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arXiv · 2012.00736

Infinite-Dimensional Programmable Quantum Processors

Martina Gschwendtner·Andreas Winter
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Abstract

A universal programmable quantum processor uses program quantum states to apply an arbitrary quantum channel to an input state. We generalize the concept of a finite-dimensional programmable quantum processor to infinite dimension assuming an energy constraint on the input and output of the target quantum channels. By proving reductions to and from finite-dimensional processors, we obtain upper and lower bounds on the program dimension required to approximately implement energy-limited quantum channels. In particular, we consider the implementation of Gaussian channels. Due to their practical relevance, we investigate the resource requirements for gauge-covariant Gaussian channels. Additionally, we give upper and lower bounds on the program dimension of a processor implementing all Gaussian unitary channels. These lower bounds rely on a direct information-theoretic argument, based on the generalization from finite to infinite dimension of a certain replication lemma for unitaries.

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Martina Gschwendtner, Andreas Winter. 2020-12-01. Infinite-Dimensional Programmable Quantum Processors. https://doi.org/10.1103/prxquantum.2.030308

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