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Title: Concurrence of superpositions

Abstract

Bounds on the concurrence of the superposition state in terms of the concurrences of the states being superposed are found in this paper. The bounds on concurrence are quite different from those on the entanglement measured by von Neumann entropy [Linden et al., Phys. Rev. Lett. 97, 100502 (2006)]. In particular, a nonzero lower bound can be provided if the states being superposed are properly constrained.

Authors:
; ;  [1]
  1. Department of Physics, Dalian University of Technology, Dalian 116024 (China)
Publication Date:
OSTI Identifier:
20982099
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022332; (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; ENTROPY; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS

Citation Formats

Yu, Chang-shui, Yi, X. X., and Song, He-shan. Concurrence of superpositions. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.022332.
Yu, Chang-shui, Yi, X. X., & Song, He-shan. Concurrence of superpositions. United States. doi:10.1103/PHYSREVA.75.022332.
Yu, Chang-shui, Yi, X. X., and Song, He-shan. Thu . "Concurrence of superpositions". United States. doi:10.1103/PHYSREVA.75.022332.
@article{osti_20982099,
title = {Concurrence of superpositions},
author = {Yu, Chang-shui and Yi, X. X. and Song, He-shan},
abstractNote = {Bounds on the concurrence of the superposition state in terms of the concurrences of the states being superposed are found in this paper. The bounds on concurrence are quite different from those on the entanglement measured by von Neumann entropy [Linden et al., Phys. Rev. Lett. 97, 100502 (2006)]. In particular, a nonzero lower bound can be provided if the states being superposed are properly constrained.},
doi = {10.1103/PHYSREVA.75.022332},
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}
}
  • The entanglement content of superpositions of quantum states is investigated based on a measure called concurrence. Given a bipartite pure state in arbitrary dimension written as the quantum superposition of two other such states, we find simple inequalities relating the concurrence of the state to that of its components. We derive an exact expression for the concurrence when the component states are biorthogonal and provide elegant upper and lower bounds in all other cases. For quantum bits, our upper bound is tighter than the previously derived bound [N. Linden et al., Phys. Rev. Lett. 97, 100502 (2006)].
  • In this paper, we use the concurrence vector as a measure of entanglement, and investigate lower and upper bounds on the concurrence of a superposition of bipartite states as a function of the concurrence of the superposed states. We show that the amount of entanglement quantified by the concurrence vector is exactly the same as that quantified by I concurrence, so that our results can be compared to those given in Phys. Rev. A 76, 042328 (2007). We obtain a tighter lower bound in the case in which the two superposed states are orthogonal. We also show that when themore » two superposed states are not necessarily orthogonal, both lower and upper bounds are, in general, tighter than the bounds given in terms of the I concurrence. An extension of the results to the case with more than two states in the superpositions is also given.« less
  • The authors describe a method of securing concurrence among asynchronous processors in the presence of undetected faults, comprising the steps of (1) invoking an authentication protocol in order to ensure that received messages were faithfully relayed by intermediate processors whether faulty or not, and (2) transmitting a target message among the processors to secure agreement as to a value within the messages such that no more than two messages need be sent.
  • The competition between direct processes and compound nuclear processes is discussed briefly. The reaction amplitude is represented as the sum of the amplitudes corresponding to direct and resonance processes. Formation of a compound nucleus affects the reaction process in 2 ways. First, the presence of resonance leads to specific distortions in the wave functions, changing the component corresponding to the direct process. Second, interference arises between the resonance and nonresonance components in the amplitude. There are indications that the 1st effect is negligibly small while the 2nd is impontant. The interference term should vanish if the cross section is averagedmore » in an energy interval containing a large number of resonances. (Ref. Zh., Fiz. 1983).« less