Simultaneous estimation of parameters and the state of an optical parametric oscillator system

Qian, Yu; Yokoyama, Shota; Dong, Dezun; McManus, David D.; Yonezawa, Hidehiro

doi:10.48550/arxiv.2111.07249

Cited by 1 publication

(3 citation statements)

References 26 publications

(51 reference statements)

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“…More discussions of quantum filters can be found in [117,16,119,120,121,114,122,123,124,125,126,127,128,129,130], and [5], among others.…”

Section: Quantum Filtermentioning

confidence: 99%

“…The Kalman canonical form (130) presented above can be used to investigate BAE measurements of quantum linear systems. (i) The quantum Kalman canonical form (130) realizes the BAE measurements of q out with respect to p in ;…”

Section: Theorem 62 [133 Proposition 21] Denotementioning

confidence: 99%

“…(ii) The quantum Kalman canonical form (130) realizes the BAE measurements of p out with respect to q in ; i.e., Ξ q in →p out (s) ≡ 0 if and only if…”

Section: Theorem 62 [133 Proposition 21] Denotementioning

confidence: 99%

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Linear quantum systems: a tutorial

Zhou¹

2022

Preprint

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The purpose of this tutorial is to give a brief introduction to linear quantum control systems. The mathematical model of linear quantum control systems is presented first, then some fundamental control-theoretic notions such as stability, controllability and observability are given, which are closely related to several important concepts in quantum information science such as decoherence-free subsystems, quantum nondemolition variables, and back-action evasion measurements. After that, quantum Gaussian states are introduced, in particular, an information-theoretic uncertainty relation is presented which often gives a better bound for mixed Gaussian states than the well-known Heisenberg uncertainty relation. The quantum Kalman filter is presented for quantum linear systems, which is the quantum analogy of the Kalman filter for classical (namely, non-quantum-mechanical) linear systems. The quantum Kalman canonical decomposition for quantum linear systems is recorded, and its application is illustrated by means of a recent experiment. As single-and multi-photon states are useful resources in quantum information technology, the response of quantum linear systems to these types of input is presented. Finally, coherent feedback control of quantum linear systems is briefly introduced, and a recent experiment is used to demonstrate the effectiveness of quantum linear systems and networks theory.

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