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arXiv:1003.0831 · Physical Review A

Resilience to decoherence of the macroscopic quantum superpositions generated by universally covariant optimal quantum cloning

Nicolò Spagnolo, Fabio Sciarrino, F. De Martini

Published Sep 27, 2010• 5 citations
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Abstract

We show that the quantum states generated by universal optimal quantum cloning of a single photon represent a universal set of quantum superpositions resilient to decoherence. We adopt the Bures distance as a tool to investigate the persistence of quantum coherence of these quantum states. According to this analysis, the process of universal cloning realizes a class of quantum superpositions that exhibits a covariance property in lossy configuration over the complete set of polarization states in the Bloch sphere.

DOI
10.1103/physreva.82.032325

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We show that the quantum states generated by universal optimal quantum cloning of a single photon represent a universal set of quantum superpositions resilient to decoherence. We adopt the Bures distance as a tool to investigate the persistence of quantum coherence of these quantum states. According to this analysis, the process of universal cloning realizes a class of quantum superpositions that exhibits a covariance property in lossy configuration over the complete set of polarization states in the Bloch sphere.
It is known that in phase-covariant quantum cloning, the equatorial states on the Bloch sphere can be cloned with a fidelity higher than the optimal bound established for universal quantum cloning. We generalize this concept to include other states on the Bloch sphere with a definite z component of spin. It is shown that once we know the z component, we can always clone a state with a fidelity higher than the universal value and that of equatorial states. We also make a detailed study of the entanglement properties of the output copies and show that the equatorial states are the only states that give rise to a separable density matrix for the outputs.
The high resilience to decoherence shown by a recently discovered macroscopic quantum superposition (MQS) generated by a quantum-injected optical parametric amplifier and involving a number of photons in excess of $5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ motivates the present theoretical and numerical investigation. The results are analyzed in comparison with the properties of the MQS based on $|\ensuremath{\alpha}⟩$ and N-photon maximally entangled states (NOON), in the perspective of the comprehensive theory of the subject by Zurek. In that perspective the concepts of ``pointer state'' and ``environment-induced superselection'' are applied to the new scheme.
We investigate the multiparticle quantum superposition and the persistence of bipartite entanglement of the output field generated by the quantum injected high-gain optical parametric amplification of a single photon. The physical configuration based on the optimal universal quantum cloning has been adopted to investigate how the entanglement and the quantum coherence of the system persists for large values of the nonlinear parametric gain ggg.