Unitary invariant discord as a measures of bipartite quantum correlations in an N-qubit quantum system

Unitary invariant discord as a measures of bipartite quantum correlations in an N-qubit quantum... We introduce a measure of quantum correlations in the N-qubit quantum system which is invariant with respect to the SU(2 N ) group of transformations of this system. This measure is a modification of the quantum discord introduced earlier and is referred to as the unitary or SU(2 N )-invariant discord. Since the evolution of a quantum system is equivalent to the proper unitary transformation, the introduced measure is an integral of motion and is completely defined by eigenvalues of the density matrix. As far as the calculation of the unitary invariant discord is rather complicated computational problem, we propose its modification which may be found in a simpler way. The case N = 2 is considered in details. In particular, it is shown that the modified SU(4)-invariant discord reaches the maximum value for a pure state. A geometric measure of the unitary invariant discord of an N-qubit state is introduced and a simple formula for this measure is derived, which allows one to consider this measure as a witness of quantum correlations. The relation of the unitary invariant discord with the quantum state transfer along the spin chain is considered. We also compare the modified SU(4)-invariant discord with the geometric measure of SU(4)-invariant discord of the two-qubit systems in the thermal equilibrium states governed by the different Hamiltonians. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Unitary invariant discord as a measures of bipartite quantum correlations in an N-qubit quantum system

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Publisher
Springer US
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0319-x
Publisher site
See Article on Publisher Site

Abstract

We introduce a measure of quantum correlations in the N-qubit quantum system which is invariant with respect to the SU(2 N ) group of transformations of this system. This measure is a modification of the quantum discord introduced earlier and is referred to as the unitary or SU(2 N )-invariant discord. Since the evolution of a quantum system is equivalent to the proper unitary transformation, the introduced measure is an integral of motion and is completely defined by eigenvalues of the density matrix. As far as the calculation of the unitary invariant discord is rather complicated computational problem, we propose its modification which may be found in a simpler way. The case N = 2 is considered in details. In particular, it is shown that the modified SU(4)-invariant discord reaches the maximum value for a pure state. A geometric measure of the unitary invariant discord of an N-qubit state is introduced and a simple formula for this measure is derived, which allows one to consider this measure as a witness of quantum correlations. The relation of the unitary invariant discord with the quantum state transfer along the spin chain is considered. We also compare the modified SU(4)-invariant discord with the geometric measure of SU(4)-invariant discord of the two-qubit systems in the thermal equilibrium states governed by the different Hamiltonians.

Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 19, 2011

References

  • Quantum entanglement
    Horodecki, R.; Horodecki, P.; Horodecki, M.; Horodecki, K.

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