This paper considers the bounded real properties for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. The paper considers complex quantum versions of the Bounded Real Lemma, the Strict Bounded Real Lemma and the Lossless Bounded Real Lemma. For the class of quantum systems under consideration, it is shown that the question of physical realizability is related to the Bounded Real and Lossless Bounded Real properties.This paper considers the bounded real properties for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. The paper considers complex quantum versions of the Bounded Real Lemma, the Strict Bounded Real Lemma and the Lossless Bounded Real Lemma. For the class of quantum systems under consideration, it is shown that the question of physical realizability is related to the Bounded Real and Lossless Bounded Real properties.

IEEE Transactions on Automatic ControlJul 29, 201075 citations

Simple Quantum Systems

Philipp O. J. Scherer

Springer eBooksJan 1, 20100 citations

Limits of control for quantum systems: Kinematical bounds on the optimization of observables and the question of dynamical realizability

S. G. Schirmer, J. V. Leahy

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for nondissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitrary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group $U(N)$ and the results of a few control computations are discussed briefly.In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for nondissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitrary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group $U(N)$ and the results of a few control computations are discussed briefly.

arXiv:quant-ph/0010032Physical Review AJan 11, 200123 citations

Quantum Systems

WORLD SCIENTIFIC (EUROPE) eBooksMay 1, 20230 citations

Upper Bounds on Fluctuation Growths of Observables in Open Quantum Systems

Newshaw Bahreyni, Paul M. Alsing, Carlo Cafaro +2 more

The upper bounds for the rate of fluctuation growth of an observable in both open and closed quantum systems have been studied actively recently. In our recent work we showed that the rate of fluctuation growth for an observable in a closed quantum system is upper bounded by the fluctuation of its corresponding velocity-like observable. That bound also indicated a tradeoff between the time derivatives of the mean and the standard deviation. In this paper we will look at open quantum systems in two cases. For the first case we find the generator of evolution for an open system employing both the Taylor expansion and the standard time-ordered evolution via the Dyson series, while in the second case we consider no specific information about the evolution of the system. We then find the rate of fluctuation growth in each case. Comparing the upper bounds for each case and considering the upper bound found for a closed system suggest that including more details by separating the contributions of the system and state dynamics seems to result in looser bounds for the rate of fluctuation growth.The upper bounds for the rate of fluctuation growth of an observable in both open and closed quantum systems have been studied actively recently. In our recent work we showed that the rate of fluctuation growth for an observable in a closed quantum system is upper bounded by the fluctuation of its corresponding velocity-like observable. That bound also indicated a tradeoff between the time derivatives of the mean and the standard deviation. In this paper we will look at open quantum systems in two cases. For the first case we find the generator of evolution for an open system employing both the Taylor expansion and the standard time-ordered evolution via the Dyson series, while in the second case we consider no specific information about the evolution of the system. We then find the rate of fluctuation growth in each case. Comparing the upper bounds for each case and considering the upper bound found for a closed system suggest that including more details by separating the contributions of the system and state dynamics seems to result in looser bounds for the rate of fluctuation growth.

quant-pharXiv:2512.10153Dec 12, 20250 citations

U(N)

and the results of a few control computations are discussed briefly.