dorsal/arxiv
View Schema\epsilon-convertibility of entangled states and extension of Schmidt rank in infinite-dimensional systems
| Authors | Masaki Owari, Samuel L. Braunstein, Kae Nemoto, Mio Murao |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609167 |
| URL | https://arxiv.org/abs/quant-ph/0609167 |
| Journal | Quantum Information and Computation, Vol. 8, No.1&2 (2008) 0030-0052 |
Abstract
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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"abstract": "By introducing the concept of $\\epsilon$-convertibility, we extend Nielsen\u0027s\nand Vidal\u0027s theorems to the entanglement transformation of infinite-dimensional\nsystems. Using an infinite-dimensional version of Vidal\u0027s theorem we derive a\nnew stochastic-LOCC (SLOCC) monotone which can be considered as an extension of\nthe Schmidt rank. We show that states with polynomially-damped Schmidt\ncoefficients belong to a higher rank of entanglement class in terms of SLOCC\nconvertibility. For the case of Hilbert spaces of countable, but infinite\ndimensionality, we show that there are actually an uncountable number of\nclasses of pure non-interconvertible bipartite entangled states.",
"arxiv_id": "quant-ph/0609167",
"authors": [
"Masaki Owari",
"Samuel L. Braunstein",
"Kae Nemoto",
"Mio Murao"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quantum Information and Computation, Vol. 8, No.1\u00262 (2008)\n 0030-0052",
"title": "\\epsilon-convertibility of entangled states and extension of Schmidt rank in infinite-dimensional systems",
"url": "https://arxiv.org/abs/quant-ph/0609167"
},
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