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arXiv:1408.2290 · The proceedings of the IEEE Conference on Control Applications/The proceedings of the ... IEEE Conference on Control Applications

Preparation of pure Gaussian states via cascaded quantum systems

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

Published Oct 1, 2014• 12 citations
arXivHTMLPDF

Abstract

This paper provides an alternative approach to the problem of preparing pure Gaussian states in a linear quantum system. It is shown that any pure Gaussian state can be generated by a cascade of one-dimensional open quantum harmonic oscillators, without any direct interaction Hamiltonians between these oscillators. This is physically advantageous from an experimental point of view. An example on the preparation of two-mode squeezed states is given to illustrate the theory.

DOI
10.1109/cca.2014.6981592

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This paper provides an alternative approach to the problem of preparing pure Gaussian states in a linear quantum system. It is shown that any pure Gaussian state can be generated by a cascade of one-dimensional open quantum harmonic oscillators, without any direct interaction Hamiltonians between these oscillators. This is physically advantageous from an experimental point of view. An example on the preparation of two-mode squeezed states is given to illustrate the theory.
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Recently, it has been demonstrated that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simpler one degree of freedom quantum harmonic oscillators together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental point of view, realizations by pure cascading, without a direct interaction Hamiltonian, would be much simpler to implement and this raises the natural question of what class of linear quantum stochastic systems are realizable by cascading alone. This paper gives a precise characterization of this class of linear quantum stochastic systems and then it is proved that, in the weaker sense of transfer function realizability, all passive linear quantum stochastic systems belong to this class. A constructive example is given to show the transfer function realization of a two degrees of freedom passive linear quantum system by pure cascading.
This paper is concerned with the generation of Gaussian invariant states in cascades of open quantum harmonic oscillators governed by linear quantum stochastic differential equations. We carry out infinitesimal perturbation analysis of the covariance matrix for the invariant Gaussian state of such a system and the related purity functional subject to inaccuracies in the energy and coupling matrices of the subsystems. This leads to the problem of balancing the state-space realizations of the component oscillators through symplectic similarity transformations in order to minimize the mean square sensitivity of the purity functional to small random perturbations of the parameters. This results in a quadratic optimization problem with an effective solution in the case of cascaded one-mode oscillators, which is demonstrated by a numerical example. The findings of the paper are applicable to robust state generation in quantum stochastic networks.
Abstract We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of ( 2 ℵ + 1 ) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of ( 2 ℵ + 1 ) -mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. This parametrization allows us to determine the steady-state entanglement properties of such quantum harmonic oscillator chains.
Recently, Nurdin, James and Doherty have demonstrated that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simple one degree of freedom quantum harmonic oscillators together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental point of view, direct interaction Hamiltonians are challenging to implement for systems with more than just a few degrees of freedom. In order to facilitate simpler experimental realizations of these systems, this paper develops a new synthesis algorithm for linear quantum stochastic systems that relies solely on field-mediated interactions, including in implementation of the direct interaction Hamiltonian. An explicit synthesis example is provided to illustrate the realization of a two degrees of freedom linear quantum stochastic system using the new algorithm.