Although the no-cloning theorem forbids perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superre...Although the no-cloning theorem forbids perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can occur for both quantum states and quantum gates. The aim of this paper is to review the central features of quantum superreplication and provide a unified view of existing results. The paper also includes new results. In particular, we show that when quantum superreplication can be achieved, it can be achieved through estimation up to an error of size O（M/N2）, where N and M are the number of input and output copies, respectively. Quantum strategies still offer an advantage for superreplication in that they allow for exponentially faster reduction of the error. Using the relation with estimation, we provide i） an alternative proof of the optimality of Heisenberg scaling in quantum metrology, ii） a strategy for estimating arbitrary unitary gates with a mean square error scaling as log N/N2, and iii） a protocol that generates O（N2） nearly perfect copies of a generic pure state U｜0） while using the corresponding gate U only N times. Finally, we point out that superreplication can be achieved using interactions among k systems, provided that k is large compared to M2/N2.展开更多
This paper considers the problem of constructing a direct coupling quantum observer for a closed linear quantum system. The proposed distributed observer consists of a network of quantum harmonic oscillators and it is...This paper considers the problem of constructing a direct coupling quantum observer for a closed linear quantum system. The proposed distributed observer consists of a network of quantum harmonic oscillators and it is shown that the observer network converges to a consensus in a time averaged sense in which each element of the observer estimates the specified output of the quantum plant. An example and simulations are included to illustrate the properties of the observer network.展开更多
In this paper, we propose an entanglement scheme for long-distance, constant-fidelity communication in quantum networks. We discuss the optimal rate of entanglement that allows for constant fidelity in both elementary...In this paper, we propose an entanglement scheme for long-distance, constant-fidelity communication in quantum networks. We discuss the optimal rate of entanglement that allows for constant fidelity in both elementary and muhihop links. We also discuss time complexity and propose the mathematical order of the rate capacity for an entanglement scheme. We propose a recursive entanglement scheme, a simultaneous entanglement scheme, and an adjacent entanglement scheme mathematically analyze these schemes. The rate capacity of the recursive and simultaneous entanglement schemes is Ω（1/e^n）, but the adjacent entanglement scheme performs better, providing a rate of lΩ（1/n）.展开更多
文摘Although the no-cloning theorem forbids perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can occur for both quantum states and quantum gates. The aim of this paper is to review the central features of quantum superreplication and provide a unified view of existing results. The paper also includes new results. In particular, we show that when quantum superreplication can be achieved, it can be achieved through estimation up to an error of size O（M/N2）, where N and M are the number of input and output copies, respectively. Quantum strategies still offer an advantage for superreplication in that they allow for exponentially faster reduction of the error. Using the relation with estimation, we provide i） an alternative proof of the optimality of Heisenberg scaling in quantum metrology, ii） a strategy for estimating arbitrary unitary gates with a mean square error scaling as log N/N2, and iii） a protocol that generates O（N2） nearly perfect copies of a generic pure state U｜0） while using the corresponding gate U only N times. Finally, we point out that superreplication can be achieved using interactions among k systems, provided that k is large compared to M2/N2.
文摘This paper considers the problem of constructing a direct coupling quantum observer for a closed linear quantum system. The proposed distributed observer consists of a network of quantum harmonic oscillators and it is shown that the observer network converges to a consensus in a time averaged sense in which each element of the observer estimates the specified output of the quantum plant. An example and simulations are included to illustrate the properties of the observer network.
文摘In this paper, we propose an entanglement scheme for long-distance, constant-fidelity communication in quantum networks. We discuss the optimal rate of entanglement that allows for constant fidelity in both elementary and muhihop links. We also discuss time complexity and propose the mathematical order of the rate capacity for an entanglement scheme. We propose a recursive entanglement scheme, a simultaneous entanglement scheme, and an adjacent entanglement scheme mathematically analyze these schemes. The rate capacity of the recursive and simultaneous entanglement schemes is Ω（1/e^n）, but the adjacent entanglement scheme performs better, providing a rate of lΩ（1/n）.
