Shibdas Roy | University of Technology Sydney (original) (raw)

Papers by Shibdas Roy

We consider classical estimators for a class of physically realizable linear quantum systems. Opt... more We consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust H∞ estimation for uncertain linear quantum systems. The estimation problem is solved by converting it to a suitably scaled H∞ control problem. The solution is obtained in the form of two algebraic Riccati equations. Relevant examples involving dynamic squeezers are presented to illustrate the efficacy of our method.

A coherent-classical estimation scheme for a class of linear quantum systems is considered. Here,... more A coherent-classical estimation scheme for a class of linear quantum systems is considered. Here, the estimator is a mixed quantum-classical system that may or may not involve coherent feedback and yields a classical estimate of a variable for the quantum plant. We demonstrate that with no coherent feedback, such coherent-classical estimation provides no improvement over purely-classical estimation, when the quantum plant or the quantum part of the estimator (called the coherent controller) is a passive annihilation operator system. However, when both the quantum plant and the coherent controller are active systems (that cannot be described by annihilation operators only), coherent-classical estimation without coherent feedback can provide improvement over purely-classical estimation in certain cases. Furthermore, we show that with coherent feedback, it is possible to get better estimation accuracies with coherent-classical estimation, as compared to classical-only estimation.

We consider a coherent-classical estimation scheme for a class of linear quantum systems. It comp... more We consider a coherent-classical estimation scheme for a class of linear quantum systems. It comprises an estimator that is a mixed quantum-classical system without involving coherent feedback. The estimator yields a classical estimate of a variable for the quantum plant. We demonstrate that for a passive plant that can be characterized by annihilation operators only, such coherent-classical estimation provides no improvement over purely-classical estimation. An example is also given which shows that if the plant is not assumed to be an annihilation operator only quantum system, it is possible to get better estimates with such coherent-classical estimation compared with purely-classical estimation.

Precise tracking of a randomly varying optical phase is key to metrology, with applications in op... more Precise tracking of a randomly varying optical phase is key to metrology, with applications in optical communication. Continuous phase estimation is known to be superior in accuracy as compared to static estimation. The underlying parameters in the signal model or the measurement itself are, however, prone to changes owing to unavoidable external noises or apparatus imperfections. The estimation process is, thus, desired to be made robust to uncertainties in these parameters. Here, homodyne phase estimations of coherent and squeezed states of light, evolving continuously under the influence of a resonant noise process, are made robust to parameter uncertainties using a robust fixed-interval smoother, designed for uncertain systems satisfying a certain integral quadratic constraint.

It is well-known that adaptive homodyne estimation of continuously varying optical phase provides... more It is well-known that adaptive homodyne estimation of continuously varying optical phase provides superior accuracy in the phase estimate as compared to adaptive or non-adaptive static estimation. However, most phase estimation schemes rely on precise knowledge of the underlying parameters of the system under measurement, and performance deteriorates significantly with changes in these parameters; hence it is desired to develop robust estimation techniques immune to such uncertainties. In related works, we have already shown how adaptive homodyne estimation can be made robust to uncertainty in an underlying parameter of the phase varying as a simplistic Ornstein-Uhlenbeck stochastic noise process. Here, we demonstrate robust phase estimation for a more complicated resonant noise process using a guaranteed cost robust filter.

Optimal phase estimation of a phase-squeezed quantum state of light has been recently shown to be... more Optimal phase estimation of a phase-squeezed quantum state of light has been recently shown to beat the coherent-state limit. Here, the estimation is made robust to uncertainties in underlying parameters using a robust fixed-interval smoother.

Adaptive homodyne estimation of a continuously evolving optical phase using time-symmetric quantu... more Adaptive homodyne estimation of a continuously evolving optical phase using time-symmetric quantum smoothing has been demonstrated experimentally to provide superior accuracy in the phase estimate compared to adaptive or nonadaptive estimation using filtering alone. Here, we illustrate how the mean-square error in the adaptive phase estimate may be further reduced below the standard quantum limit for the stochastic noise process considered by using a Rauch-Tung-Striebel smoother as the estimator, alongwith an optimal Kalman filter in the feedback loop. Further, the estimation using smoothing can be made robust to uncertainties in the underlying parameters of the noise process modulating the system phase to be estimated. This has been done using a robust fixed-interval smoother designed for uncertain systems satisfying a certain integral quadratic constraint.

Recently, it has been demonstrated experimentally that adaptive estimation of a continuously vary... more Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in the adaptive phase estimate may be further reduced for the stochastic noise process considered by using an optimal Kalman filter in the feedback loop. Further, the estimation process can be made robust to fluctuations in the underlying parameters of the noise process modulating the system phase to be estimated. This has been done using a guaranteed cost robust filter.

Computing Research Repository, Jan 1, 2011

Recently, a novel GHZ/W graphical calculus has been established to study and reason more intuitiv... more Recently, a novel GHZ/W graphical calculus has been established to study and reason more intuitively about interacting quantum systems. The compositional structure of this calculus was shown to be well-equipped to sufficiently express arbitrary mutlipartite quantum states equivalent under stochastic local operations and classical communication (SLOCC). However, it is still not clear how to explicitly identify which graphical properties lead to what states. This can be achieved if we have well-behaved normal forms for arbitrary graphs within this calculus. This article lays down a first attempt at realizing such normal forms for a restricted class of such graphs, namely simple and regular graphs. These results should pave the way for the most general cases as part of future work.

Electronic Proceedings in Theoretical Computer Science, Jan 1, 2010

Graphical calculi for representing interacting quantum systems serve a number of purposes: compos... more Graphical calculi for representing interacting quantum systems serve a number of purposes: compositionally, intuitive graphical reasoning, and a logical underpinning for automation. The power of these calculi stems from the fact that they embody generalized symmetries of the structure of quantum operations, which, for example, stretch well beyond the Choi-Jamiolkowski isomorphism. One such calculus takes the GHZ and W states as its basic generators. Here we show that this language allows one to encode standard rational calculus, with the GHZ state as multiplication, the W state as addition, the Pauli X gate as multiplicative inversion, and the Pauli Z gate as additive inversion.

We consider classical estimators for a class of physically realizable linear quantum systems. Opt... more We consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust H∞ estimation for uncertain linear quantum systems. The estimation problem is solved by converting it to a suitably scaled H∞ control problem. The solution is obtained in the form of two algebraic Riccati equations. Relevant examples involving dynamic squeezers are presented to illustrate the efficacy of our method.

A coherent-classical estimation scheme for a class of linear quantum systems is considered. Here,... more A coherent-classical estimation scheme for a class of linear quantum systems is considered. Here, the estimator is a mixed quantum-classical system that may or may not involve coherent feedback and yields a classical estimate of a variable for the quantum plant. We demonstrate that with no coherent feedback, such coherent-classical estimation provides no improvement over purely-classical estimation, when the quantum plant or the quantum part of the estimator (called the coherent controller) is a passive annihilation operator system. However, when both the quantum plant and the coherent controller are active systems (that cannot be described by annihilation operators only), coherent-classical estimation without coherent feedback can provide improvement over purely-classical estimation in certain cases. Furthermore, we show that with coherent feedback, it is possible to get better estimation accuracies with coherent-classical estimation, as compared to classical-only estimation.

We consider a coherent-classical estimation scheme for a class of linear quantum systems. It comp... more We consider a coherent-classical estimation scheme for a class of linear quantum systems. It comprises an estimator that is a mixed quantum-classical system without involving coherent feedback. The estimator yields a classical estimate of a variable for the quantum plant. We demonstrate that for a passive plant that can be characterized by annihilation operators only, such coherent-classical estimation provides no improvement over purely-classical estimation. An example is also given which shows that if the plant is not assumed to be an annihilation operator only quantum system, it is possible to get better estimates with such coherent-classical estimation compared with purely-classical estimation.

Precise tracking of a randomly varying optical phase is key to metrology, with applications in op... more Precise tracking of a randomly varying optical phase is key to metrology, with applications in optical communication. Continuous phase estimation is known to be superior in accuracy as compared to static estimation. The underlying parameters in the signal model or the measurement itself are, however, prone to changes owing to unavoidable external noises or apparatus imperfections. The estimation process is, thus, desired to be made robust to uncertainties in these parameters. Here, homodyne phase estimations of coherent and squeezed states of light, evolving continuously under the influence of a resonant noise process, are made robust to parameter uncertainties using a robust fixed-interval smoother, designed for uncertain systems satisfying a certain integral quadratic constraint.

It is well-known that adaptive homodyne estimation of continuously varying optical phase provides... more It is well-known that adaptive homodyne estimation of continuously varying optical phase provides superior accuracy in the phase estimate as compared to adaptive or non-adaptive static estimation. However, most phase estimation schemes rely on precise knowledge of the underlying parameters of the system under measurement, and performance deteriorates significantly with changes in these parameters; hence it is desired to develop robust estimation techniques immune to such uncertainties. In related works, we have already shown how adaptive homodyne estimation can be made robust to uncertainty in an underlying parameter of the phase varying as a simplistic Ornstein-Uhlenbeck stochastic noise process. Here, we demonstrate robust phase estimation for a more complicated resonant noise process using a guaranteed cost robust filter.

Optimal phase estimation of a phase-squeezed quantum state of light has been recently shown to be... more Optimal phase estimation of a phase-squeezed quantum state of light has been recently shown to beat the coherent-state limit. Here, the estimation is made robust to uncertainties in underlying parameters using a robust fixed-interval smoother.

Adaptive homodyne estimation of a continuously evolving optical phase using time-symmetric quantu... more Adaptive homodyne estimation of a continuously evolving optical phase using time-symmetric quantum smoothing has been demonstrated experimentally to provide superior accuracy in the phase estimate compared to adaptive or nonadaptive estimation using filtering alone. Here, we illustrate how the mean-square error in the adaptive phase estimate may be further reduced below the standard quantum limit for the stochastic noise process considered by using a Rauch-Tung-Striebel smoother as the estimator, alongwith an optimal Kalman filter in the feedback loop. Further, the estimation using smoothing can be made robust to uncertainties in the underlying parameters of the noise process modulating the system phase to be estimated. This has been done using a robust fixed-interval smoother designed for uncertain systems satisfying a certain integral quadratic constraint.

Recently, it has been demonstrated experimentally that adaptive estimation of a continuously vary... more Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in the adaptive phase estimate may be further reduced for the stochastic noise process considered by using an optimal Kalman filter in the feedback loop. Further, the estimation process can be made robust to fluctuations in the underlying parameters of the noise process modulating the system phase to be estimated. This has been done using a guaranteed cost robust filter.

Computing Research Repository, Jan 1, 2011

Recently, a novel GHZ/W graphical calculus has been established to study and reason more intuitiv... more Recently, a novel GHZ/W graphical calculus has been established to study and reason more intuitively about interacting quantum systems. The compositional structure of this calculus was shown to be well-equipped to sufficiently express arbitrary mutlipartite quantum states equivalent under stochastic local operations and classical communication (SLOCC). However, it is still not clear how to explicitly identify which graphical properties lead to what states. This can be achieved if we have well-behaved normal forms for arbitrary graphs within this calculus. This article lays down a first attempt at realizing such normal forms for a restricted class of such graphs, namely simple and regular graphs. These results should pave the way for the most general cases as part of future work.

Electronic Proceedings in Theoretical Computer Science, Jan 1, 2010

Graphical calculi for representing interacting quantum systems serve a number of purposes: compos... more Graphical calculi for representing interacting quantum systems serve a number of purposes: compositionally, intuitive graphical reasoning, and a logical underpinning for automation. The power of these calculi stems from the fact that they embody generalized symmetries of the structure of quantum operations, which, for example, stretch well beyond the Choi-Jamiolkowski isomorphism. One such calculus takes the GHZ and W states as its basic generators. Here we show that this language allows one to encode standard rational calculus, with the GHZ state as multiplication, the W state as addition, the Pauli X gate as multiplicative inversion, and the Pauli Z gate as additive inversion.