Nonmaximally entangled bases and their application in entanglement purification via swapping

Journal Article · Tue Mar 01 04:00:00 EST 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.71.032331· OSTI ID:20650369

Koniorczyk, Matyas; Buzek, Vladimir ^[1]

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1. Research Centre for Quantum Information, Institute of Physics, Slovak Academy of Sciences Dubravska cesta 9, 845 11 Bratislava (Slovakia)

Four basis vectors of the Hilbert space of two qubits have the property that if three of them are product states, then the fourth one has to be a product state as well. We address the following situation: Consider a set of orthogonal vectors, each exhibiting a certain degree of entanglement. What is the bound on entanglement of the rest of the basis vectors to form a complete orthonormal basis? Specifically, we present an orthonormal basis, the {xi} basis in the Hilbert space of two qubits, with one product state and three equally entangled states. The maximum of the so available entanglement is quantified. A close-to-optimal protocol is presented for entanglement purification via entanglement swapping of two-qubit states. It is based on a suitably chosen nonmaximally entangled basis and carried out in a single step without any ancillas. A similar application of the {xi} basis is examined. In this latter case, all the involved entangled states have different and nonorthogonal Schmidt decompositions and, except for some possibly resulting states, none of them are maximally entangled. Entanglement of single pair purification is not conserved on average in this case.

• OSTI ID: 20650369
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 71; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
CORRELATIONS
ENERGY LEVELS
HILBERT SPACE
INFORMATION THEORY
QUANTUM MECHANICS
QUANTUM NUMBERS
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VECTORS