Optimal fidelity for a quantum channel may be attained by nonmaximally entangled states

Abstract

To establish an entangled state of optimal fidelity between two distant observers when the available quantum channel is noisy, is a central problem in quantum information theory. We consider an instance of this problem for two-qubit systems when only a single use of the channel and local post-processing by trace preserving operations are allowed. We show that the optimal fidelity is obtained only when part of an appropriate nonmaximally entangled state is transmitted through the channel. The entanglement of this state can be vanishingly small when the channel becomes very noisy. Moreover, in the optimal case no further local processing is required to enhance the fidelity. We further show that local post-processing can enhance fidelity if and only if the amount of noise is larger than a critical value and entanglement of the transmitted state is bounded from below. A notable consequence of these results is that the ordering of states under an entanglement monotone can be reversed even when the states undergo the same local interaction via a trace-preserving completely positive map.arXiv:1209.3494v1 [quant-ph]

Fighting noise with noise in realistic quantum teleportation

“…The results given here and in Ref. [16] are a counterintuitive fact since for pure state inputs and pure state channels (no noise) more entanglement leads to more efficiency.…”

“…(38)), which was first noticed in Ref. [16] when the input state is always pure. Here we show that even if the input state is mixed we still have the same feature.…”

“…[14,16,17], is quite clear: When noise is taken into account in analyzing the performance of a quantum communication protocol we should not expect the optimal settings for the noiseless case to hold anymore. Moreover, sometimes counterintuitive optimal settings occur and, therefore, we should always analyze the types of noise we are going to face in any realistic implementation of a particular protocol and determine those optimal settings on a case-by-case basis.…”

“…[12]. However, it is not, in general, an easy experimental task to implement the optimal quantum operations, and more feasible options leading to * Electronic address: rigolin@ufscar.br an enhancement in the performance of the standard teleportation protocol are desired [13][14][15][16][17].…”

Probabilistic quantum teleportation via thermal entanglement

“…A workaround to bypass those problems using only local operations and classical communication is entanglement distillation [7], where several copies of non-maximally entangled mixed states are converted into one maximally entangled pure state. A different approach is based on the modification of the standard teleportation protocols [1][2][3], adapting them to operate directly with non- * Electronic address: rigolin@ufscar.br maximally entangled states [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”