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arXiv:quant-ph/9906039

Teleportation via generalized measurements, and conclusive teleportation

Tal Mor, Paweł Horodecki

Published Jun 14, 1999• 16 citations
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Abstract

In this work we show that teleportation is a special case of a generalized Einstein, Podolsky, Rosen (EPR) non-locality. Based on the connection between teleportation and generalized measurements we define conclusive teleportation. We show that perfect conclusive teleportation can be obtained with any pure entangled state, and it can be arbitrarily approached with a particular mixed state.

DOI
10.48550/arxiv.quant-ph/9906039

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In this work we show that teleportation is a special case of a generalized Einstein, Podolsky, Rosen (EPR) non-locality. Based on the connection between teleportation and generalized measurements we define conclusive teleportation. We show that perfect conclusive teleportation can be obtained with any pure entangled state, and it can be arbitrarily approached with a particular mixed state.
We show two new aspects of teleportation based on generalized measurements: I. We present an alternative approach to teleportation based on ``generating ρρρ-ensembles at spacetime separation''; This approach provides a better understanding of teleportation. II. We define the concept of {\em conclusive teleportation} and we show how to teleport a quantum state using any pure entangled state; we show how to use the conclusive teleportation as a criterion for non-locality.
An unknown quantum state can be teleported by using quantum measurements and the maximally entangled Einstein-Podolsky-Rosen (EPR) pair. It is well known that the usual nonclassical teleportation that cannot be simulated by the seminal classical measure-prepare strategy can be demonstrated with all entangled states. Herein, we propose a benchmark which reveals that not all such nonclassical teleportations are truly quantum mechanical. Rather, there exists a more robust classical-teleportation model, which includes the measure-prepare mimicry as a special case, that can describe certain nonclassical teleportations. Invalidating such a general classical model indicates genuine quantum teleportation wherein both the pair state and the measurement are truly quantum mechanical. We prove that EPR steering empowers genuine quantum teleportations, rather than entanglement. The benchmark can be readily used in practical experiments for ensuring that genuine quantum teleportation is implemented. The results presented herein provide strict criteria for implementing quantum-information processing where genuine quantum teleportation is indispensable.
Summary form only given. Characterizing the entanglement of a general bipartite quantum system is a difficult problem. Most measures involve difficult extremizations and their physical motivation is not always clear. In this paper we propose an experimental measure of entanglement based on a modified version of the familiar teleportation protocol of Bennett et al. (1993). Briefly, teleportation traditionally involves two parties, Alice and Bob. Initially, Alice has a qubit in an unknown quantum state which she would like to communicate to Bob and Bob has two qubits in an entangled Einstein-Podolsky-Rosen (EPR) pair. To accomplish this transfer, Bob shares one qubit of his EPR pair with Alice. She then performs a joint measurement or Bell measurement on her two qubits and relays this information back to Bob over a classical channel. Bob then uses the outcome of Alice's Bell measurement to transform his qubit, with a local unitary transformation, into the original quantum state, always with a fidelity of one.
A scheme to teleport an unknown two qubit state from Alice (the sender) to Bob (the receiver) using two Einstein Podolsky Rosen (EPR) pairs is presented, each EPR pair being shared by both Alice and Bob. Firstly, Alice combines each of the two particles in the teleported state with an EPR particle and makes Bell state measurement on each combination. Then she transmits the outcomes of her measurements to Bob classically. According to Alice′s measurement results, Bob can perform appropriate unitary operations on his two EPR particles to retrieve the initial state.