Joint Remote Preparation of a Multipartite GHZ-class State

Abstract

For two parties sharing the original state, a scheme for remote preparation of the two-particle entangled state by three partial two-particle entangled states as the quantum channel is presented, and then directly generalize the scheme for remotely preparing a multipartite GHZ-class state for M senders. It is shown that the receiver can obtain the unknown state with certain probability under the condition that only and only if all the senders collaborate with each other. The N -particle projective measurement and the von Neumann measurement are needed in our scheme. The probability of the successful remote state preparation and classical communication cost are calculated.

Deterministic Joint Remote Preparation of an Arbitrary Qubit via Einstein-Podolsky-Rosen Pairs

“…Using (20) and (21) in (12)- (15) we see that, conditioned on the outcomes klm, Charlie's qubit C would collapse, up to a global phase factor, into a certain state labeled | klm C , all of which are collected in Table 1.…”

“…As a per se feature of RSP, the preparer knows the full information encoded in the to-be-prepared quantum state, that may appear unwanted in some circumstances. To avoid this feature, joint remote state preparation (JRSP) protocols [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] have recently been designed, in which there are N ≥ 2 preparers [19], who jointly perform the task but no one among them is able to identify the full content of the encoded information. Experimental architecture of JRSP has also been dealt with in Ref.…”

Nonmaximal Entanglement Can Make Joint Remote State Preparation Absolutely Secure

“…For example, if the coefficients of the state to be prepared are all real or for an ensemble of some special states, the measurement bases for the preparers may be simplified so as to significantly increase the success probability [20]. Existing protocols for JRSP of multiqubit states [21] can also be made absolutely secure with resort to the strategy of using nonmaximal entanglement combined with proper information splitting as described in this paper.…”

“…JRSP is an interesting multiparty quantum task that has recently attracted attention in the quantum information community from both theoretical [12][13][14][15][16][17][18][19][20][21] and experimental architecture [22] points of view. In contrast to the well-known remote state preparation (RSP) [23] in which one party has complete classical knowledge of a quantum state |Ψ to be faithfully prepared at a remote party's location, in JRSP there are several inferiors who are assigned by a superior to jointly prepare the state |Ψ for a remote receiver.…”

“…So the superior can secretly split the information of the state |Ψ into pieces each of which is given to an inferior to exclude leakage of full information about |Ψ to any of the inferiors. Both maximally and nonmaximally entangled states have been used as the quantum channel for JRSP and the security level of all the existing protocols [12][13][14][15][16][17][18][19][20][21][22] is that any subgroup of the inferiors cannot exactly identify the state |Ψ but all the inferiors together can. Like in blind quantum computation [24], it is highly desirable also for JRSP to have absolute security in the sense that neither an individual nor the entire group of the participants (i.e., all the inferiors plus the receiver) can precisely infer the sate |Ψ .…”