Perfect controlled joint remote state preparation independent of entanglement degree of the quantum channel

doi:10.1016/j.physleta.2014.10.030

Physics Letters A

Volume 378, Issue 48, 14 November 2014, Pages 3582-3585

https://doi.org/10.1016/j.physleta.2014.10.030 Get rights and content

Highlights

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Controlled joint remote state preparation is considered.
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Quantum circuit is proposed to produce task-oriented partially entangled channel.
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The quantum channel parameter is given to the supervisor (not to the receiver).
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Unit success probability without additional resource/operations/measurement.
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Perfection is achieved regardless of the shared entanglement degree.

Abstract

We construct a quantum circuit to produce a task-oriented partially entangled state and use it as the quantum channel for controlled joint remote state preparation. Unlike most previous works, where the parameters of the quantum channel are given to the receiver who can accomplish the task only probabilistically by consuming auxiliary resource, operation and measurement, here we give them to the supervisor. Thanks to the knowledge of the task-oriented quantum channel parameters, the supervisor can carry out proper complete projective measurement, which, combined with the feed-forward technique adapted by the preparers, not only much economizes (simplifies) the receiver's resource (operation) but also yields unit total success probability. Notably, such apparent perfection does not depend on the entanglement degree of the shared quantum channel. Our protocol is within the reach of current quantum technologies.

Introduction

Quantum information encoded in quantum states provides a totally new way of information processing that enables to execute intriguing tasks which would not be possible by means of traditional classical methods [1]. Transferring a quantum state faithfully and securely between remote locations is primarily important in quantum communication, especially in distributed quantum computation [2]. However, direct transfer of the state is not encouraged since the security may be threatened by en route enemies who are supposed to be capable of doing anything allowed by the laws of Nature. Interestingly, with the aid of prior shared entangled resource, the state transfer can be done only by means of local operations and communication of very limited classical information. Most notable is the celebrated protocol devised in Ref. [3] by which an unknown quantum state can be teleported. Later, a simpler protocol was introduced allowing remote preparation of a known state using the same quantum resource as in quantum teleportation but without Bell measurement and with lesser classical communication. Such protocol is referred to as remote state preparation (RSP) [4], [5], [6]. The drawbacks of RSP are: (i) the full identity of the to-be-prepared state is disclosed to the preparer and (ii) unit success probability cannot be achieved in general. To overcome these drawbacks a new method, called joint remote state preparation (JRSP) [7], [8], was proposed. In JRSP there are several preparers, each of them allowed to know only a partial information of the state to be prepared so that no subsets of them are able to infer the state, thus resolving the drawback (i). Furthermore, by adapting specific techniques such as feed-forward measurements [9] (i.e., measurements are done in sequence and the earlier measurement result determines the future measurement basis), JRSP can be made successful all the time [10], [11], [12], [13], thus resolving the drawback (ii).

In practice it often appears necessary to quantumly control a global task. This can be realized by adding a supervisor who has the right at the last minute to decide completion of a task after carefully considering all the concerned situations, including non-technical issues. Controlled teleportation [14], [15], controlled RSP [16], controlled quantum secret sharing [17], controlled secure direct communication [18], controlled logic gates [19], etc., have been studied in detail.

In this Letter, we are interested in controlled JRSP [20], [21], [22], [23]. To be able to control in a quantum way, the supervisor has to share beforehand with the preparers as well as with the receiver a quantum resource served as the quantum channel which is commonly thought to be maximally entangled for best performance. For example, a maximally entangled quantum channel together with feed-forward measurements leads to unit success probability [21], [22], [23]. Nevertheless, the following scenario may happen. Assume that during the entanglement distribution for sharing an outside enemy succeeds to capture the qubits of the entangled channel on their way to the supervisor and the receiver and replaces them by fake ones. If so, the enemy can manipulate the captured qubits exactly the same way as the supervisor and the receiver are supposed to do, thus faithfully obtain the state of interest, while the receiver gets a wrong one. A possible solution to cope with such kind of attack is using a partially entangled resource whose identifying parameters are kept confidential from any outsider. Usually the parameters of the partially entangled resource are assumed to be known by the receiver [21], [22], who can use this knowledge to recover the desired state from the collapsed state at his/her hand. The cost to pay for the recovery process is the compulsory requirement of auxiliary qubits, auxiliary two-qubit gates as well as measurements on the auxiliary qubits, not talking about the fact that the total success probability is always less than 100%. To reduce the overall cost and to boost the total success probability, the knowledge of the parameters of the partially entangled channel is transferred from the receiver to the supervisor who carries out optimal positive operator-valued measure (POVM) measurements on his/her qubit(s) to guide the receiver to reconstruct the desired state without consuming any auxiliary resources. Regretfully, POVM measurements are per se not complete (the states corresponding to different outcomes are not mutually orthogonal), so there is always a finite probability of failure when an ambiguous outcome is obtained. In fact, the success probability is higher but never reaches 1 [23]. The remaining thing thus rests on the quantum channel. Generally speaking, for an intended task there might exist suitable resources via which the task's performance would be the best. Such resources can be named task-oriented resources [24]. Are there any resources to be served as the quantum channel for perfect controlled JRSP (i.e., with unit success probability without additional resources/operations)? We find out that the answer is positive. How to produce such a resource and how to employ it to perform controlled JRSP perfectly is the purpose of the present Letter. An added interesting feature is that the perfection is independent of the entanglement degree of the shared task-oriented quantum channel, as opposed to all the previous protocols.

Section snippets

The task and the task-oriented quantum channel

Suppose that the state to be prepared for a remote party, called the receiver Bob, has the form $| ψ 〉 = e^{- i φ / 2} \cos (η / 2) | 0 〉 + e^{i φ / 2} \sin (η / 2) | 1 〉,$ whose identity is fully characterized by two angles η and φ. The value of angle η is given to Alice 1, while that of angle φ to Alice 2, who serve as the two preparers. Clearly, no one of the two preparers alone is able to infer $| ψ 〉$ . Let Charlie be the supervisor who, as Bob, knows nothing about $| ψ 〉$ . As mentioned in Introduction, the four parties should share

Entanglement-degree–independent perfect controlled joint remote state preparation

Given the quantum channel state $| Q 〉$ in Eq. (2), we now describe in detail how the two Alices can jointly prepare for Bob the state $| ψ 〉$ of the form (1) under quantum control of Charlie. The necessary actions that the participants should do in sequence are illustrated in Fig. 2.

Concretely, the protocol begins with Alice 1 applying a rotation $R_{y} (- η)$ on her qubit, then measuring it in the computational basis ${{| 0 〉}_{A_{1}}, {| 1 〉}_{A_{1}}}$ . She but no one else can do that since η is known only to her. Let the

Conclusion

In conclusion, we have proposed perfect performance of controlled JRSP via the quantum channel in terms of a suitably chosen nonmaximally entangled resource $| Q 〉$ of Eq. (2), whose entanglement degree is determined by a single parameter θ. We first construct the quantum circuit to output the state $| Q 〉$ and then present the steps for preparing a quantum state $| ψ 〉$ in the form of Eq. (1) for a remote receiver (Bob) by two preparers (Alice 1 and Alice 2), each of them knows only a partial information

Acknowledgements

This work is supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under project No. 103.01-2014.02.

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View full text

Perfect controlled joint remote state preparation independent of entanglement degree of the quantum channel

Highlights

Abstract

Introduction

Section snippets

The task and the task-oriented quantum channel

Entanglement-degree–independent perfect controlled joint remote state preparation

Conclusion

Acknowledgements

Phys. Lett. A

Opt. Commun.

Quantum Computation and Quantum Information

Phys. Rev. Lett.

Phys. Rev. A

Phys. Rev. A

Phys. Rev. Lett.

J. Phys. B, At. Mol. Opt. Phys.

J. Phys. B, At. Mol. Opt. Phys.

Nature

Int. J. Theor. Phys.

J. Phys. A, Math. Theor.

Quantum Inf. Process.

Phys. Rev. A

Phys. Rev. A

Quantum Inf. Process.

Phys. Scr.

Phys. Rev. A

Phys. Rev. B