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arXiv:quant-ph/0510130

Teleportation from a Projection Operator Point of View

Noam Erez A

Published Oct 17, 2005• 4 citations
arXivHTMLPDF

Abstract

The process of quantum state teleportation is described from the point of view of the properties of projections onto one-dimensional subspaces. It is introduced as a generalization of the remote preparation of a known state by use of an EPR pair. The discrete and continuous cases are treated in a unified way. The conceptual and calculational simplicity is pedagogically advantageous.

DOI
10.48550/arxiv.quant-ph/0510130

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The process of quantum state teleportation is described from the point of view of the properties of projections onto one-dimensional subspaces. It is introduced as a generalization of the remote preparation of a known state by use of an EPR pair. The discrete and continuous cases are treated in a unified way. The conceptual and calculational simplicity is pedagogically advantageous.
In contrast to discrete-variable teleportation, a quantum state is imperfectly transferred from a sender to a remote receiver in a continuous-variable setting. We recall the ingenious scheme proposed by Braunstein and Kimble for teleporting a one-mode state of the quantum radiation field. By analyzing this protocol, we have previously proven the factorization of the characteristic function of the output state. This indicates that teleportation is a noisy process that alters, to some extent, the input state. Teleportation with a two-mode Gaussian EPR state can be described in terms of the superposition of a distorting field with the input one. Here we analyze the one-mode Gaussian distorting-field state. Some of its most important properties are determined by the statistics of a positive EPR operator in the two-mode Gaussian resource state. We finally examine the fidelity of teleportation of a coherent state when using an arbitrary resource state.
The possibility of teleportation is by sure the most interesting consequence of quantum non-separability. So far, however, teleportation schemes have been formulated by use of state vectors and considering individual entities only. In the present article the feasibility of teleportation is examined on the basis of the rigorous ensemble interpretation of quantum mechanics (not to be confused with a mere treatment of noisy EPR pairs) leading to results which are unexpected from the usual point of view.
The possibility of teleportation is by sure the most interesting consequence of quantum non-separability. So far, however, teleportation schemes have been formulated by use of state vectors and considering individual entities only. In the present article the feasibility of teleportation is examined on the basis of the rigorous ensemble interpretation of quantum mechanics (not to be confused with a mere treatment of noisy EPR pairs) leading to results which are unexpected from the usual point of view.
The possibility of teleportation is by sure the most interesting consequence of quantum non-separability. So far, however, teleportation schemes have been formulated by use of state vectors and considering individual entities only. In the present article the feasibility of teleportation is examined on the basis of the rigorous ensemble interpretation of quantum mechanics (not to be confused with a mere treatment of noisy EPR pairs) leading to results which are unexpected from the usual point of view.
By quantum teleportation an unknown quantum state is destroyed at a sending place while its perfect replica state appears at a remote place via dual quantum and classical channels. Quantum teleportation allows for the transmission of quantum information to a distant location despite the impossibility of measuring or broadcasting the information to be transmitted. e classical teleportation is like a fax in which one could scan an object and send the information so that the object can be reconstructed at the destination. In this conventional facsimile transmission, the original object is scanned to extract partial information about it. e scanned information is then sent to the receiving station, where it is used to produce an approximate copy of the original object. e original object remains intact a er the scanning process. By contrast, in quantum teleportation, the uncertainty principle forbids any scanning process from extracting all the information in a quantum state. e nonlocal property of quantum mechanics enables the striking phenomenon of quantum teleportation. Bennett and coworkers28 showed that a quantum state can be teleported, provided one does not know that state, using a celebrated and paradoxical feature of quantum mechanics known as the Einstein-Podolsky-Rosen (EPR) e ect.11 ey found a way to scan out part of the information from an object A, which one wishes to teleport, while causing the remaining part of the information to pass to an object B, via the EPR e ect. In this process, two objects B and C form an entangled pair; object C is taken to the sending station, while object B is taken to the receiving station. At the sending station, object C is scanned together with the original object A, yielding some information and totally disrupting the state of A and C. e scanned information is sent to the receiving station, where it is used to select one of several treatments to be applied to object B, thereby putting B into an exact replica of the former state of A.