…In view of our results in [22,23,24] we have the following general precise upper bounds on the maximal violation Υ…”

Section: General Boundsmentioning

confidence: 77%

“…S×···×S of all S × · · · × S-setting Bell inequalities admits the upper bounds [22,23,24] which are more specific than the general bounds (38)-(41). Namely, for all d ≥ 2, N ≥ 2 :…”

Section: N-qudit Ghz Statementioning

confidence: 99%

Quantifying Tolerance of a Nonlocal Multi-Qudit State to Any Local Noise

Loubenets

2018

Entropy

View full text Add to dashboard Cite

We present a general approach for quantifying tolerance of a nonlocal N-partite state to any local noise under different classes of quantum correlation scenarios with arbitrary numbers of settings and outcomes at each site. This allows us to derive new precise bounds in d and N on noise tolerances for: (i) an arbitrary nonlocal N-qudit state; (ii) the N-qudit Greenberger-Horne-Zeilinger (GHZ) state; (iii) the N-qubit W state and the N-qubit Dicke states, and to analyse asymptotics of these precise bounds for large N and d.

show abstract

Specifying nonlocality of a pure bipartite state and analytical relations between measures for bipartite nonlocality and entanglement

Loubenets¹,

Namkung²

2022

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

For a multipartite quantum state, the maximal violation of all Bell inequalities constitutes a measure of its nonlocality [Loubenets, \emph{J. Math. Phys}. 53, 022201 (2012)]. In the present article, for the maximal violation of Bell inequalities by a pure bipartite state, possibly infinite-dimensional, we derive \emph{a new upper bound} \emph{expressed in terms of the Schmidt coefficients of this state. } This new upper bound allows us also to specify \emph{general analytical relations }between the maximal violation of Bell inequalities by a bipartite quantum state, pure or mixed, and such entanglement measures for this state as "negativity" and "concurrence". To our knowledge, no any general analytical relations between measures for bipartite nonlocality and entanglement have been reported in the literature though, for a general bipartite state, specifically such relations are important for the entanglement certification and quantification scenarios. As an example, we apply our new results to finding upper bounds on nonlocality of bipartite coherent states intensively discussed last years in the literature in view of their experimental implementations.

show abstract

New concise upper bounds on quantum violation of general multipartite Bell inequalities

Cited by 8 publications

References 19 publications

Bell’s Nonlocality in a General Nonsignaling Case: Quantitatively and Conceptually

Bell’s Nonlocality in a General Nonsignaling Case: Quantitatively and Conceptually

Quantifying Tolerance of a Nonlocal Multi-Qudit State to Any Local Noise

Specifying nonlocality of a pure bipartite state and analytical relations between measures for bipartite nonlocality and entanglement

Contact Info

Product

Resources

About