Generalization of the Peres criterion for local realism through nonextensive entropy
| dc.creator | Tsallis, Constantino | |
| dc.creator | Lloyd, Seth | |
| dc.creator | Baranger, Michel | |
| dc.date | 2000-07-28 | |
| dc.date.accessioned | 2026-07-07T06:00:30Z | |
| dc.date.available | 2026-07-07T06:00:30Z | |
| dc.description | A bipartite spin-1/2 system having the probabilities $\frac{1+3x}{4}$ of being in the Einstein-Podolsky-Rosen entangled state $|Ψ^-$$> \equiv \frac{1}{\sqrt 2}(|$$\uparrow>_A|$$\downarrow>_B$$-|$$\downarrow>_A|$$\uparrow>_B)$ and $\frac{3(1-x)}{4}$ of being orthogonal, is known to admit a local realistic description if and only if $x<1/3$ (Peres criterion). We consider here a more general case where the probabilities of being in the entangled states $|Φ^{\pm}$$> \equiv \frac{1}{\sqrt 2}(|$$\uparrow>_A|$$\uparrow>_B \pm |$$\downarrow>_A|$$\downarrow>_B)$ and $|Ψ^{\pm}$$> \equiv \frac{1}{\sqrt 2}(|$$\uparrow>_A|$$\downarrow>_B \pm |$$\downarrow>_A|$$\uparrow>_B)$ (Bell basis) are given respectively by $\frac{1-x}{4}$, $\frac{1-y}{4}$, $\frac{1-z}{4}$ and $\frac{1+x+y+z}{4}$. Following Abe and Rajagopal, we use the nonextensive entropic form $S_q \equiv \frac{1- Tr ρ^q}{q-1} (q \in \cal{R}; $$S_1$$= -$ $Tr$ $ ρ\ln ρ)$ which has enabled a current generalization of Boltzmann-Gibbs statistical mechanics, and determine the entire region in the $(x,y,z)$ space where local realism is admissible. For instance, in the vicinity of the EPR state, classical realism is possible if and only if $x+y+z<1$, which recovers Peres' criterion when $x=y=z$. In the vicinity of the other three states of the Bell basis, the situation is identical. A critical-phenomenon-like scenario emerges. These results illustrate the computational power of this new nonextensive-quantum-information procedure. | |
| dc.description | Figures 1a, 1b, 2 and 3 | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0007112 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0007112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/88990 | |
| dc.subject | Quantum Physics | |
| dc.title | Generalization of the Peres criterion for local realism through nonextensive entropy | |
| dc.type | text |