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Journal of Physics B Atomic Molecular and Optical Physics

Joint remote preparation of a general two-qubit state

Nguyen Ba An

Published May 26, 2009• 115 citations
Publisher

Abstract

We propose a set of novel protocols to remotely prepare a general two-qubit state by joint actions of two separate people who independently share the classical knowledge of the state, without and with quantum control of a supervisor. Various quantum resources are used as the quantum channel. Although the execution complexity differs for different protocols, the total success probability is protocol independent.

DOI
10.1088/0953-4075/42/12/125501

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We propose a set of novel protocols to remotely prepare a general two-qubit state by joint actions of two separate people who independently share the classical knowledge of the state, without and with quantum control of a supervisor. Various quantum resources are used as the quantum channel. Although the execution complexity differs for different protocols, the total success probability is protocol independent.
Designing quantum protocols with unit success probability is highly desirable from a viewpoint of the overall resource cost. In this work, we propose a new deterministic protocol for joint remote preparation of the most general two-qubit state using the same quantum/classical resource as in [An et al., Phys. Lett. A {\bf 375} (2011) 3570] and, at the same time, retaining the passive role of the receiver as in [Xiao et al., J. Phys. B: At. Mol. Opt. Phys. {\bf 44} (2011) 075501], which employs a different kind of nonlocal resource. From a practical point of view, this protocol proves most suitable in situations when only Einstein- Podelsky-Rosen pairs are supplied and the receiver is not capable of performing any measurements nor controlled-NOT gates.
Transferring a quantum state from one location to another without physically sending the state itself through open space is a special global task that can only be carried out thanks to the laws of nature, namely the principles of quantum mechanics. In this work, we devise protocols for two senders to jointly prepare the most general two-qubit state for a receiver under the supervision of a controller by using three different types of quantum channels, all of which are non-maximally entangled. First, we propose the schemes to produce the quantum channels concerned, and then we present the concrete steps required to execute the protocols, highlighting the issue of why shared non-maximal entanglement is intentionally used instead of maximal entanglement.
The protocols for controlled remote state preparation of a single qubit and a general two-qubit state are presented in this paper. The general pure three-qubit states are chosen as shared quantum channel, which are not Local operations and classical communication (LOCC) equivalent to the mostly used GHz state. This is the first time that general pure three-qubit states have been introduced to complete remote state preparation. The probability of successful preparation is presented. Moreover, in some special cases, the successful probability could reach a unit value.
By joint actions of two separate two-qubit projective measurements, I present a new protocol for remotely preparing a two-qubit state via the shared three bipartite entanglements. The success probability and the classical communication cost are also minutely calculated. Then I concisely generalize it to multi-party case and multi-qubit state case, respectively. In contrast to the previous schemes [Int. J. Theor. Phys.48 (2009) 2005; Int. J. Theor. Phys.46 (2007) 2378; Commun. Theor. Phys.47 (2007) 247], this protocol has distinct advantages overwhelming the above ones as far as quantum resource consumption and quantum operation difficulty or intensity are concerned.
We show that any M ≥ 2 distant parties who independently share the complete classical knowledge of a secret qubit state can collectively prepare the state at another remote location. Two distinct schemes for such a task are proposed: one via a single (M + 1)-partite GHZ-type state and the other via M EPR-type pairs. Analytical expressions of the total success probability are derived explicitly for both the schemes. Of interest is the M-dependence of both the success probability and the receiver's action. We also construct simple quantum circuits for the two-qubit operators whose execution is necessary to accomplish the schemes.