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Science China Information Sciences

Quantum correlations generation and distribution in a universal covariant quantum cloning circuit

Xi-Jun Ren

Published Apr 1, 2017• 1 citation
Publisher
DOI
10.1007/s11432-016-0569-2

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The Variational Quantum Cloning algorithm uses machine learning to obtain through optimization a circuit capable of generating approximate clones from unknown input quantum states. We adapt this algorithm to a boson sampling photonic platform formed exclusively by phase-shifters and beam-splitters, which is not universal but it still allows us to achieve quantum advantage. We have been able to obtain results through simulations reaching optimal fidelities for 1 to 2 universal cloning and also 1 to 2 and 1 to 3 phase-covariant cloning. This project demonstrates the capabilities of this type of photonic platforms and it can be used as a reference to adapt other variational algorithms to them.
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.
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.