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arXiv:quant-ph/0304006

Exact remote state preparation for multiparties

Pankaj Agrawal, Preeti Parashar, Arun Kumar Pati

Published Apr 1, 2003• 4 citations
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Abstract

We discuss the exact remote state preparation protocol of special ensembles of qubits at multiple locations. We also present generalization of this protocol for higher dimensional Hilbert space systems for multiparties. Using the `dark states', the analogue of singlet EPR pair for multiparties in higher dimension as quantum channel, we show several instances of remote state preparation protocol using multiparticle measurement and classical communication.

DOI
10.48550/arxiv.quant-ph/0304006

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We discuss the exact remote state preparation protocol of special ensembles of qubits at multiple locations. We also present generalization of this protocol for higher dimensional Hilbert space systems for multiparties. Using the `dark states', the analogue of singlet EPR pair for multiparties in higher dimension as quantum channel, we show several instances of remote state preparation protocol using multiparticle measurement and classical communication.
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.
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.
We present a two-step deterministic remote state preparation protocol for an arbitrary quhit with the aid of a three-particle Greenberger—Horne—Zeilinger state. Generalization of this protocol for higher-dimensional Hilbert space systems among three parties is also given. We show that only single-particle von Neumann measurements, local operations, and classical communication are necessary. Moreover, since the overall information of the quantum state can be divided into two different pieces, which may be at different locations, this protocol may be useful in the quantum information field.
Remote state preparation is the variant of quantum state teleportation in which the sender knows the quantum state to be communicated. The original paper introducing teleportation established minimal requirements for classical communication and entanglement but the corresponding limits for remote state preparation have remained unknown until now: previous work has shown, however, that it not only requires less classical communication but also gives rise to a tradeoff between these two resources in the appropriate setting. We discuss this problem from first principles, including the various choices one may follow in the definitions of the actual resources. Our main result is a general method of remote state preparation for arbitrary states of many qubits, at a cost of 1 bit of classical communication and 1 bit of entanglement per qubit sent. In this "universal" formulation, these ebit and cbit requirements are shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then yields the exact tradeoff curve for memoryless sources of pure states (including the case of incomplete knowledge of the ensemble probabilities), based on the recently established quantum-classical tradeoff for visible quantum data compression. A variation of that method allows us to solve the even more general problem of preparing entangled states between sender and receiver (i.e., purifications of mixed state ensembles). The paper includes an extensive discussion of our results, including the impact of the choice of model on the resources, the topic of obliviousness, and an application to private quantum channels and quantum data hiding.