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Quantum Information Processing

A scheme for remote state preparation of a general pure qubit with optimized classical communication cost

Congyi Hua, Yi-Xin Chen

Published Dec 10, 2014• 14 citations
Publisher
DOI
10.1007/s11128-014-0897-5

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How to uses shared entanglement and forward classical communication to remotely prepare an arbitrary (mixed or pure) state has been fascinating quantum information scientists. A constructive scheme has been given by Berry for remotely preparing a general pure state with a pure entangled state and finite classical communication. Based on this scheme, for high-dimensional systems it is possible to use a coding of the target state to optimize the classical communication cost. Unfortunately, for low-dimensional systems such as a pure qubit the coding method is inapplicable. Because qubit plays a central role in quantum information theory, we propose an optimization procedure which can be used to minimize the classical communication cost in the remote preparation of a general pure qubit. Interestingly, our optimization procedure is linked to the uniform arrangement of $N$ points on the Bloch sphere, which provides a geometric description.

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Optimizing scheme for probabilistic remote preparation of a two-qubit state

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We study the following task: Alice is given a classical description of a rank-kkk projector PPP on Cd\mathbb{C}^dCd, and Alice and Bob want to prepare the quantum state P/kP/kP/k on Bob's side using shared entanglement and classical communication. The general form of this task is known as remote state preparation (RSP). We give nearly-matching lower and upper bounds for the entanglement cost and communication cost for RSP of the states P/kP/kP/k. Ours are the first nearly matching upper and lower bounds for RSP of mixed states, and in the special case of pure states, our lower bound outperforms the best previously known lower bound. Our results show that any pure entangled state that can be used to do RSP of these states with o(d)o(d)o(d) bits of communication, can distill log⁡d\log dlogd ebits of entanglement, and conversely, any state that can distill log⁡d\log dlogd ebits of entanglement can be used to do RSP of these states efficiently. As applications of our results, we rederive a previously-known incompressibility result for states of the form P/kP/kP/k, and give a new entanglement-assisted communication protocol for the equality function that uses 12log⁡n+O(1)\frac{1}{2}\log n + O(1)21​logn+O(1) many ebits, and O(1)O(1)O(1) communication.
How to uses shared entanglement and forward classical communication to remotely prepare an arbitrary (mixed or pure) state has been fascinating quantum information scientists. A constructive scheme has been given by Berry for remotely preparing a general pure state with a pure entangled state and finite classical communication. Based on this scheme, for high-dimensional systems it is possible to use a coding of the target state to optimize the classical communication cost. Unfortunately, for low-dimensional systems such as a pure qubit the coding method is inapplicable. Because qubit plays a central role in quantum information theory, we propose an optimization procedure which can be used to minimize the classical communication cost in the remote preparation of a general pure qubit. Interestingly, our optimization procedure is linked to the uniform arrangement of NNN points on the Bloch sphere, which provides a geometric description.