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arXiv:1601.02501

A Generalized Formulation of Probabilistic Quantum Teleportation

Jianhao M. Yang

Published Jan 3, 2016• 0 citations
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Abstract

Teleporation with partially entangled quantum channel cannot achieve unit fidelity and unit probability. We show that the conditions for faithful teleportation of a pure state or a mixed state can be described by the same general relation $\rho_{q}\rho_{m} = pI$, where $\rho_{q}$ is the reduced density matrix of the quantum channel, $\rho_{m}$ is the reduced density matrix of the measurement basis, and $p$ is the probability of faithful teleportaion. These conditions are unchanged under unitary transformation. We also prove that using a four dimensional partially entangled quantum channel, it is not possible to find a set of orthogonal measurement basis that contains more than two faithfully teleporting measurements.

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Teleporation with partially entangled quantum channel cannot achieve unit fidelity and unit probability. We show that the conditions for faithful teleportation of a pure state or a mixed state can be described by the same general relation ρqρm=pI\rho_{q}\rho_{m} = pIρq​ρm​=pI, where ρq\rho_{q}ρq​ is the reduced density matrix of the quantum channel, ρm\rho_{m}ρm​ is the reduced density matrix of the measurement basis, and ppp is the probability of faithful teleportaion. These conditions are unchanged under unitary transformation. We also prove that using a four dimensional partially entangled quantum channel, it is not possible to find a set of orthogonal measurement basis that contains more than two faithfully teleporting measurements.
In this study,we will investigate the problem of teleportation of an arbitrary two-qubit state.Firstly,we show how the two-qubit state can be teleported with unit fidelity and unit probability by using a maximally entangled four-dimensional qudit pair as a quantum channel.Then,we put forward a scheme for probabilistic teleporting the state with unit fidelity via a partially entangled quantum qudit channel.The probability of successful teleportation is determined by the smallest Schmidt coefficient of the entangled qudit pair.
Quantum teleportation is a fundamental protocol in quantum information science, whose performance is conventionally evaluated under the assumption of ideal Bell-state measurements. In realistic implementations, however, joint measurements are often imperfect and can deviate from maximally entangled bases due to coherent errors in entangling operations. In this work, we analytically show how the entanglement of joint measurements determines teleportation performance, and we propose a strategy to overcome the limitations imposed by partially entangled joint measurements to recover the unit teleportation fidelity with a nonzero success probability. This is achieved by optimizing a reversing operation on the teleported state to compensate for the known coherent deformation of the Bell-state measurement. We then derive an exact equation revealing a quantitative relation between measurement entanglement, channel entanglement, and the success probability to realize the unit-fidelity two-qubit teleportation. We illustrate our results using elegant joint measurements and realistic coherent error models arising from imperfect entangling operations in quantum systems. Our work provides fundamental insight into the role of measurement entanglement in quantum teleportation and offers a practical framework for achieving faithful teleportation without requiring substantial modifications to existing hardware.
We describe a new protocol where, by using a non-maximally entangled basis as the measurement basis, one can use a general pure entangled state as a resource for quantum teleportation. Using this protocol one can teleport a state with unit fidelity though less than unit probability. We also use the more natural language of quantum operations to describe this probabilistic teleportation. We also provide success and failure probabilities for this protocol. This scheme could be of use in real experiments which may be tested in the near future.
Four partially entangled two-particle states are used as the quantum channel.Two schemes for probabilistic teleportation of an arbitrary four-particle entangled state are presented.The entangled state can be perfectly teleported probabilistically from the sender to the receiver if the sender performs four Bell-state measurements while the receiver introduces auxiliary particles and performing appropriate unitary transformations.Based on transformation operator,the theoretical explanation of two schemes is given by utilizing the relation of the transformation operators.