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International Journal of Quantum Information

EXACT REMOTE STATE PREPARATION FOR MULTIPARTIES USING DARK STATES

Pankaj Agrawal, Preeti Parashar, Arun Kumar Pati

Published Sep 1, 2003• 26 citations
Publisher

Abstract

We discuss the exact remote state preparation (RSP) protocol of special ensembles of qubits at multiple locations. Generalization of this protocol for higher dimensional Hilbert space systems for multiparties is also presented. Using the "dark states", for multiparties in higher dimensions as quantum channels, we show several instances of remote state preparation protocol using multiparticle measurement and classical communication. We find that not all dark states can be used for exact remote state preparation, nevertheless any superposition of dark states can be used for exact RSP in a probabilistic manner.

DOI
10.1142/s0219749903000243

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We discuss the exact remote state preparation (RSP) protocol of special ensembles of qubits at multiple locations. Generalization of this protocol for higher dimensional Hilbert space systems for multiparties is also presented. Using the "dark states", for multiparties in higher dimensions as quantum channels, we show several instances of remote state preparation protocol using multiparticle measurement and classical communication. We find that not all dark states can be used for exact remote state preparation, nevertheless any superposition of dark states can be used for exact RSP in a probabilistic manner.
Remote state preparation (RSP) is a technique to transmit quantum states with classical communication and previously shared entanglement. In this paper, we consider RSP in a multiparty setting. A simple yet nontrivial case is studied, where there is one sender and two receivers. We put forth a broadcasting method for developing multiparty RSP protocols. We show that this method can remotely prepare arbitrary states by consuming classical and quantum resources. For preparing highly entangled states, the proposed method achieves the lower bound for the amount of consumed resources asymptotically.
A single photon in a superposition of ddd modes naturally encode a ddd-dimensional quantum system, a so-called qudit. We show that such superpositions can be leveraged to achieve a quantum speed-up of remote remote state preparation (RSP): a primitive for several quantum network protocols. For a superposition over d≥2d\geq 2d≥2 modes, the photon state can encode up to Log2(d){\rm Log}_2(d)Log2​(d) qubits, which we exploit in a proposed reflection based RSP protocol with multiple variations. For single qubit RSP, we achieve a performance comparable to the best known existing schemes but with reduced requirements for phase stabilization. For many qubit RSP the achievable success rates remain high despite needing exponentially many temporal modes, since only one photon needs to be transmitted and detected to prepare multiple qubits. By simultaneously preparing many qubits at once, we bypass limited qubit lifetimes limited qubit lifetimes and improve fidelities beyond what is achievable with existing RSP protocols.
We extend exact deterministic remote state preparation (RSP) with minimal classical communication to quantum systems of continuous variables. We show that, in principle, it is possible to remotely prepare states of an ensemble that is parametrized by infinitely many real numbers---i.e., by a real function---while the classical communication cost is one real number only. We demonstrate continuous variable RSP in three examples using (i) quadrature measurement and phase-space displacement operations, (ii) measurement of the optical phase and unitaries shifting the same, and (iii) photon counting and photon number shift.
We characterize the class of remote state preparation (RSP) protocols that use only forward classical communication and entanglement, deterministically prepare an exact copy of a general state, and do so obliviously-without leaking further information about the state to the receiver. We prove that any such protocol can be modified to require from the sender only a single specimen of the state, without increasing the classical communication cost. This implies Lo's conjectured lower bound on the cost for these protocols. We relate our RSP protocols to the private quantum channels and establish a one-to-one correspondence between them.
Known quantum pure states of a qudit can be remotely prepared onto a group of particles of qubits exactly or probabilistically with the aid of two-level Einstein--Podolsky--Rosen states. We present a protocol for such kind of remote state preparation. We are mainly focused on the remote preparation of the ensembles of equatorial states and those of states in real Hilbert space. In particular, a kind of states of qudits in real Hilbert space have been shown to be remotely prepared in faith without the limitation of the input space dimension.