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arXiv:1207.2188 · Physical Review A

Quantum teleportation via maximum-confidence quantum measurements

Leonardo Neves, M. A. Solís-Prosser, A. Delgado, O. Jiménez

Published Jun 25, 2012• 20 citations
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Abstract

We investigate the problem of teleporting unknown qudit states via pure quantum channels with nonmaximal Schmidt rank. This process is mapped to the problem of discriminating among nonorthogonal symmetric states which are linearly dependent and equally likely. It is shown that by applying an optimized maximum-confidence (MC) measurement for accomplishing this task, one reaches the maximum possible teleportation fidelity after a conclusive event in the discrimination process, which in turn occurs with the maximum success probability. In this case, such fidelity depends only on the Schmidt rank of the channel and it is larger than the optimal one achieved, deterministically, by the standard teleportation protocol. Furthermore, we show that there are quantum channels for which it is possible to apply a $k$-stage sequential MC measurement in the discrimination process such that a conclusive event at any stage leads to a teleportation fidelity above the aforementioned optimal one and, consequently, increases the overall success probability of teleportation with a fidelity above this limit.

DOI
10.1103/physreva.85.062322

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We investigate the problem of teleporting unknown qudit states via pure quantum channels with nonmaximal Schmidt rank. This process is mapped to the problem of discriminating among nonorthogonal symmetric states which are linearly dependent and equally likely. It is shown that by applying an optimized maximum-confidence (MC) measurement for accomplishing this task, one reaches the maximum possible teleportation fidelity after a conclusive event in the discrimination process, which in turn occurs with the maximum success probability. In this case, such fidelity depends only on the Schmidt rank of the channel and it is larger than the optimal one achieved, deterministically, by the standard teleportation protocol. Furthermore, we show that there are quantum channels for which it is possible to apply a kkk-stage sequential MC measurement in the discrimination process such that a conclusive event at any stage leads to a teleportation fidelity above the aforementioned optimal one and, consequently, increases the overall success probability of teleportation with a fidelity above this limit.
We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure (POVM) that maximizes our confidence in identifying each state in the set and minimizes the probability of obtaining inconclusive results. The physical realization of this POVM is completely determined and it is shown that after an inconclusive outcome, the input states may be mapped into a new set of equiprobable symmetric states, restricted, however, to a subspace of the original qudit Hilbert space. By applying the MC measurement again onto this new set, we can still gain some information about the input states, although with less confidence than before. This leads us to introduce the concept of sequential maximum-confidence (SMC) measurements, where the optimized MC strategy is iterated in as many stages as allowed by the input set, until no further information can be extracted from an inconclusive result. Within each stage of this measurement our confidence in identifying the input states is the highest possible, although it decreases from one stage to the next. In addition, the more stages we accomplish within the maximum allowed, the higher will be the probability of correct identification. We will discuss an explicit example of the optimal SMC measurement applied in the discrimination among four symmetric qutrit states and propose an optical network to implement it.
Quantum teleportation of qudits is revisited. In particular, we analyze the case where the quantum channel corresponds to a nonmaximally entangled state and show that the success of the protocol is directly related to the problem of distinguishing nonorthogonal quantum states. The teleportation channel can be seen as a coherent superposition of two channels, one of them being a maximally entangled state, thus leading to perfect teleportation, and the other, corresponding to a nonmaximally entangled state living in a subspace of the d-dimensional Hilbert space. The second channel leads to a teleported state with reduced fidelity. We calculate the average fidelity of the process and show its optimality.
Symmetric N→MN \to MN→M telecloning and remote quantum state inference
Teleporting unknown quantum states between distant nodes of a network is a significant feature of quantum communication. Few studies, however, have been conducted on N→MN \to MN→M telecloning, in which NNN copies of an unknown quantum state are optimally teleported to M≥NM \geq NM≥N receivers. Previous work requires global POVMs on all copies and auxiliaries; here, we show that symmetric N→MN \to MN→M telecloning can be probabilistically performed using only sequential (or parallel) Bell state measurements (BSMs), allowing the copies to be spatially separated. When successful, the fidelity of each receiver's reduced state saturates the bound imposed by the no-cloning theorem, with the probability of success being independent of MMM. In the case of an `unsuccessful' BSM, we show that the teleportation fidelity is likely to remain high, with the measurement outcome also providing information about the closest Pauli eigenbasis to the unknown state being telecloned. In this sense, each receiver can remotely infer the unknown quantum state with a level of confidence that scales with the number of copies, even if the fidelity of their own reduced state is sub-optimal. We additionally analyze the required resources to ensure the classical-communication fidelity bound is surpassed, both in terms of two-qubit inseparability and varying classes of multipartite entanglement. Surprisingly, we uncover that, at a given iteration of the protocol, pairwise entanglement is not always necessary to increase the teleportation fidelity and is never required to beat the classical bound for N≥2N \geq 2N≥2.
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We analyze entanglement swapping (ES) of partially entangled pure states with arbitrary Schmidt rank from the perspective of quantum state discrimination. It is shown that the standard deterministic ES protocol is related with an optimal minimum-error strategy. In this case the amount of entanglement of the states resulting from swapping is, in general, lower than the maximum achievable for the quantum channels involved. In this regard, we show that the ES protocol can be probabilistically improved resorting to optimal maximum-confidence (MC) discrimination strategy. Additionally, we show that the success probability of achieving entanglement above a prescribed value from standard deterministic ES can be increased by applying sequential MC measurements.