Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0009092 · International Journal of Modern Physics A

SPIN DISTRIBUTIONS FOR BIPARTITE QUANTUM SYSTEMS

A. R. Usha Devi

Published Jul 10, 2002• 1 citation
arXivHTMLPDF

Abstract

We carryout a comparative study of spin distributions defined over the sphere for bipartite quantum spin assemblies. We analyze Einstein–Podolsky–Rosen–Bohm (EPRB) spin correlations in a spin-s singlet state using these distributions. We observe that in the classical limit of s → ∞, EPRB spin distributions turn out to be delta functions, thus reflecting the perfect anticorrelation property of two-spin vectors associated with a spin-s singlet state.

DOI
10.1142/s0217751x02010601

Related papers

Relativistic Einstein-Podolsky-Rosen correlations for vector and tensor states

Paweł Caban, Jakub Rembieliński, Marta Włodarczyk

We calculate and investigate the relativistic correlation function for bipartite systems of spin-$1/2$ particles in vector states and spin-$1$ particles in tensor states. We show that the relativistic correlation function, which depends on particle momenta, may have local extrema. Furthermore, the momentum dependence of the correlation functions for two choices of the relativistic spin operator may be significantly different.

arXiv:1011.5880•Physical Review A•Mar 14, 2011•3 citations

Bivalued ‘click’–‘no-click’ probabilities for EPRB spin correlations

A. R. Usha Devi, Swarnamala Sirsi

We derive non-local bivalued probabilities of click or no-click outcomes—corresponding respectively to detection or no-detection of the particles—where each of the Einstein–Podolsky–Rosen–Bohm (EPRB) pair of particles is observed in only one of the (2s + 1) possible spin projection channels. In the case of observations in maximum spin down channels, our results coincide exactly with those given by Wódkiewicz 3. We analyse the nature of correlation between the click–no-click results with the help of non-local conditional probabilities and information entropies. We observe that the violation of co-planar BC inequalities is essentially due to stronger correlations between the click–no-click outcomes in the spin projection channels |λa| = |λb|. This observation is also supported by spin transmission Bell inequalitites.

Journal of Physics A Mathematical and General•Mar 3, 2005•1 citation

Nonlocality in Einstein–Podolsky–Rosen Spin Correlations

A. R. Usha Devi, Swarnamala Sirsi, G. Ramachandran

We study the nonlocal nature of EPR correlations of two spin j particles entangled in a singlet state using the quantum-mechanical joint probabilities.

International Journal of Modern Physics A•Nov 20, 1997•1 citation

On the concept of Einstein–Podolsky–Rosen states and their structure

Richard F. Arens, Veeravalli S. Varadarajan

In this paper the notion of an EPR state for the composite S of two quantum systems S1,S2, relative to S2 and a set 𝒪 of bounded observables of S2, is introduced in the spirit of the classical examples of Einstein–Podolsky–Rosen and Bohm. We restrict ourselves mostly to EPR states of finite norm. The main results are contained in Theorems 3–6 and imply that if EPR states of finite norm relative to (S2,O) exist, then the elements of 𝒪 have discrete probability distributions and the Von Neumann algebra generated by 𝒪 is essentially imbeddable inside S1 by an antiunitary map. The EPR states then correspond to the different imbeddings and certain additional parameters, and are explicitly given by formulas which generalize the famous example of Bohm. If 𝒪 generates all bounded observables, S2 must be of finite dimension and can be imbedded inside S1 by an antiunitary map, and the EPR states relative to S2 are then in canonical bijection with the different imbeddings of S2 inside S1; moreover they are then given by formulas which are exactly those of the generalized Bohm states. The notion of EPR states of infinite norm is also explored and it is shown that the original state of Einstein–Podolsky–Rosen can be realized as a renormalized limit of EPR states of finite quantum systems considered by Weyl, Schwinger, and many others. Finally, a family of states of infinite norm generalizing the Einstein–Podolsky–Rosen example is explicitly given.

arXiv:quant-ph/9910066•Journal of Mathematical Physics•Feb 1, 2000•29 citations

Classical Limit of Entangled Correlations

K. Wódkiewicz

Generalizations of Bell's inequalities for Einstein Podolsky and Rosen entangled correlations for arbitrary spin s are discussed.Violations of local realism and the classical limit of quantum nonlocality for large s are discussed.The role of the polarization and of the spin alignment in the violation of the Bell inequalities are investigated.A Bayes analysis of entangled correlations is performed using the nonlocal quantum distribution.The local but nonpositive Einstein Podolsky and Rosen quantum distribution is investigated in the limit when s → .The classical limit of the quantum Malus 1aw for arbitrary spin s is formulated in terms of the spin patl integrals.

Acta Physica Polonica A•Jul 1, 1994•10 citations

Perspective of Einstein-Podolsky-Rosen spin correlations in the phase-space formulation for arbitrary values of the spin

G. S. Agarwal

We consider the Einstein-Podolsky-Rosen correlation between two spins with arbitrary j values using the phase-space description of the angular-momentum operators [G. S. Agarwal, Phys. Rev. A 24, 2889 (1981)]. The phase-space formulation provides insight into hidden-variable theories and enables us to understand why Bell's inequalities are violated. We use the analogs of the Wigner function and the P function for the analysis of the correlations. We show that the Wigner function for the singlet state becomes positive in the limit j\ensuremath{\rightarrow}\ensuremath{\infty}. We also show the extent to which Bell's inequalities can be violated for higher spins and present physical quantities, the correlations between which would violate Bell's inequalities.

Physical Review A•Jun 1, 1993•39 citations
We carryout a comparative study of spin distributions defined over the sphere for bipartite quantum spin assemblies. We analyze Einstein–Podolsky–Rosen–Bohm (EPRB) spin correlations in a spin-s singlet state using these distributions. We observe that in the classical limit of s → ∞, EPRB spin distributions turn out to be delta functions, thus reflecting the perfect anticorrelation property of two-spin vectors associated with a spin-s singlet state.
We calculate and investigate the relativistic correlation function for bipartite systems of spin-1/21/21/2 particles in vector states and spin-111 particles in tensor states. We show that the relativistic correlation function, which depends on particle momenta, may have local extrema. Furthermore, the momentum dependence of the correlation functions for two choices of the relativistic spin operator may be significantly different.
We derive non-local bivalued probabilities of click or no-click outcomes—corresponding respectively to detection or no-detection of the particles—where each of the Einstein–Podolsky–Rosen–Bohm (EPRB) pair of particles is observed in only one of the (2s + 1) possible spin projection channels. In the case of observations in maximum spin down channels, our results coincide exactly with those given by Wódkiewicz 3. We analyse the nature of correlation between the click–no-click results with the help of non-local conditional probabilities and information entropies. We observe that the violation of co-planar BC inequalities is essentially due to stronger correlations between the click–no-click outcomes in the spin projection channels |λa| = |λb|. This observation is also supported by spin transmission Bell inequalitites.
In this paper the notion of an EPR state for the composite S of two quantum systems S1,S2, relative to S2 and a set 𝒪 of bounded observables of S2, is introduced in the spirit of the classical examples of Einstein–Podolsky–Rosen and Bohm. We restrict ourselves mostly to EPR states of finite norm. The main results are contained in Theorems 3–6 and imply that if EPR states of finite norm relative to (S2,O) exist, then the elements of 𝒪 have discrete probability distributions and the Von Neumann algebra generated by 𝒪 is essentially imbeddable inside S1 by an antiunitary map. The EPR states then correspond to the different imbeddings and certain additional parameters, and are explicitly given by formulas which generalize the famous example of Bohm. If 𝒪 generates all bounded observables, S2 must be of finite dimension and can be imbedded inside S1 by an antiunitary map, and the EPR states relative to S2 are then in canonical bijection with the different imbeddings of S2 inside S1; moreover they are then given by formulas which are exactly those of the generalized Bohm states. The notion of EPR states of infinite norm is also explored and it is shown that the original state of Einstein–Podolsky–Rosen can be realized as a renormalized limit of EPR states of finite quantum systems considered by Weyl, Schwinger, and many others. Finally, a family of states of infinite norm generalizing the Einstein–Podolsky–Rosen example is explicitly given.
Generalizations of Bell's inequalities for Einstein Podolsky and Rosen entangled correlations for arbitrary spin s are discussed.Violations of local realism and the classical limit of quantum nonlocality for large s are discussed.The role of the polarization and of the spin alignment in the violation of the Bell inequalities are investigated.A Bayes analysis of entangled correlations is performed using the nonlocal quantum distribution.The local but nonpositive Einstein Podolsky and Rosen quantum distribution is investigated in the limit when s → .The classical limit of the quantum Malus 1aw for arbitrary spin s is formulated in terms of the spin patl integrals.
We consider the Einstein-Podolsky-Rosen correlation between two spins with arbitrary j values using the phase-space description of the angular-momentum operators [G. S. Agarwal, Phys. Rev. A 24, 2889 (1981)]. The phase-space formulation provides insight into hidden-variable theories and enables us to understand why Bell's inequalities are violated. We use the analogs of the Wigner function and the P function for the analysis of the correlations. We show that the Wigner function for the singlet state becomes positive in the limit j\ensuremath{\rightarrow}\ensuremath{\infty}. We also show the extent to which Bell's inequalities can be violated for higher spins and present physical quantities, the correlations between which would violate Bell's inequalities.