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Title: Direct measurement of concurrence for atomic two-qubit pure states

Abstract

We propose a general scheme to measure the concurrence of an arbitrary two-qubit pure state in atomic systems. The protocol is based on one- and two-qubit operations acting on two available copies of the bipartite system, and followed by a global qubit readout. We show that it is possible to encode the concurrence in the probability of finding all atomic qubits in the ground state. Two possible scenarios are considered: atoms crossing three-dimensional microwave cavities and trapped ion systems.

Authors:
; ; ;  [1];  [2];  [3]
  1. Departamento de Fisica, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago (Chile)
  2. Physics Department, ASC, and CeNS, Ludwig-Maximilians-Universitaet, Theresienstrasse 37, D-80333 Munich (Germany)
  3. (Peru)
Publication Date:
OSTI Identifier:
20982249
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032303; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; GROUND STATES; IONS; MICROWAVE RADIATION; PROBABILITY; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUBITS; THREE-DIMENSIONAL CALCULATIONS; TRAPPING

Citation Formats

Romero, G., Lopez, C. E., Lastra, F., Retamal, J. C., Solano, E., and Seccion Fisica, Departamento de Ciencias, Pontificia Universidad Catolica del Peru, Apartado 1761, Lima. Direct measurement of concurrence for atomic two-qubit pure states. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.032303.
Romero, G., Lopez, C. E., Lastra, F., Retamal, J. C., Solano, E., & Seccion Fisica, Departamento de Ciencias, Pontificia Universidad Catolica del Peru, Apartado 1761, Lima. Direct measurement of concurrence for atomic two-qubit pure states. United States. doi:10.1103/PHYSREVA.75.032303.
Romero, G., Lopez, C. E., Lastra, F., Retamal, J. C., Solano, E., and Seccion Fisica, Departamento de Ciencias, Pontificia Universidad Catolica del Peru, Apartado 1761, Lima. Thu . "Direct measurement of concurrence for atomic two-qubit pure states". United States. doi:10.1103/PHYSREVA.75.032303.
@article{osti_20982249,
title = {Direct measurement of concurrence for atomic two-qubit pure states},
author = {Romero, G. and Lopez, C. E. and Lastra, F. and Retamal, J. C. and Solano, E. and Seccion Fisica, Departamento de Ciencias, Pontificia Universidad Catolica del Peru, Apartado 1761, Lima},
abstractNote = {We propose a general scheme to measure the concurrence of an arbitrary two-qubit pure state in atomic systems. The protocol is based on one- and two-qubit operations acting on two available copies of the bipartite system, and followed by a global qubit readout. We show that it is possible to encode the concurrence in the probability of finding all atomic qubits in the ground state. Two possible scenarios are considered: atoms crossing three-dimensional microwave cavities and trapped ion systems.},
doi = {10.1103/PHYSREVA.75.032303},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • We study a relation between the concurrence of assistance and the Mermin inequality on three-qubit pure states and claim that if a three-qubit pure state has a minimal concurrence of assistance greater than 1/2 then the state violates some Mermin inequality. In this work, we analytically show that our claim holds for several classes and also find that it can be generalized to the set of all three-qubit pure states by exploiting previous numerical work [C. Emary and C. W. J. Beenakker, Phys. Rev. A 69, 032317 (2004)].
  • We study the ordering of two-qubit states with respect to the degree of bipartite entanglement using the Wootters concurrence - a measure of the entanglement of formation - and the negativity - a measure of the entanglement cost under the positive-partial-transpose-preserving operations. For two-qubit pure states, the negativity is the same as the concurrence. However, we demonstrate analytically on simple examples of various mixtures of Bell and separable states that the entanglement measures can impose different orderings on the states. We show which states, in general, give the maximally different predictions (i) when one of the states has the concurrencemore » greater but the negativity smaller than those for the other state and (ii) when the states are entangled to the same degree according to one of the measures, but differently according to the other.« less
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  • In this Brief Report we show the relation between three-qubit entanglement invariants and two-qubit concurrence with the help of projective measurements. How to use these invariants to represent the entanglement property of three-qubit pure states is also investigated.
  • The average entanglement of random pure states of an NxN composite system is analyzed. We compute the average value of the determinant D of the reduced state, which forms an entanglement monotone. Calculating higher moments of the determinant, we characterize the probability distribution P(D). Similar results are obtained for the rescaled Nth root of the determinant, called the G concurrence. We show that in the limit N{yields}{infinity} this quantity becomes concentrated at a single point G{sub *}=1/e. The position of the concentration point changes if one consider an arbitrary NxK bipartite system, in the joint limit N,K{yields}{infinity}, with K/N fixed.