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Europhysics Letters (EPL)

The state evolution formulation of teleportation for continuous variables

Junxiang Zhang, Changde Xie, Fuli Li, Shi-Yao Zhu, Muhammad Suhail Zubairy

Published Nov 1, 2001• 5 citations
Publisher

Abstract

The quantum teleportation of continuous variables is formulated through the state evolution in the Schrödinger picture from the viewpoint of general quantum-mechnical measurement theory. This method provides the connection between the teleportation and the reversible quantum operations. In this way, the state evolution process of teleportation can be presented clearly step by step, the criterium of teleportation for a coherent state is also deduced.

DOI
10.1209/epl/i2001-00544-3

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The quantum teleportation of continuous variables is formulated through the state evolution in the Schrödinger picture from the viewpoint of general quantum-mechnical measurement theory. This method provides the connection between the teleportation and the reversible quantum operations. In this way, the state evolution process of teleportation can be presented clearly step by step, the criterium of teleportation for a coherent state is also deduced.
Measurements used in quantum teleportation are examined from the standpoint of the general theory of quantum-mechanical measurements. It is shown that in order to find a teleported state, it is sufficient to know only the resolution of the identity operator (positive operator-valued measure) generated by the respective instrument (the quantum operation determining the change in the state of the system as a result of the measurement) in the state space of the system, rather than the instrument itself. A protocol for quantum teleportation of the state of a system with a nondegenerate continuous spectrum based on a measurement which corresponds to a certain nonorthogonal resolution of the identity operator is proposed.
The measurement procedures used in quantum teleportation are analyzed from the viewpoint of the general theory of quantum-mechanical measurements. It is shown that to find the teleported state one should only know the identity resolution (positive operator-valued measure) generated by the corresponding instrument (quantum operation describing the system state change caused by the measurement) rather than the instrument itself. A quantum teleportation protocol based on a measurement associated with a non-orthogonal identity resolution is proposed for a system with non-degenerate continuous spectrum.