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arXiv:quant-ph/0508067 · Infinite Dimensional Analysis Quantum Probability and Related Topics

NEW SCHEME OF QUANTUM TELEPORTATION

Andrzej Kossakowski, Makoto Ohya

Published Sep 1, 2007• 10 citations
arXivHTMLPDF

Abstract

A new scheme for quantum teleportation is presented, in which teleportation channel from Alice to Bob is always linear and complete (total) teleportation can occur even when an entangled state between Alice and Bob is not maximal.
DOI
10.1142/s021902570700283x

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The quantum teleportation has been discussed by several articles, and in most of models, perfect quantum teleportation can be occured if the entangled state between Alice and Bob is maximal. Recently, Kossakowski and Ohya reformulated the teleportation process and proposed a new scheme of perfect teleportation where a non-maximal entangled state is used [3]. In this paper, we introduce two models designed according to the KO formalism. The first one is called m-level perfect teleportation. We show that a non-maximal entangled state used in this model is realizable in optical techniques. In the second model, a new operation is added to a conventional teleportation process, which is called and implemented before Alice's measurement. We show availabilities of the filtering for sucess probabilities of teleportation.
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.
We have explicitly shown a teleportation scheme which allows Alice to probabilistically teleport an unknown 2-particle entangled state to either of the two receivers,Bob or Charlie,by using a non-maximally entangled 5-particle state as quantum channel.The scheme can be generalized to teleport an unknown N-(particle) entangled state to M receivers using a(N·M+1)-particle state as quantum channel at the expense of performing one CNOT operation,N·M Hadamard operations,appropriate unitary transformation without performing Bell-state measurement.