Characteristics and benchmarks of entanglement of mixed states: The two-qubit case

We propose that the entanglement of mixed states is characterized properly in terms of a probability density function P{sub {rho}}(E). There is a need for such a measure since the prevalent measures (such as concurrence and negativity) for two-qubit systems are rough benchmarks and not monotones of...

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Bibliographic Details
Published in:	Physical review. A, Atomic, molecular, and optical physics Vol. 77; no. 2
Main Authors:	Bhardwaj, Shanthanu, Ravishankar, V.
Format:	Journal Article
Language:	English
Published:	United States 01-02-2008
Subjects:	CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS FOCUSING MIXED STATE NUCLEAR MAGNETIC RESONANCE PHASE TRANSFORMATIONS PROBABILITY QUANTUM COMPUTERS QUANTUM ENTANGLEMENT QUANTUM MECHANICS QUBITS SPECIFICATIONS SU-2 GROUPS
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Summary:	We propose that the entanglement of mixed states is characterized properly in terms of a probability density function P{sub {rho}}(E). There is a need for such a measure since the prevalent measures (such as concurrence and negativity) for two-qubit systems are rough benchmarks and not monotones of each other. Focusing on the two-qubit states, we provide an explicit construction of P{sub {rho}}(E) and show that it is characterized by a set of parameters of which concurrence is but one particular combination. P{sub {rho}}(E) is manifestly invariant under SU(2)xSU(2) transformations. It can, in fact, reconstruct the state up to local operations--with the specification of at most four additional parameters. Finally, the measure resolves the controversy regarding the role of entanglement in quantum computation in NMR systems.
ISSN:	1050-2947 1094-1622
DOI:	10.1103/PhysRevA.77.022322