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arXiv:0904.4316 · Physical Review Letters

Anomalous Lack of Decoherence of the Macroscopic Quantum Superpositions Based on Phase-Covariant Quantum Cloning

F. De Martini, Fabio Sciarrino, Nicolò Spagnolo

Published Sep 1, 2009• 16 citations
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Abstract

We show that all macroscopic quantum superpositions (MQS) based on phase-covariant quantum cloning are characterized by an anomalous high resilence to the decoherence processes. The analysis supports the results of recent MQS experiments and leads to conceive a useful conjecture regarding the realization of complex decoherence-free structures for quantum information, such as the quantum computer.

DOI
10.1103/physrevlett.103.100501

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We show that all macroscopic quantum superpositions (MQS) based on phase-covariant quantum cloning are characterized by an anomalous high resilence to the decoherence processes. The analysis supports the results of recent MQS experiments and leads to conceive a useful conjecture regarding the realization of complex decoherence-free structures for quantum information, such as the quantum computer.
The high resilience to de-coherence shown by a recently discovered Macroscopic Quantum Superposition (MQS) involving a number of photons in excess of 5 x 10^4 motivates the present theoretical and numerical investigation. The results are placed in close comparison with the properties of the well known MQS based on |alpha> states. The very critical decoherence properties of the latter MQS are found to be fully accounted for, in a direct a simple way, by a unique "universal" function: indeed a new property of the quantum "coherent states".
It is known that a macroscopic quantum superposition (MQS), when it is exposed to an environment, decoheres at a rate scaling with the separation of its component states in phase space. This is more or less consistent with the well-known proposition that a more macroscopic quantum state is reduced more quickly to a classical state in general. Effects of initial mixedness, however, on the subsequent decoherence of MQSs have been less known. We study the evolution of a highly mixed MQS interacting with an environment and compare it with that of a pure MQS having the same size as the central distance between its component states. Although the decoherence develops more rapidly for the mixed MQS in short times, its rate can be significantly suppressed after a certain time and becomes smaller than the decoherence rate of its corresponding pure MQS. In an optics experiment to generate a MQS, our result has the practical implication that nonclassicality of a MQS can still be observable in moderate times, even though a large amount of noise is added to the initial state.
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.
This work reports on an extended research endeavor focused on the theoretical and experimental realization of a macroscopic quantum superposition (MQS) made up of photons. This intriguing, fundamental quantum condition is at the core of a famous argument conceived by Schr\"odinger in 1935. The main experimental challenge to the actual realization of this object resides generally in unavoidable and uncontrolled interactions with the environment, i.e., ``decoherence,'' leading to the cancellation of any evidence of the quantum features associated with the macroscopic system. The present scheme is based on a nonlinear process, ``quantum-injected optical parametric amplification,''which, by a linearized cloning process maps the quantum coherence of a single-particle state, i.e., a microqubit, onto a macroqubit consisting of a large number MMM of photons in quantum superposition. Since the adopted scheme was found resilient to decoherence, a MQS demonstration was carried out experimentally at room temperature with $M\ensuremath{\ge}{10}^{4}$. The result led to an extended study of quantum cloning, quantum amplification, and quantum decoherence. The related theory is outlined and several experiments are reviewed, such as the test of the ``no-signaling theorem'' and the dynamical interaction of the photon MQS with a Bose-Einstein condensate. In addition, the consideration of the microqubit-macroqubit entanglement regime is extended to macroqubit-macroqubit conditions. The MQS interference patterns for large MMM are revealed in the experiment and bipartite microqubit-macroqubit entanglement was also demonstrated for a limited number of generated particles: $M\ensuremath{\precsim}12$. Finally, the perspectives opened by this new method for further studies on quantum foundations and quantum measurement are considered.
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.