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arXiv:quant-ph/0410190

Remote state preparation using non-maximally entangled states

Lin Chen, Yixin Chen

Published Oct 25, 2004• 0 citations
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Abstract

We present a scheme in which any pure qubit $|ϕ=\cosθ|0+\sinθe^{i\varp hi}|1$ could be remotely prepared by using minimum classical bits and the previously shared non-maximally entangled states, on condition that the receiver holds the knowledge of $θ$. Several methods are available to check the trade-off between the necessary entanglement resource and the achievable fidelity.

DOI
10.48550/arxiv.quant-ph/0410190

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In a process of remote state preparation, the universality of quantum channel is an essential ingredient. That is, one quantum channel should be feasible to remotely prepare any given qubit state. This problem appears in a process where one uses non-maximally entangled state as the passage. We present a scheme in which any given qubit |ϕ⟩ = cos θ|0⟩+sin θ e i φ |1⟩ could be remotely prepared by using minimum classical bits and the previously shared non-maximally entangled state with a high fidelity, under the condition that the receiver holds the knowledge of θ. This condition is helpful to reduce the necessary amount of quantum channels, which is proven to be a low quantity to realize the universality. We also give several methods to investigate the trade-off between this amount and the achievable fidelity of the protocol.
We propose a deterministic remote state preparation scheme for photon polarization qubit states, where entanglement, local operations, and classical communication are used. By consuming one maximally entangled state and two classical bits, an arbitrary (either pure or mixed) qubit state can be prepared deterministically at a remote location. We experimentally demonstrate the scheme by remotely preparing 121212 pure states and 666 mixed states. The fidelities between the desired and achieved states are all higher than 0.990.990.99 and have an average of 0.99470.99470.9947.
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We present many ensembles of states that can be remotely prepared by using minimum classical bits from Alice to Bob and their previously shared entangled state and prove that we have found all the ensembles in two-dimensional case. Furthermore we show that any pure quantum state can be remotely and faithfully prepared by using finite classical bits from Alice to Bob and their previously shared nonmaximally entangled state though no faithful quantum teleportation protocols can be achieved by using a nonmaximally entangled state.
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We introduce a multipartite communication scheme, with the aim to enable the senders to remotely and obliviously provide the receivers with an arbitrary amount of multipartite entanglement. The scheme is similar to remote state preparation (RSP). However, we show that even though the receivers are restricted to local unitary operations, the required resources for remote entanglement preparation are less than for RSP. In order to do so we introduce a canonical form of arbitrary multipartite pure states describing an arbitrary number of qubits. Moreover, we show that if the receivers are enabled to perform arbitrary local operations and classical communication, the required resources can drastically be reduced. We employ this protocol to derive robust entanglement purification protocols for arbitrary pure states and show that it can also be used for sending classical information.