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AIP conference proceedings

Mathematical problems of quantum teleportation

Yoshiharu Tanaka, Masanari Asano, Masanori Ohya, Andrei Yu. Khrennikov, Gregg S. Jaeger, Maximilian Schlosshauer, Gregor Weihs

Published Jan 1, 2011• 0 citations
Publisher

Abstract

It has been considered that a maximal entangled state is needed for complete quantum teleportation. However, Kossakowski and Ohya proposed a scheme of complete teleportation for nonmaximal entangled state [1]. Basing on their scheme, we proposed a teleportation model of 2‐level state with a non‐maximal entangled state [2]. In the present study, we construct its expanded model, in which Alice can teleport m‐level state even if non‐maximal entangled state is used.

DOI
10.1063/1.3578743

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It has been considered that a maximal entangled state is needed for complete quantum teleportation. However, Kossakowski and Ohya proposed a scheme of complete teleportation for nonmaximal entangled state [1]. Basing on their scheme, we proposed a teleportation model of 2‐level state with a non‐maximal entangled state [2]. In the present study, we construct its expanded model, in which Alice can teleport m‐level state even if non‐maximal entangled state is used.
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.
Recently, Kossakowski and Ohya (K-O) proposed a new teleportation scheme which enables perfect teleportation even for a nonmaximal entangled state [A. Kossakowski and M. Ohya, Infinite Dimensional Analysis Quantum Probability and Related Topics 10, 411 (2007)]. To discuss a physical realization of the K-O scheme, we propose a model based on quantum optics. In our model, we take a superposition of Schr\"odinger's cat states as an input state being sent from Alice to Bob, and their entangled state is generated by a photon number state through a beam splitter. When the average photon number for our input states is equal to half the number of photons into the beam splitter, our model has high fidelity.