arXiv:quant-ph/0109028

Variable length universal entanglement concentration by local operations and its application to teleportation and dense coding

Masahito Hayashi, Keiji Matsumoto

Published Sep 5, 2001• 18 citations

Abstract

Using invariance of the $n$-th tensored state w.r.t. the $n$-th symmetric group, we propose a 'variable length' universal entanglement concentration without classical communication. Like variable length data compression, arbitrary unknown states are concentrated into perfect Bell states and not approximate Bell states and the number of Bell states obtained is equal to the optimal rate asymptotically with the probability 1. One of the point of our scheme is that we need no classical communication at all. Using this method, we can construct a universal teleportation and a universal dense coding.

DOI: 10.48550/arxiv.quant-ph/0109028

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arXiv:quant-ph/0109028

Variable length universal entanglement concentration by local operations and its application to teleportation and dense coding

Masahito Hayashi, Keiji Matsumoto

Published Sep 5, 2001• 18 citations

arXiv HTML PDF

Abstract

Using invariance of the

n

-th tensored state w.r.t. the

n

-th symmetric group, we propose a 'variable length' universal entanglement concentration without classical communication. Like variable length data compression, arbitrary unknown states are concentrated into perfect Bell states and not approximate Bell states and the number of Bell states obtained is equal to the optimal rate asymptotically with the probability 1. One of the point of our scheme is that we need no classical communication at all. Using this method, we can construct a universal teleportation and a universal dense coding.

DOI: 10.48550/arxiv.quant-ph/0109028

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This paper describes the construction of a quantum universal variable-length source code in which, independent of information source, both of the average error and the probability that the coding rate is greater than the entropy rate H(/spl rho/~/sub p/), tend to 0. If H(/spl rho/~/sub p/) is estimated, and compress the coding rate to the admissible rate H(/spl rho/~/sub p/) with a probability close to 1. However, when we perform a naive measurement for the estimation of H(/spl rho/~/sub p/), the input state is demolished. By smearing the measurement, we successfully treat the trade-off between the estimation of H(/spl rho/~/sub p/) and the nondemolition of the input state. Our protocol can be used not only for the Schumacher's compression but also for the compression of entangled states.This paper describes the construction of a quantum universal variable-length source code in which, independent of information source, both of the average error and the probability that the coding rate is greater than the entropy rate H(/spl rho/~/sub p/), tend to 0. If H(/spl rho/~/sub p/) is estimated, and compress the coding rate to the admissible rate H(/spl rho/~/sub p/) with a probability close to 1. However, when we perform a naive measurement for the estimation of H(/spl rho/~/sub p/), the input state is demolished. By smearing the measurement, we successfully treat the trade-off between the estimation of H(/spl rho/~/sub p/) and the nondemolition of the input state. Our protocol can be used not only for the Schumacher's compression but also for the compression of entangled states.

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Using invariance of the

n

-th tensored state w.r.t. the

n

H(rho_p)

, tend to 0. If

H(rho_p)

is estimated, we can compress the coding rate to the admissible rate

H(rho_p)

with a probability close to 1. However, when we perform a naive measurement for the estimation of

H(rho_p)

, the input state is demolished. By smearing the measurement, we successfully treat the trade-off between the estimation of

H(rho_p)

and the non-demolition of the input state. Our protocol can be used not only for the Schumacher's scheme but also for the compression of entangled states.

n

-tensored pure state, and is optimal for all the protocols which concentrates entanglement from unknown pure states, in the sense of failure probability. In the proof of optimality, the statistical estimation theory plays a key role, for concentrated entanglement gives a natural estimate of the entropy of entanglement.