Minimal control power of the controlled teleportation

Abstract

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 threetangles. 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.

Localizable entanglement as a necessary resource of controlled quantum teleportation

“…It is well-known that in a pure-state regime the generalized GHZ state and a group of W-class states 19 are useful for controlled teleportation 18 . In order to verify whether mixed states which belong to GHZ-class and W-class are also suitable for CQT both fidelities, given by Eqs ( 5 ) and ( 6 ), need to be determined.…”

“…an unknown state of a single qubit can be teleported from sender to receiver with fidelity only with the permission of the controller. Without controller’s participation the teleportation fidelity (henceforth referred to as the non-conditioned fidelity F NC ) is no better than the fidelity of a classical channel, 17 , 18 . Here, the question whether entanglement is a necessary resource for CQT is much more sophisticated.…”

“…( 2 ) is meaningful if and only if the non-conditioned fidelity what implies immediately that none of pure separable and pure biseparable states are useful for CQT. The CQT protocol has been successfully investigated via several classes of partially tripartite entangled pure states 16 – 18 , in particular the generalized GHZ states. Therefore, the tripartite entanglement can be considered as a necessary resource of CQT 15 , 18 , 22 , 23 .…”

Transmission losses in optical qubits for controlled teleportation

“…Finally, it would be interesting to expand our analysis of losses and optical encodings to the multiqubit scenario discussed in [52,53]. In particular, it may be the case that the interplay between dissipation and non-orthogonality, appearing in the coherent states, may have consequences in the minimal control power [53]. Additionally, as damping impacts the knowledge the controller has on the channel (changes the state entropy), it might be of interest to include losses in the discussion proposed in [54].…”

Minimal control power of controlled dense coding and genuine tripartite entanglement

“…The controller in each protocol can control the channel capacity and the teleportation fidelity of the other two parties, respectively. Recently, the concepts of control power (CP) and minimal control power (MCP) of the controlled teleportation have been suggested to quantify how much teleportation fidelity can be controlled by the controller [18][19][20][21] . CP is defined as the difference between teleportation fidelities with and without the controller's assistance.…”