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arXiv:quant-ph/0012092 · Physical Review A

Conclusive teleportation of ad-dimensional unknown state

Wonmin Son, Jinhyoung Lee, M. S. Kim, Y.-J. Park

Published Nov 14, 2001• 82 citations
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Abstract

We formulate a conclusive teleportation protocol for a system in d-dimensional Hilbert space utilizing the positive operator-valued measurement. The conclusive teleportation protocol ensures some perfect teleportation events when the channel is only partially entangled, at the expense of lowering the overall average fidelity. We discuss how much information remains in the inconclusive parts of the teleportation.

DOI
10.1103/physreva.64.064304

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We formulate a conclusive teleportation protocol for a system in d-dimensional Hilbert space utilizing the positive operator-valued measurement. The conclusive teleportation protocol ensures some perfect teleportation events when the channel is only partially entangled, at the expense of lowering the overall average fidelity. We discuss how much information remains in the inconclusive parts of the teleportation.
A conclusive teleportation protocol of a d -dimensional two-particle unknown quantum state using three d -dimensional particles in an arbitrary pure state is proposed. A sender teleports the unknown state conclusively to a receiver by using the positive operator valued measure(POVM) and introducing an ancillary qudit to perform the generalized Bell basis measurement. We calculate the optimal teleportation fidelity. We also discuss and analyse the reason why the information on the teleported state is lost in the course of the protocol.
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.
In this paper we generalize the standard teleportation to the conclusive teleportation case which can teleport an arbitrary d-dimensional N-particle unknown state via the partially entangled quantum channel. We show that only if the quantum channel satisfies a constraint condition can the most general d-dimensional N-particle unknown state be perfect conclusively teleported. We also present a method for optimal conclusively teleportation of the N-particle states and for constructing the joint POVM which can discern the quantum states on the sender's (Alice's) side. Two typical examples are given so that one can see how our method works.
In this paper we present an optimal protocol by which an unknown state on a Hilbert space of dimension N can be approximately stored in an M-dimensional quantum system or be approximately teleported via an M-dimensional quantum channel. The fidelity of our procedure is determined for pure states as well as for mixed states and states that are entangled with auxiliary quantum systems of varying Hilbert-space dimension, and it is compared with theoretical results for the maximally achievable fidelity.
Quantum teleportation provides a way to transfer unknown quantum states from one system to another via an entangled state as a quantum channel without physical transmission of the object itself. The entangled channel, measurement performed by the sender (Alice), and classical information sent to the receiver (Bob) are three key ingredients in the procedure, which need to cooperate with each other. To study the relationship among the three parts, we propose a scheme for perfect teleportation of a qubit through a high-dimensional quantum channel in a pure state with two equal largest Schmidt coefficients. The scheme requires less entanglement of Alice's measurement but more classical bits than the original scheme via a Bell state. The two quantities increase with the entanglement of the quantum channel when its dimension is fixed and thereby can be regard as Alice's necessary capabilities to use the quantum channel. And the two capabilities appear complementary to each other.