skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantum-mechanical realization of a Popescu-Rohrlich box

Abstract

We consider quantum ensembles which are determined by pre- and post-selection. Unlike the case of only preselected ensembles, we show that in this case the probabilities for measurement outcomes at intermediate times satisfy causality only rarely; such ensembles can in general be used to signal between causally disconnected regions. We show that under restrictive conditions, there are certain nontrivial bipartite ensembles which do satisfy causality. These ensembles give rise to a violation of the Clauser-Horne-Shimony-Holt inequality, which exceeds the maximal quantum violation given by Tsirelson's bound B{sub CHSH}{<=}2{radical}(2) and obtains the Popescu-Rohrlich bound for the maximal violation, B{sub CHSH}{<=}4. This may be regarded as an a posteriori realization of supercorrelations, which have recently been termed Popescu-Rohrlich boxes.

Authors:
; ;  [1]
  1. School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978 (Israel)
Publication Date:
OSTI Identifier:
20982061
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022102; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CAUSALITY; CORRELATIONS; PROBABILITY; QUANTUM MECHANICS; VIOLATIONS

Citation Formats

Marcovitch, Samuel, Reznik, Benni, and Vaidman, Lev. Quantum-mechanical realization of a Popescu-Rohrlich box. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.022102.
Marcovitch, Samuel, Reznik, Benni, & Vaidman, Lev. Quantum-mechanical realization of a Popescu-Rohrlich box. United States. doi:10.1103/PHYSREVA.75.022102.
Marcovitch, Samuel, Reznik, Benni, and Vaidman, Lev. Thu . "Quantum-mechanical realization of a Popescu-Rohrlich box". United States. doi:10.1103/PHYSREVA.75.022102.
@article{osti_20982061,
title = {Quantum-mechanical realization of a Popescu-Rohrlich box},
author = {Marcovitch, Samuel and Reznik, Benni and Vaidman, Lev},
abstractNote = {We consider quantum ensembles which are determined by pre- and post-selection. Unlike the case of only preselected ensembles, we show that in this case the probabilities for measurement outcomes at intermediate times satisfy causality only rarely; such ensembles can in general be used to signal between causally disconnected regions. We show that under restrictive conditions, there are certain nontrivial bipartite ensembles which do satisfy causality. These ensembles give rise to a violation of the Clauser-Horne-Shimony-Holt inequality, which exceeds the maximal quantum violation given by Tsirelson's bound B{sub CHSH}{<=}2{radical}(2) and obtains the Popescu-Rohrlich bound for the maximal violation, B{sub CHSH}{<=}4. This may be regarded as an a posteriori realization of supercorrelations, which have recently been termed Popescu-Rohrlich boxes.},
doi = {10.1103/PHYSREVA.75.022102},
journal = {Physical Review. A},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • We present a scheme for realization of quantum-mechanical weak values of observables using entangled photons produced in parametric down-conversion. We consider the case when the signal and idler modes are respectively in a coherent state and vacuum. We use a low-efficiency detector to detect the photons in the idler mode. This weak detection leads to a large displacement and fluctuations in the signal field's quantum state which can be studied by monitoring the photon number and quadrature distributions. This also demonstrates the effect of weak measurement of one partner on its twin.
  • The wave functions with the most general boundary conditions consistent with the conservation of probability for a free particle inside a box [Phys. Rev. D 42, 1194 (1990)] are calculated. The exact Green's functions and propagators for some special cases are obtained and a semiclassical approach for the propagators is considered. Finally, the influence of the boundary conditions over the path integral's formalism is briefly discussed.
  • We present a scheme to achieve maximally entangled states, controlled phase-shift gate, and SWAP gate for two superconducting-quantum-interference-device (SQUID) qubits, by placing SQUIDs in a microwave cavity. We also show how to transfer quantum information from one SQUID qubit to another. In this scheme, no transfer of quantum information between the SQUIDs and the cavity is required, the cavity field is only virtually excited and thus the requirement on the quality factor of the cavity is greatly relaxed.
  • A simultaneous, contextual experimental demonstration of the two processes of cloning an input qubit vertical bar {psi}> and of flipping it into the orthogonal qubit vertical bar {psi}{sup perpendicular>} is reported. The adopted experimental apparatus, a quantum-injected optical parametric amplifier is transformed simultaneously into a universal optimal quantum cloning machine and into a universal-NOT quantum-information gate. The two processes, indeed forbidden in their exact form for fundamental quantum limitations, were found to be universal and optimal, i.e., the measured fidelity of both processes F<1 was found close to the limit values evaluated by quantum theory. A contextual theoretical and experimentalmore » investigation of these processes, which may represent the basic difference between the classical and the quantum worlds, can reveal in a unifying manner the detailed structure of quantum information. It may also enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics.« less