Simultaneous continuous measurement of photon-counting and homodyne detection on a free photon field: dynamics of state reduction and the mutual influence of measurement backaction

Kuramochi, Yui; Watanabe, Yu; Ueda, Masahito

doi:10.1088/1751-8113/46/42/425303

Cited by 5 publications

(19 citation statements)

References 44 publications

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“…Furthermore, this commutativity condition enables us to derive a quantum filter corresponding to multiple Figure 4 also shows that the SSE formulated in Ref. [2] gives a biased expectation compared with the analytical result. measurement outputs.…”

Section: Discussionmentioning

confidence: 83%

“…In this case, the quantum filter average of the number operator converges to the analytical prediction (45) when the trial number is increased. Figure 4 also shows that the SSE formulated in [2] gives a biased average compared with the analytical result. …”

Section: Simulation Resultsmentioning

confidence: 94%

“…(40a) in the limiting case r = 0, which would correspond to a jump process with zero arrival rate. The paper [2] claims to consider the case of simultaneous jump and diffusion measurement processes, but the above comparison shows that it does not account for the required beam splitter. The equivalence of the unnormalized SSE in Ref.…”

Section: Comparison With Results In Ref [2]mentioning

confidence: 99%

“…[2], the unnormalized evolution of photon counting and homodyne detections requires the addition of the two measurement operations, but with the appropriate beam splitter gain.…”

Section: Comparison With Results In Ref [2]mentioning

confidence: 99%

“…Then, we derive a general, multiplemeasurement quantum filter as an extension of a single-measurement quantum filter [1]. As an application we explicitly obtain the quantum filter corresponding to homodyne detection and photon counting at the output ports of a beam splitter, correcting an earlier result [2]. …”

mentioning

confidence: 92%

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Quantum filtering for multiple diffusive and Poissonian measurements

Emzir¹,

Woolley²,

Petersen³

2015

J. Phys. A: Math. Theor.

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Abstract. We provide a rigorous derivation of a quantum filter for the case of multiple measurements being made on a quantum system. We consider a class of measurement processes which are functions of bosonic field operators, including combinations of diffusive and Poissonian processes. This covers the standard cases from quantum optics, where homodyne detection may be described as a diffusive process and photon counting may be described as a Poissonian process. We obtain a necessary and sufficient condition for any pair of such measurements taken at different output channels to satisfy a commutation relationship. Then, we derive a general, multiplemeasurement quantum filter as an extension of a single-measurement quantum filter [1]. As an application we explicitly obtain the quantum filter corresponding to homodyne detection and photon counting at the output ports of a beam splitter, correcting an earlier result [2].

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Section: Discussionmentioning

confidence: 83%

Section: Simulation Resultsmentioning

confidence: 94%

Section: Comparison With Results In Ref [2]mentioning

confidence: 99%

“…[2], the unnormalized evolution of photon counting and homodyne detections requires the addition of the two measurement operations, but with the appropriate beam splitter gain.…”

Section: Comparison With Results In Ref [2]mentioning

confidence: 99%

mentioning

confidence: 92%

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Quantum filtering for multiple diffusive and Poissonian measurements

Emzir¹,

Woolley²,

Petersen³

2015

J. Phys. A: Math. Theor.

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A quantum extended Kalman filter

Emzir

Woolley

Petersen

2017

J. Phys. A: Math. Theor.

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A stochastic filter uses a series of measurements over time to produce estimates of unknown variables based on a dynamic model [1]. For a quantum system, such an algorithm is provided by a quantum filter [2], which is also known as a stochastic master equation (SME) [3]. For a linear quantum system subject to linear measurements and Gaussian noise, the quantum filter reduces to a quantum Kalman filter [4,5]. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to non-commutative quantum stochastic differential equations (QSDEs). We will show that there are conditions under which a filter similar to the classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problems with 'state-dependent' covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems which involve multiple modes, nonlinear Hamiltonians and simultaneous jump-diffusive measurements.

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Quantum state engineering by steering in the presence of errors

Medina-Guerra,

Kumar,

Gornyi

et al. 2024

Phys. Rev. Research

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Quantum state engineering plays a vital role in various applications in the field of quantum information. Different strategies, including drive-and-dissipation, adiabatic cooling, and measurement-based steering, have been proposed for state generation and manipulation, each with its upsides and downsides. Here, we address a class of measurement-based state engineering protocols where a sequence of generalized measurements is employed to steer a quantum system toward a desired (pure or mixed) target state. Previously studied measurement-based protocols relied on idealized procedures and avoided exploration of the effects of various errors stemming from imperfections of experimental realizations and external noise. We employ the quantum trajectory formalism to provide a detailed analysis of the robustness of these steering protocols against multiple classes of errors. We study a set of realistic errors that can be classified as dynamic or static, depending on whether they remain unchanged while running the protocol. More specifically, we investigate the impact of the erroneous choice of detector-system coupling, erroneous re-initialization of the detector state following a measurement step, fluctuating steering directions, and environmentally induced errors in the detector-system interaction. We show that the protocol remains fully robust against the erroneous choice of detector-system coupling parameters and presents reasonable robustness against other types of errors. Our analysis employs various quantifiers such as fidelity, trace distance, and linear entropy to characterize the protocol's robustness and provide analytical results for these quantifiers against various errors. We introduce averaging hierarchies of stochastic equations describing individual quantum trajectories associated with detector readouts. Subsequently, we demonstrate the commutation between the classical expectation value and the time-ordering operator of the exponential of a Hamiltonian with multiplicative white noise, as well as the commutation of the expectation value and the partial trace with respect to detector outcomes. Our ideas are implemented and demonstrated for a specific class of steering platforms, addressing a single qubit. Published by the American Physical Society 2024

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Simultaneous continuous measurement of photon-counting and homodyne detection on a free photon field: dynamics of state reduction and the mutual influence of measurement backaction

Cited by 5 publications

References 44 publications

Quantum filtering for multiple diffusive and Poissonian measurements

Quantum filtering for multiple diffusive and Poissonian measurements

A quantum extended Kalman filter

Quantum state engineering by steering in the presence of errors

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