Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1104.4382 · Journal of Physics A Mathematical and Theoretical

Faithful teleportation with arbitrary pure or mixed resource states

Ming‐Jing Zhao, Zong-Guo Li, Shao-Ming Fei, Zhi‐Xi Wang, Xianqing Li‐Jost

Published Apr 21, 2011• 10 citations
arXivHTMLPDF

Abstract

We study faithful teleportation systematically with arbitrary entangled states as resources. The necessary conditions of mixed states to complete perfect teleportation are proved. Based on these results, the necessary and sufficient conditions of faithful teleportation of an unknown state |ϕ⟩ in with an entangled resource ρ in and are derived. It is shown that for ρ in , ρ must be a maximally entangled state, while for ρ in , ρ must be a pure maximally entangled state. Moreover, we show that the sender's measurements must be all projectors of maximally entangled pure states. The relations between the entanglement of the formation of the resource states and faithful teleportation are also discussed.

DOI
10.1088/1751-8113/44/21/215302

Related papers

Maximally entangled state can be a mixed state

Zong-Guo Li, Ming‐Jing Zhao, Shao-Ming Fei +2 more

We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other entanglement measures, this conclusion is still proven right. This result is a supplementary to the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states, for example, these states can be used as a resource for faithful teleportation and they can be distinguished perfectly by local operations and classical communication.

arXiv:0906.5445•Jun 30, 2009•3 citations

Localizable entanglement as a necessary resource of controlled quantum teleportation

Artur Barasiński, Ievgen I. Arkhipov, Jiŕí Svozilík

We analyze the controlled teleportation protocol through three-qubit mixed states. In particular, we investigate the relation between the faithfulness of the controlled teleportation scheme and entanglement. While our knowledge concerning controlled teleportation and entanglement in pure states is well established, for mixed states it is considerably much harder task and very little has been done in this field. Here, we present counterintuitive results that provide a new light on controlled teleportation protocol. It is shown that even mixed biseparable states are useful for this protocol along with genuine entangled three-qubit states.

Scientific Reports•Oct 8, 2018•26 citations

Mixed maximally entangled states

Z. G. Li, Mengliu Zhao, Shao-Ming Fei +2 more

We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other entanglement measures, this conclusion is still proven right. This result is a supplementary to the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states, for example, these states can be used as a resource for faithful teleportation and they can be distinguished perfectly by local operations and classical communication.

Quantum Information and Computation•Jan 1, 2012•21 citations

A Generalized Formulation of Probabilistic Quantum Teleportation

Jianhao M. Yang

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.

arXiv:1601.02501•Jan 3, 2016•0 citations

Optimal quantum teleportation with an arbitrary pure state

Konrad Banaszek

We present an elementary derivation of the maximum fidelity attainable in teleportation using a single copy of two d-level systems in an arbitrary pure state. This derivation provides a complete set of necessary and sufficient conditions for optimal teleportation protocols. We also discuss the information on the teleported particle that is revealed in course of the protocol using a nonmaximally entangled state.

arXiv:quant-ph/0002088•Physical Review A•Jul 13, 2000•85 citations

Quantum Teleportation: from Pure to Mixed States and Standard to Optimal

Sergio A Albeverio, S.M. Fei, Wen‐Li Yang

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.

arXiv:quant-ph/0308009•Aug 1, 2003•0 citations
We study faithful teleportation systematically with arbitrary entangled states as resources. The necessary conditions of mixed states to complete perfect teleportation are proved. Based on these results, the necessary and sufficient conditions of faithful teleportation of an unknown state |ϕ⟩ in with an entangled resource ρ in and are derived. It is shown that for ρ in , ρ must be a maximally entangled state, while for ρ in , ρ must be a pure maximally entangled state. Moreover, we show that the sender's measurements must be all projectors of maximally entangled pure states. The relations between the entanglement of the formation of the resource states and faithful teleportation are also discussed.
We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other entanglement measures, this conclusion is still proven right. This result is a supplementary to the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states, for example, these states can be used as a resource for faithful teleportation and they can be distinguished perfectly by local operations and classical communication.
We analyze the controlled teleportation protocol through three-qubit mixed states. In particular, we investigate the relation between the faithfulness of the controlled teleportation scheme and entanglement. While our knowledge concerning controlled teleportation and entanglement in pure states is well established, for mixed states it is considerably much harder task and very little has been done in this field. Here, we present counterintuitive results that provide a new light on controlled teleportation protocol. It is shown that even mixed biseparable states are useful for this protocol along with genuine entangled three-qubit states.
We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other entanglement measures, this conclusion is still proven right. This result is a supplementary to the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states, for example, these states can be used as a resource for faithful teleportation and they can be distinguished perfectly by local operations and classical communication.
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.
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.