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

Physical Review A

Controlled teleportation of qubit states: Relation between teleportation faithfulness, controller's authority, and tripartite entanglement

Artur Barasiński, Jiŕí Svozilík

Published Jan 4, 2019• 21 citations
Publisher

Abstract

We consider the controlled quantum teleportation performed on a single copy of entangled three-qubit pure states and show how the fidelity of teleportation and the control power are related to the tripartite entanglement measures, namely, three-tangle and genuine concurrence. We characterize the states with extreme properties, and use them to derive tight lower and upper bounds on both the teleportation fidelity and control power for a given amount of entanglement. Furthermore, we discuss the usefulness of these two quantities for experimental detection and/or quantification of tripartite entanglement. In particular, we present the results which imply that the control power cannot be considered as a candidate for a degree of three-qubit entanglement complementary to the three-tangle as conjectured recently [K. Jeong, J. Kim, and S. Lee, Phys. Rev. A 93, 032328 (2016)]. Furthermore, we prove a mutual relation between teleportation fidelity and control power which provides attainable limits of the controller's authority for existing controlled teleportation schemes. Although those relations are derived for pure states, their extensions for mixed states are also examined.

DOI
10.1103/physreva.99.012306

Related papers

Minimal control power of the controlled teleportation

Kabgyun Jeong, Jaewan Kim, Soojoon Lee

We generalize the control power of a perfect controlled teleportation of an entangled three-qubit pure state, suggested by Li and Ghose [Phys. Rev. A 90, 052305 (2014)], to the control power of a general controlled teleportation of a multiqubit pure state. Thus, we define the minimal control power, and calculate the values of the minimal control power for a class of general three-qubit Greenberger-Horne-Zeilinger (GHZ) states and the three-qubit $W$ class whose states have zero three-tangles. Moreover, we show that the standard three-qubit GHZ state and the standard three-qubit $W$ state have the maximal values of the minimal control power for the two classes, respectively. This means that the minimal control power can be interpreted as not only an operational quantity of a three-qubit quantum communication but also a degree of three-qubit entanglement. In addition, we calculate the values of the minimal control power for general $n$-qubit GHZ states and the $n$-qubit $W$-type states.

arXiv:1509.05165•Physical Review A•Mar 21, 2016•26 citations

Generalization of port-based teleportation and controlled teleportation capability

Kabgyun Jeong, Jaewan Kim, Soojoon Lee

As a variant of the original quantum teleportation, port-based teleportation has been proposed, and its various kinds of useful applications in quantum information processing have been explored. Two users in the port-based teleportation initially share an arbitrary pure state, which can be represented by applying one user's local operation to a bipartite maximally entangled state. If the maximally entangled state is a $2M$-qudit state, then it can be expressed as $M$ copies of a two-qudit maximally entangled state, where $M$ is the number of ports. We here consider a generalization of the original port-based teleportation obtained from employing copies of an arbitrary bipartite (mixed) resource instead of copies of a pure maximally entangled one. By means of the generalization, we construct a concept of controlled port-based teleportation by combining controlled teleportation with port-based teleportation, and analyze its performance in terms of several meaningful quantities such as the teleportation fidelity, the entanglement fidelity, and the fully entangled fraction. In addition, we present quantities called the control power and the minimal control power for the controlled version on a given tripartite quantum state.

arXiv:2002.12651•Physical Review A•Jul 10, 2020•17 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

Control power in perfect controlled teleportation via partially entangled channels

Xihan Li, Shohini Ghose

We analyze and evaluate perfect controlled teleportation via three-qubit entangled channels from the point of view of the controller. The key idea in controlled teleportation is that the teleportation is performed only with the participation of the controller. We calculate a quantitative measure of the controller's power and establish a lower bound on the control power required for controlled teleportation. We show that the maximally entangled Greenberger-Horne-Zeilinger state is a suitable channel for controlled teleportation of arbitrary single qubits---the controller's power meets the bound and the teleportation fidelity without the controller's permission is no better than the fidelity of a classical channel. We also construct partially entangled channels that exceed the bound for controlled teleportation of a restricted set of states called the equatorial states. We calculate the minimum entanglement required in these channels to exceed the bound. Moreover, we find that in these restricted controlled teleportation schemes, the partially entangled channels can outperform maximally entangled channels with respect to the controller's power. Our results provide an alternative perspective on controlled teleportation schemes and are of practical interest since we propose useful partially entangled channels.

arXiv:1410.1196•Physical Review A•Nov 5, 2014•69 citations

Entanglement of three-qubit pure states in terms of teleportation capability

Soojoon Lee, Jaewoo Joo, Jaewan Kim

We define an entanglement measure, called the partial tangle, which represents the residual two-qubit entanglement of a three-qubit pure state. By its explicit calculations for three-qubit pure states, we show that the partial tangle is closely related to the faithfulness of a teleportation scheme over a three-qubit pure state.

arXiv:quant-ph/0502157•Physical Review A•Aug 12, 2005•37 citations

Contrasting Effects of Control on Fidelity and Fidelity Deviation in Controlled Teleportation

Jeonghyeon Shin, Minjin Choi

Teleportation performance is commonly characterized by the average teleportation fidelity, while its variation over input states provides additional information captured by the fidelity deviation. In controlled teleportation, the controller's measurement introduces an additional source of fidelity variation through its measurement outcomes. We investigate the fidelity deviation in controlled teleportation with three-qubit pure states. We derive a lower bound on the fidelity deviation and show that it is attainable together with the maximal average teleportation fidelity. Among the measurements attaining the maximal average fidelity, however, the fidelity deviation can vary depending on the controller's measurement. We further examine the effect of controller assistance by comparing controlled teleportation with direct teleportation using the reduced state. Unlike the maximal average fidelity, which cannot decrease with controller assistance, the minimal fidelity deviation is not necessarily reduced by controller assistance. In particular, for any W-class pure state, controller assistance cannot reduce the fidelity deviation. These results reveal contrasting effects of control on teleportation fidelity and its deviation in controlled teleportation.

quant-pharXiv:2609.01988•Sep 3, 2026•0 citations
We consider the controlled quantum teleportation performed on a single copy of entangled three-qubit pure states and show how the fidelity of teleportation and the control power are related to the tripartite entanglement measures, namely, three-tangle and genuine concurrence. We characterize the states with extreme properties, and use them to derive tight lower and upper bounds on both the teleportation fidelity and control power for a given amount of entanglement. Furthermore, we discuss the usefulness of these two quantities for experimental detection and/or quantification of tripartite entanglement. In particular, we present the results which imply that the control power cannot be considered as a candidate for a degree of three-qubit entanglement complementary to the three-tangle as conjectured recently [K. Jeong, J. Kim, and S. Lee, Phys. Rev. A 93, 032328 (2016)]. Furthermore, we prove a mutual relation between teleportation fidelity and control power which provides attainable limits of the controller's authority for existing controlled teleportation schemes. Although those relations are derived for pure states, their extensions for mixed states are also examined.
We generalize the control power of a perfect controlled teleportation of an entangled three-qubit pure state, suggested by Li and Ghose [Phys. Rev. A 90, 052305 (2014)], to the control power of a general controlled teleportation of a multiqubit pure state. Thus, we define the minimal control power, and calculate the values of the minimal control power for a class of general three-qubit Greenberger-Horne-Zeilinger (GHZ) states and the three-qubit WWW class whose states have zero three-tangles. Moreover, we show that the standard three-qubit GHZ state and the standard three-qubit WWW state have the maximal values of the minimal control power for the two classes, respectively. This means that the minimal control power can be interpreted as not only an operational quantity of a three-qubit quantum communication but also a degree of three-qubit entanglement. In addition, we calculate the values of the minimal control power for general nnn-qubit GHZ states and the nnn-qubit WWW-type states.
As a variant of the original quantum teleportation, port-based teleportation has been proposed, and its various kinds of useful applications in quantum information processing have been explored. Two users in the port-based teleportation initially share an arbitrary pure state, which can be represented by applying one user's local operation to a bipartite maximally entangled state. If the maximally entangled state is a 2M2M2M-qudit state, then it can be expressed as MMM copies of a two-qudit maximally entangled state, where MMM is the number of ports. We here consider a generalization of the original port-based teleportation obtained from employing copies of an arbitrary bipartite (mixed) resource instead of copies of a pure maximally entangled one. By means of the generalization, we construct a concept of controlled port-based teleportation by combining controlled teleportation with port-based teleportation, and analyze its performance in terms of several meaningful quantities such as the teleportation fidelity, the entanglement fidelity, and the fully entangled fraction. In addition, we present quantities called the control power and the minimal control power for the controlled version on a given tripartite quantum state.
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 analyze and evaluate perfect controlled teleportation via three-qubit entangled channels from the point of view of the controller. The key idea in controlled teleportation is that the teleportation is performed only with the participation of the controller. We calculate a quantitative measure of the controller's power and establish a lower bound on the control power required for controlled teleportation. We show that the maximally entangled Greenberger-Horne-Zeilinger state is a suitable channel for controlled teleportation of arbitrary single qubits---the controller's power meets the bound and the teleportation fidelity without the controller's permission is no better than the fidelity of a classical channel. We also construct partially entangled channels that exceed the bound for controlled teleportation of a restricted set of states called the equatorial states. We calculate the minimum entanglement required in these channels to exceed the bound. Moreover, we find that in these restricted controlled teleportation schemes, the partially entangled channels can outperform maximally entangled channels with respect to the controller's power. Our results provide an alternative perspective on controlled teleportation schemes and are of practical interest since we propose useful partially entangled channels.
Teleportation performance is commonly characterized by the average teleportation fidelity, while its variation over input states provides additional information captured by the fidelity deviation. In controlled teleportation, the controller's measurement introduces an additional source of fidelity variation through its measurement outcomes. We investigate the fidelity deviation in controlled teleportation with three-qubit pure states. We derive a lower bound on the fidelity deviation and show that it is attainable together with the maximal average teleportation fidelity. Among the measurements attaining the maximal average fidelity, however, the fidelity deviation can vary depending on the controller's measurement. We further examine the effect of controller assistance by comparing controlled teleportation with direct teleportation using the reduced state. Unlike the maximal average fidelity, which cannot decrease with controller assistance, the minimal fidelity deviation is not necessarily reduced by controller assistance. In particular, for any W-class pure state, controller assistance cannot reduce the fidelity deviation. These results reveal contrasting effects of control on teleportation fidelity and its deviation in controlled teleportation.