Quantum filtering for multiple diffusive and Poissonian measurements

Emzir, Muhammad F.; Woolley, Matthew J.; Petersen, Ian R.

doi:10.1088/1751-8113/48/38/385302

Cited by 13 publications

(25 citation statements)

References 32 publications

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“…In quantum optics, quantum filters, also known as quantum trajectories or stochastic master equations, are of great importance in measurement feedback control [50,52,23,53]. The problems of quantum filtering for systems driven by Gaussian states, including vacuum state, thermal state, coherent state, and squeezed state, have been well studied, see, e.g., [17,12,34,18]. On the other hand, as single-and multi-photon states can nowadays be generated in real experiments [39,49,51,31,29,36,32,47], more and more research has been concentrated on atomic excitation [49,4,43,40] and quantum filter design [28,26,45,14,20,3] for systems driven by single or multiple photons.…”

Section: Introductionmentioning

confidence: 99%

Quantum filtering for a two-level atom driven by two counter-propagating photons

Dong

Amini

2019

Quantum Inf Process

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The purpose of this paper is to propose quantum filters for a twolevel atom driven by two continuous-mode counter-propagating photons and under continuous measurements. Two scenarios of multiple measurements, 1) homodyne detection plus photodetection, and 2) two homodyne detections, are discussed. Filtering equations for both cases are derived explicitly. As demonstration, the two input photons with rising exponential and Gaussian pulse shapes are used to excite a two-level atom under two homodyne detection measurements. Simulations reveal scaling relations between atom-photon coupling and photonic pulse shape for maximum atomic excitation.

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Section: Introductionmentioning

confidence: 99%

Quantum filtering for a two-level atom driven by two counter-propagating photons

Dong

Amini

2019

Quantum Inf Process

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“…In quantum optics, the familiar formalism of quantum filtering considers incident lights in Gaussian states, including the vacuum state, coherent states, thermal states, and squeezed states [22]- [24]. This is natural as Gaussian states are commonly used in quantum optics laboratories and have been well studied.…”

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confidence: 99%

Continuous-Mode MultiPhoton Filtering

Song¹,

Zhang²,

Xi³

2016

SIAM J. Control Optim.

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Abstract. The purpose of this paper is to derive filters for an arbitrary open quantum system driven by a light wavepacket prepared in a continuous-mode multi-photon state. A continuous-mode multi-photon state is a state of a travelling light wavepacket that contains a definite number of photons and is characterised by a temporal (or equivalently spectral) profile. After the interaction with the system, the outgoing light can be monitored by means of homodyne detection or photodetection. Filters for both measurement schemes are derived in this paper. Unlike the vacuum or the coherent state case, the annihilation operator of the light field acting on a multi-photon state changes the state by annihilating a photon, and this makes the traditional filtering techniques inapplicable. To circumvent this difficulty, we adopt a non-Markovian embedding technique proposed in [1] for the study of the single-photon filtering problem. However, the multi-photon nature of the problem addressed in this paper makes the study much more mathematically involved. Moreover, as demonstrated by an example -a two-level system driven by a continuous-mode two-photon state, multi-photon filters can reveal interesting strong nonlinear optical phenomena absent in both the single-photon state case and the continuous-mode Fock state case.Key words. Open quantum systems, Quantum filtering, Multi-photon states.AMS subject classifications. 93E11, 81Q931. Introduction. When light impinges on a quantum system, e.g., an atom or a quantum-mechanical oscillator, partial system information may be carried away by the outgoing light. The outgoing light can be directed to another quantum system, thus serving as a (directional) link to facilitate cascade connection [2]- [6]. Alternatively, the outgoing light may be continuously monitored to produce photocurrent, on which the state of the quantum system can be conditioned. The stochastic evolution of the conditional system state is commonly called a quantum trajectory. A quantum filter can be designed to estimate quantum trajectories In quantum optics, the familiar formalism of quantum filtering considers incident lights in Gaussian states, including the vacuum state, coherent states, thermal states, and squeezed states [22]-[24]. This is natural as Gaussian states are commonly used in quantum optics laboratories and have been well studied. With the advent of modern experimental technology, nowadays, non-Gaussian states such as single-photon states, multi-photon states and Schrodinger cat states, can be reliably generated and manipulated. Therefore, very recently, there is a growing interest in deriving quantum filters for such non-Gaussian states. For example, filters have been derived for quantum systems driven by light fields prepared in single-photon states or cat states [1,21,25].Single-photon states and multi-photon states are very useful resources in quantum computing, quantum communication, and quantum cryptography [26]-[38] and references therein. Roughly speaking, a continuous-mode n-photon state ...

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“…This is another benefit, since for the SME, the MISE could make a huge difference if the initial state needs a higher order Hilbert space basis, see Figure 1b. Figure 3 shows an optical cavity with the simultaneous homodyne detection and photon counting setup as considered in [12]. The involvement of photon counting in this optical setup makes the covariance matrix of the measurement R state-dependent.…”

Section: Estimating the Quadratures Of Multiple Optical Modes With A mentioning

confidence: 99%

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 filtering for multiple diffusive and Poissonian measurements

Cited by 13 publications

References 32 publications

Quantum filtering for a two-level atom driven by two counter-propagating photons

Quantum filtering for a two-level atom driven by two counter-propagating photons

Continuous-Mode MultiPhoton Filtering

A quantum extended Kalman filter

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