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arXiv:1503.07949 · Scientific Reports

Two-copy Quantum Teleportation

Quan Quan, Ming-Jing Zhao, Shao-Ming Fei, Heng Fan, Wen‐Li Yang, Gui-Lu Long

Published Sep 12, 2018• 10 citations
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Abstract

We investigate two-copy scenario of quantum teleportation based on Bell measurements. The detailed protocol is presented and the general expression of the corresponding optimal teleportation fidelity is derived, which is given by the two-copy fully entangled fraction that is invariant under local unitary transformations. We prove that under a specific case of the protocol, which is significant for improving the optimal fidelity, the set of states with their two-copy fully entangled fractions bounded by a threshold value that required for useful two-copy teleportation is convex and compact. Hence the witness operators exist to separate states that are useful for two-copy teleportation from the rest ones. Moreover, we show that the optimal fidelity of two-copy teleportation surpasses that of the original one copy teleportation.

DOI
10.1038/s41598-018-31918-0

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We investigate two-channel scenarios of optimal quantum teleportation based on Bell measurements and GHZ measurements. The detailed protocols are presented and the general expressions of the optimal teleportation fidelities are derived, which turn out to be functions of two-channel fully entangled fractions -- invariants under local unitary transformations. We prove that the set of states which are useful for two-channel teleportation is convex and compact. Hence witness operators exist to separate states that are useful for optimal teleportation from the rest ones. Moreover, we show that our two-channel teleportation fidelity is better than the usual one channel ones. The corresponding experimental schemes for two-channel teleportation of photon states are also presented.
Teleportation for pure states, mixed states with standard and optimal protocols are introduced and investigated systematically. An explicit equation governing the teleportation of finite dimensional quantum pure states by a generally given non-local entangled state is presented. For the teleportation of a mixed state with an arbitrary mixed state resource, an explicit expression is obtained for the quantum channel associated with the standard teleportation protocol. The corresponding transmission fidelity is calculated. It is shown that the standard teleportation protocol is not optimal. The optimal quantum teleportation is further studied, its fidelity is given and shown to be related to the fully entangled fraction of the quantum resource, rather than the single fraction as in the standard teleportation protocol.
Abstract Quantum teleportation with an arbitrary two-qubit state can be appropriately characterized in terms of maximal fidelity and fidelity deviation. The former quantifies optimality of the process and is defined as the maximal average fidelity achievable within the standard protocol and local unitary strategies, whereas the latter, defined as the standard deviation of fidelity over all input states, is a measure of fidelity fluctuations. The maximal fidelity for a two-qubit state is known and is given by a simple formula that can be exactly computed, but no such formula is known for the fidelity deviation. In this paper, we derive an exact computable formula for the fidelity deviation in optimal quantum teleportation with an arbitrary state of two qubits. From this formula, we obtain the dispersion-free condition, also known as the universality condition: the condition that all input states are teleported equally well and provide a necessary and sufficient condition for a state to be both useful (maximal fidelity larger than the classical bound) and universal (zero fidelity deviation). We also show that for any given maximal fidelity, larger than the classical bound, there always exist dispersion-free or universal states and argue that such states are the most desirable ones within the set of useful states. We illustrate these results with well-known families of two-qubit states: pure entangled states, Bell-diagonal states, and subsets of X states.
We consider a single copy of a mixed state of two qubits and derive the optimal trace-preserving local operations assisted by classical communication such as to maximize the fidelity of teleportation that can be achieved with this state. These optimal local operations turn out to be implementable by one-way communication and always yield a teleportation fidelity larger than 2/3 if the original state is entangled. This maximal achievable fidelity is an entanglement measure and turns out quantifying the minimal amount of mixing required to destroy the entanglement in a quantum state.