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epsilon-convertibility of entangled states and extension of Schmidt rank in infinite-dimensional systems

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JournalQUANTUM INFORMATION COMPUTATION
DatePublished - Jan 2008
Issue number1-2
Volume8
Number of pages23
Pages (from-to)30-52
Original languageEnglish

Abstract

By introducing the concept of E-convertibility, we extend Nielsen's and Vidal's theorems to the entanglement transformation of infinite-dimensional systems. Using an infinite-dimensional version of Vidal's theorem we derive a new stochastic-LOCC (SLOCC) monotone which can be considered as an extension of the Schmidt rank. We show that states with polynomially-damped Schmidt coefficients belong to a higher rank of entanglement class in terms of SLOCC convertibility. For the case of Hilbert spaces of countable, but infinite dimensionality, we show that there are actually an uncountable number of classes of pure non-interconvertible bipartite entangled states.

    Research areas

  • entanglement, LOCC, infinite dimension, continuous variable, CONTINUOUS VARIABLE SYSTEMS, QUANTUM, TRANSFORMATIONS, CRITERION, CHANNELS, THEOREM

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