M D Srinivas
Articles written in Pramana – Journal of Physics
Volume 12 Issue 6 June 1979 pp 699-705 Quantum Mechanics
It is noted that the Heisenberg uncertainty relations set a lower bound on the product of variances of two observables
Volume 16 Issue 3 March 1981 pp 173-199 Quantum Mechanics
Apart from serving as a parameter in describing the evolution of a system, time appears also as an observable property of a system in experiments where one measures ‘the time of occurrence’ of an event associated with the system. However, while the observables normally encountered in quantum theory (and characterized by self-adjoint operators or projection-valued measures) correspond to instantaneous measurements, a time of occurrence measurement involves continuous observations being performed on the system to monitor when the event occurs. It is argued that a time of occurrence observable should be represented by a positive-operator-valued measure on the interval over which the experiment is carried out. It is shown that while the requirement of time-translation invariance and the spectral condition rule out the possibility of a self-adjoint time operator (Pauli’s theorem), they do allow for time of occurrence observables to be represented by suitable positive-operator-valued measures. It is also shown that the uncertainty in the time of occurrence of an event satisfies the time-energy uncertainty relation as a consequence of the time-translation invariance, only if the time of occurrence experiment is performed on the entire time axis.
Volume 17 Issue 3 September 1981 pp 203-216 Optics
A complete solution is given to the problem of calculating the dead time corrections to the counting statistics of an arbitrary doubly stochastic Poisson process with a non-negative random intensity function. It is shown that for the particular case of an optical field with constant intensity, the general dead time modified counting formula leads to a corrected version of results earlier derived by Bedard.
Volume 17 Issue 3 September 1981 pp 217-227 Optics
The recent formulation of the quantum theory of photodetection, based on the quantum theory of continuous measurements, is extended to the case of a (nonideal) detector which has non-zero dead time. A general result is proven which expresses the dead time modified counting statistics in terms of the counting statistics of an
Volume 19 Issue 2 August 1982 pp 159-173 Quantum Mechanics
This paper is devoted to a study of some of the basic conditions which have to be satisfied by a hidden variable theory in order that it can reproduce the quantum mechanical probabilities. Of course one such condition, which emerges from the important theorem of Bell, is that a hidden variable theory has to be non-local. It is shown that a hidden variable theory is also incompatible with the conventional interpretation of mixed states and the mixing operation in quantum theory. It is therefore concluded that, apart from being non-local, a hidden variable theory would also necessarily violate the usual assumption of quantum theory that the density operator provides an adequate characterization of any ensemble of systems, pure or mixed.
Volume 24 Issue 5 May 1985 pp 673-684 Quantum Mechanics
An entropic formulation of uncertainty relations is obtained for the case of successive measurements. The lower bound on the overall uncertainty, that is obtained for the case of successive measurements, is shown to be larger than the recently derived Deutsch-Partovi lower bound on the overall uncertainty in the case of distinct measurements.
Volume 25 Issue 4 October 1985 pp 369-375 Quantum Statistics
We review the recent investigations on the improved formulation of uncertainty relations which employ the information-theoretic entropy rather than variance as a measure of uncertainty. We show that this formulation also brings out clearly the relation between the overall uncertainty and the quantum mechanical interference due to measurements.
Volume 30 Issue 4 April 1988 pp 259-277 Quantum Mechanics
The fundamental prescriptions of quantum theory have so far remained incomplete in that there is no satisfactory prescription for the joint probabilities of successive observations of arbitrary sequence of observables. The joint probability formula derived by Wigner is based on the collapse postulate due to Von Neuman and Lüders and is applicable only to observables with purely discrete spectra. Earlier attempts to generalize the collapse postulate to observables with continuous spectra have been unsatisfactory as they lead to only finitely additive (and not
Volume 35 Issue 3 September 1990 pp 303-315 Research Articles
We investigate the question of local causality at the statistical level in Einstein-Podolsky-Rosen (EPR) type situations, taking into account the most general class of measurements envisaged in quantum theory. The condition for local causality at the statistical level used in this paper pertains to the invariance of statistics of measurements on one sub-system with respect to the choice and type of measurements on its correlated partner in the EPR-type examples. Our analysis is based on a criterion for measurements performed on one of the EPR sub-systems, which is more general than the criterion used in the earlier treatments. We discuss both non-absorptive measurements (where the system is available for further observation after the measurement is performed) as well as absorptive measurements (where the system is absorbed in the process of a particular outcome being realized). We show that in the case of arbitrary non-absorptive measurements characterized by operationvalued measures, the requirement of local causality at the statistical level is satisfied and in the process we identify the key inputs in such a proof. We also obtain the specific conditions under which an absorptive measurement satisfies local causality at the statistical level.
Volume 47 Issue 1 July 1996 pp 1-23 Review
We present an overview of the quantum theory of continuous measurements and discuss some of its important applications in quantum optics. Quantum theory of continuous measurements is the appropriate generalization of the conventional formulation of quantum theory, which is adequate to deal with counting experiments where a detector monitors a system continuously over an interval of time and records the times of occurrence of a given type of event, such as the emission or arrival of a particle.
We first discuss the classical theory of counting processes and indicate how one arrives at the celebrated photon counting formula of Mandel for classical optical fields. We then discuss the inadequacies of the so called quantum Mandel formula. We explain how the unphysical results that arise from the quantum Mandel formula are due to the fact that the formula is obtained on the basis of an erroneous identification of the coincidence probability densities associated with a continuous measurement situation. We then summarize the basic framework of the quantum theory of continuous measurements as developed by Davies. We explain how a complete characterization of the counting process can be achieved by specifying merely the measurement transformation associated with the change in the state of the system when a single event is observed in an infinitesimal interval of time.
In order to illustrate the applications of the quantum theory of continuoius measurements in quantum optics, we first derive the photon counting probabilities of a single-mode free field and also of a single-mode field in interaction with an external source. We then discuss the general quantum counting formula of Chmara for a multi-mode electromagnetic field coupled to an external source. We explain how the Chmara counting formula is indeed the appropriate quantum generalization of the classical Mandel formula. To illustrate the fact that the quantum theory of continuous measurements has other diverse applications in quantum optics, besides the theory of photodetection, we summarize the theory of ‘quantum jumps’ developed by Zoller, Marte and Walls and Barchielli, where the continuous measurements framework is employed to evaluate the statistics of photon emission events in the resonance fluorescence of an atomic system.
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