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Acta Sinica Quantum Optica

Quantum Cloning of Continuous-variable Entangled States

Jiangrui Gao

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

In this paper,we discuss the asymmetric cloning process of continuous variable entangled states.By changing the reflectivity of both beam splitters,we theoretically analyze the entanglement properties of the output entangled states of the Local e-cloner using the CV entanglement criteria.It is shown that the entanglement degrees of two cloned entangled states are different.

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Journal of Physics B Atomic Molecular and Optical Physics•Nov 3, 2014•7 citations
In this paper,we discuss the asymmetric cloning process of continuous variable entangled states.By changing the reflectivity of both beam splitters,we theoretically analyze the entanglement properties of the output entangled states of the Local e-cloner using the CV entanglement criteria.It is shown that the entanglement degrees of two cloned entangled states are different.
We consider the quantum cloning of continuous variable entangled states. This is achieved by introducing two symmetric entanglement cloning machines (or eee-cloners): a local eee-cloner and a global eee-cloner; where we look at the preservation of entanglement in the clones under the condition that the fidelity of the clones is maximized. These cloning machines are implemented using simple linear optical elements such as beam splitters and homodyne detection along with squeeze gates. We show that the global eee-cloner out-performs the local eee-cloner both in terms of the fidelity of the cloned states as well as the strength of the entanglement of the clones. There is a minimum strength of entanglement (3 dB using the inseparability criterion) of the input state of the global eee-cloner that is required to preserve the entanglement in the clones.
We extend the technique of conditional preparation to a quantum cloning machine, and present a protocol of 1 → 2 conditional cloning of squeezed state and entanglement states. It is shown that the entanglement degree of the cloned entangled states can be well preserved even when the fidelity between the input and output states is beyond the limit of 4/9. This scheme is practicable since only the linear elements of beam splitters, homodyne detections, optical modulations and electrical trigger system, are involved.
Cloning machines, that is, transformations that achieve the best approximate copying of a quantum state compatible with the no-cloning theorem, have been a fundamental research topic over the last five years. This study is of particular significance given the close connection between quantum cloning and quantum cryptography: using an optimal cloner generally makes it possible to obtain a tight bound on the best individual eavesdropping strategy in a quantum cryptosystem. In this Chapter, the issue of cloning a continuous-variable quantum system will be analyzed, and a Gaussian cloning transformation will be introduced. This cloner, which copies equally well any two canonically conjugate continuous variables, duplicates all coherent states with a same fidelity (F=2/3). The optical implementation of this cloner and its extension to N-to-M cloners will also be discussed. Finally, the use of this cloner for the security assessment of a quantum key distribution scheme relying on continuous (Gaussian) key carriers will be sketched.
We analyze a reversibility of optimal Gaussian $\stackrel{\ensuremath{\rightarrow}}{1}2$ quantum cloning of a coherent state using only local operations on the clones and classical communication between them and propose a feasible experimental test of this feature. Performing Bell-type homodyne measurement on one clone and anticlone, an arbitrary unknown input state (not only a coherent state) can be restored in the other clone by applying appropriate local unitary displacement operation. We generalize this concept to a partial reversal of the cloning using only local operations and classical communication (LOCC) and we show that this procedure converts the symmetric cloner to an asymmetric cloner. Further, we discuss a distributed LOCC reversal in optimal $\stackrel{\ensuremath{\rightarrow}}{1}M$ Gaussian cloning of coherent states which transforms it to optimal $\stackrel{\ensuremath{\rightarrow}}{1}{M}^{\ensuremath{'}}$ cloning for ${M}^{\ensuremath{'}}<M.$ Assuming the quantum cloning as a possible eavesdropping attack on quantum communication link, the reversibility can be utilized to improve the security of the link even after the attack.
Continuous variable entanglement can be produced in nonlinear systems or via the interference of squeezed states. In many optical systems such as parametric down conversion, the production of two perfectly symmetric subsystems is usually assumed when demonstrating the existence of entanglement. This symmetry simplifies the description of entanglement. However, asymmetry in entanglement may arise naturally in a real experiment, or be intentionally introduced in a given quantum information protocol. These asymmetries can emerge from having the output beams experience different losses and environmental contamination, or from the availability of non-identical input quantum states in quantum communication protocols. In this paper, we present a visualization of entanglement using quadrature amplitude plots of the twin beams. We quantitatively discuss the strength of asymmetric entanglement using EPR and inseparability criteria and theoretically show that the optimal beamsplitter ratio for entanglement is dependent on the asymmetries and may not be 50 : 50. To support this theory, we present experimental results showing one particular asymmetric entanglement where a 78 : 22 beamsplitter is optimal for observing entanglement.