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arXiv:quant-ph/0307100 · IEEE Transactions on Information Theory

Remote Preparation of Quantum States

C.H. Bennett, Patrick M. Hayden, Debbie Leung, Peter W. Shor, Andreas Winter

Published Jan 1, 2005• 143 citations
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Abstract

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.

DOI
10.1109/tit.2004.839476

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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.
Abstract—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. Index Terms—Cryptography, entanglement, large deviations, teleportation, tradeoff. I.
Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown quantum state. Remote state preparation (RSP) has the same goal, but the sender knows classically what state is to be transmitted. We show that the asymptotic classical communication cost of RSP is one bit per qubit--half that of teleportation--and even less when transmitting part of a known entangled state. We explore the tradeoff between entanglement and classical communication required for RSP, and discuss RSP capacities of general quantum channels.
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.
We consider the problem of communicating quantum states by simultaneously making use of a noiseless classical channel, a noiseless quantum channel, and shared entanglement. We specifically study the version of the problem in which the sender is given knowledge of the state to be communicated. In this setting, a trade-off arises between the three resources, some portions of which have been investigated previously in the contexts of the quantum-classical trade-off in data compression, remote state preparation, and superdense coding of quantum states, each of which amounts to allowing just two out of these three resources. We present a formula for the triple resource trade-off that reduces its calculation to evaluating the data compression trade-off formula. In the process, we also construct protocols achieving all the optimal points. These turn out to be achievable by trade-off coding and suitable time sharing between optimal protocols for cases involving two resources out of the three mentioned above.
Quantum information theory has revolutionized the way in which information is processed using quantum resources such as entangled states, local operations and classical communications. Two important protocols in quantum communications are quantum teleportation and remote state preparation. In quantum teleportation neither the sender nor the receiver know the identity of a state. In remote state preparation the sender knows the state which is to be remotely prepared without ever physically sending the object or the complete classical description of it. Using one unit of entanglement and one classical bit Alice can remotely prepare a photon (from special ensemble) of her choice at Bob's laboratory. In remote state measurement Alice asks Bob to simulate any single particle measurement statistics on an arbitrary photon. In this talk we will present these ideas and discuss the latest developments and future open problems.
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.