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European Quantum Electronics Conference (EQEC)

Asymmetric universal entangling machine

D. B. Horoshko, S. Ya. Kilin, Mikhail I. Kolobov

Published Jan 18, 2006• 0 citations
Publisher

Abstract

This paper proves the existence of universal quantum machine and deduce the entangling transformation of the optimal one for a d-level system S and a d/sup 2/-level ancilla A. The introduced machine turns out to be a generalization to a number of widely investigated universal quantum devices such as the symmetric and asymmetric quantum cloners, the symmetric quantum entangler, the quantum information distributor and the universal-NOT gate.

DOI
10.1109/eqec.2005.1567486

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This paper proves the existence of universal quantum machine and deduce the entangling transformation of the optimal one for a d-level system S and a d/sup 2/-level ancilla A. The introduced machine turns out to be a generalization to a number of widely investigated universal quantum devices such as the symmetric and asymmetric quantum cloners, the symmetric quantum entangler, the quantum information distributor and the universal-NOT gate.
We give a definition of an asymmetric universal entangling machine which entangles a system in an unknown state to a specially prepared ancilla. The machine produces a fixed state-independent amount of entanglement in exchange for a fixed degradation of the system state fidelity. We describe explicitly such a machine for any quantum system having d levels and prove its optimality. We show that a d 2-dimensional ancilla is sufficient for reaching optimality. The introduced machine is a generalization to a number of widely investigated universal quantum devices such as the symmetric and asymmetric quantum cloners, the symmetric and antisymmetric quantum entanglers, the quantum information distributor and the universal-NOT gate.
We present a unified universal quantum cloning machine, which combines several different existing universal cloning machines together, including the asymmetric case. In this unified framework, the identical pure states are projected equally into each copy initially constituted by input and one half of the maximally entangled states. We show explicitly that the output states of those universal cloning machines are the same. One importance of this unified cloning machine is that the cloning procession is always the symmetric projection, which reduces dramatically the difficulties for implementation. Also, it is found that this unified cloning machine can be directly modified to the general asymmetric case. Besides the global fidelity and the single-copy fidelity, we also present all possible arbitrary-copy fidelities.
We show that for any Hilbert-space dimension, the optimal $\stackrel{\ensuremath{\rightarrow}}{1}2$ universal quantum cloner can be constructed from essentially the same quantum circuit, i.e., we find a universal design for universal cloners. In the case of infinite dimensions (which includes continuous variable quantum systems) the universal cloner reduces to an essentially classical device. More generally, we construct a universal quantum circuit for distributing qudits in any dimension which acts covariantly under generalized displacements and momentum kicks. The behavior of this covariant distributor is controlled by its initial state. We show that suitable choices for this initial state yield both universal cloners and optimized cloners for limited alphabets of states related by generalized phase-space displacements.