scholarly journals Analysis of single-particle nonlocality through the prism of weak measurements

2020 ◽  
Vol 18 (01) ◽  
pp. 1941024
Author(s):  
Danko Georgiev ◽  
Eliahu Cohen
Keyword(s):  
Functional Dependence ◽  
Hidden Variables ◽  
Quantum Probability ◽  
Weak Values ◽  
Weak Measurements ◽  
Hidden Variable ◽  
Major Interest ◽  
Complex Valued ◽  
Hidden Variable Models ◽  
Local Hidden Variable

Although regarded today as an important resource in quantum information, nonlocality has yielded over the years many conceptual conundrums. Among the latter are nonlocal aspects of single particles which have been of major interest. In this paper, the nonlocality of single quanta is studied in a square nested Mach–Zehnder interferometer with spatially separated detectors using a delayed choice modification of quantum measurement outcomes that depend on the complex-valued weak values. We show that if spacelike separated Bob and Alice are allowed to freely control their quantum devices, the geometry of the setup constrains the local hidden variable models. In particular, hidden signaling and a list of contextual instructions are required to split a quantum state characterized by a positive Wigner function into two quantum states with nonpositive Wigner functions. This implies that local hidden variable models could rely neither on only two hidden variables for position and momentum, nor on simultaneous factorizability of both the hidden probability densities and weights of splitting to reproduce the correct quantum distributions. While our analysis does not fully exclude the existence of nonfactorizable local hidden variable models, it demonstrates that the recently proposed weak values of quantum histories necessitate contextual splitting of prior commitments to measurement outcomes, due to functional dependence on the total Feynman sum that yields the complex-valued quantum probability amplitude for the studied quantum transition. This analysis also highlights the quantum nature of weak measurements.

scholarly journals Algorithmic Construction of Local Hidden Variable Models for Entangled Quantum States

2016 ◽  
Vol 117 (19) ◽  
Author(s):  
Flavien Hirsch ◽  
Marco Túlio Quintino ◽  
Tamás Vértesi ◽  
Matthew F. Pusey ◽  
Nicolas Brunner
Keyword(s):  
Quantum States ◽  
Hidden Variable ◽  
Entangled Quantum States ◽  
Algorithmic Construction ◽  
Hidden Variable Models ◽  
Local Hidden Variable

scholarly journals On local-hidden-variable no-go theorems

2006 ◽  
Vol 84 (6-7) ◽  
pp. 633-638 ◽  
Author(s):  
A A Méthot
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables ◽  
Complete Theory ◽  
Variable Theory ◽  
Hidden Variable ◽  
Similarities And Differences ◽  
Hidden Variable Theories ◽  
03.65 Ud ◽  
Local Hidden Variable

The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow. PACS Nos.: 03.65.–w, 03.65.Ud, 03.65.Ta

scholarly journals Incompatible local hidden-variable models of quantum correlations

2012 ◽  
Vol 86 (3) ◽  
Author(s):  
Wiesław Laskowski ◽  
Marcin Markiewicz ◽  
Tomasz Paterek ◽  
Marcin Wieśniak
Keyword(s):  
Quantum Correlations ◽  
Hidden Variable ◽  
Hidden Variable Models ◽  
Local Hidden Variable

scholarly journals Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constantKG(3)

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 3 ◽  
Author(s):  
Flavien Hirsch ◽  
Marco Túlio Quintino ◽  
Tamás Vértesi ◽  
Miguel Navascués ◽  
Nicolas Brunner
Keyword(s):  
Upper Bound ◽  
Singlet State ◽  
Entangled States ◽  
Werner State ◽  
Hidden Variable ◽  
Werner States ◽  
Projective Measurements ◽  
Hidden Variable Models ◽  
Local Hidden Variable

We consider the problem of reproducing the correlations obtained by arbitrary local projective measurements on the two-qubit Werner stateρ=v|ψ−⟩⟨ψ−|+(1−v)14via a local hidden variable (LHV) model, where|ψ−⟩denotes the singlet state. We show analytically that these correlations are local forv=999×689×10−6cos2⁡(π/50)≃0.6829. In turn, as this problem is closely related to a purely mathematical one formulated by Grothendieck, our result implies a new bound on the Grothendieck constantKG(3)≤1/v≃1.4644. We also present a LHV model for reproducing the statistics of arbitrary POVMs on the Werner state forv≃0.4553. The techniques we develop can be adapted to construct LHV models for other entangled states, as well as bounding other Grothendieck constants.

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