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arXiv:1608.02698 · IEEE Conference on Decision and Control (CDC)

Pure Gaussian quantum states from passive Hamiltonians and an active local dissipative process

Shan Ma, Matthew J. Woolley, Ian R. Petersen, Naoki Yamamoto

Published Dec 1, 2016• 7 citations
arXivHTMLPDF

Abstract

We investigate the problem of preparing a pure Gaussian state via reservoir engineering. In particular, we consider a linear quantum system with a passive Hamiltonian and with a single reservoir which acts only on a single site of the system. We then give a full parametrization of the pure Gaussian states that can be prepared by this type of quantum system.

DOI
10.1109/cdc.2016.7798640

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We investigate the problem of preparing a pure Gaussian state via reservoir engineering. In particular, we consider a linear quantum system with a passive Hamiltonian and with a single reservoir which acts only on a single site of the system. We then give a full parametrization of the pure Gaussian states that can be prepared by this type of quantum system.
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This paper provides some necessary and sufficient conditions for a general Markovian Gaussian master equation to have a unique pure steady state. The conditions are described by simple matrix equations; thus the so-called environment engineering problem for pure-Gaussian-state preparation can be straightforwardly dealt with in the linear algebraic framework. In fact, based on one of those conditions, for an arbitrary given pure Gaussian state, we obtain a complete parametrization of the Gaussian master equation having that state as a unique steady state; this leads to a systematic procedure for engineering a desired dissipative system. We demonstrate some examples including Gaussian cluster states.
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