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تسجيل مستخدم جديدProtective Measurements: Probing Single Quantum Systems
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Tabish Qureshi
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Making measurements on single quantum systems is considered difficult, almost impossible if the state is a-priori unknown. Protective measurements suggest a possibility to measure single quantum systems and gain some new information in the process. Protective measurement is described, both in the original and generalized form. The degree to which the system and the apparatus remain entangled in a protective measurement, is assessed. A possible experimental test of protective measurements is discussed.
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We study protective quantum measurements in the presence of an environment and decoherence. We consider the model of a protectively measured qubit that also interacts with a spin environment during the measurement. We investigate how the coupling to
the environment affects the two characteristic properties of a protective measurement, namely, (i) the ability to leave the state of the system approximately unchanged and (ii) the transfer of information about expectation values to the apparatus pointer. We find that even when the interaction with the environment is weak enough not to lead to appreciable decoherence of the initial qubit state, it causes a significant broadening of the probability distribution for the position of the apparatus pointer at the conclusion of the measurement. This washing out of the pointer position crucially diminishes the accuracy with which the desired expectation values can be measured from a readout of the pointer. We additionally show that even when the coupling to the environment is chosen such that the state of the system is immune to decoherence, the environment may still detrimentally affect the pointer readout.
In this article we propose an alternate model for the so called {it protective measurements}, more appropriately {it adiabatic measurements} of a spin 1/2 system where the {it apparatus} is also a quantum system with a {em finite dimensional Hilbert
space}. This circumvents several technical as well as conceptual issues that arise when dealing with an infinite dimensional Hilbert space as in the analysis of conventional Stern-Gerlach experiment. Here also it is demonstrated that the response of the detector is continuous and it {it directly} measures {em expectation values without altering the state of the system}(when the unknown original state is a {it nondegenerate eigenstate of the system Hamiltonian}, in the limit of {em ideal} adiabatic conditions. We have also computed the corrections arising out of the inevitable departures from ideal adiabaticity i.e the time of measurement being large but finite. To overcome the {em conceptual} difficulties with a {it quantum apparatus}, we have simulated a {it classical apparatus} as a {em large} assembly of spin-1/2 systems. We end this article with a conclusion and a discussion of some future issues.
This paper presents a proof-of-principle scheme for the protective measurement of a single photon. In this scheme, the photon is looped arbitrarily many times through an optical stage that implements a weak measurement of a polarization observable fo
llowed by a strong measurement protecting the state. The ability of this scheme to realize a large number of such interaction-protection steps means that the uncertainty in the measurement result can be drastically reduced while maintaining a sufficient probability for the photon to survive the measurement.
We investigate the effect of conditional null measurements on a quantum system and find a rich variety of behaviors. Specifically, quantum dynamics with a time independent $H$ in a finite dimensional Hilbert space are considered with repeated strong
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