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

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

2006-09-21

arxiv.org/abs/quant-ph/0609167v4

Quantum Information and Computation, Vol. 8, No.1&2 (2008) 0030-0052

Physics

Quantum Physics

23page, the third version. small typos changed

Scientific paper

By introducing the concept of $\epsilon$-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.

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