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Register a new userQuantum Disturbance without State Change: Defense of State-Dependent Error-Disturbance Relations
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Masanao Ozawa
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The uncertainty principle states that a measurement inevitably disturbs the system, while it is often supposed that a quantum system is not disturbed without state change. Korzekwa, Jennings, and Rudolph [Phys. Rev. A 89, 052108 (2014)] pointed out a conflict between those two views, and concluded that state-dependent formulations of error-disturbance relations are untenable. Here, we reconcile the conflict by showing that a quantum system is disturbed without state change, in favor of the recently obtained universally valid state-dependent error-disturbance relations.
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Heisenbergs uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report improved n
We formulate a new error-disturbance relation, which is free from explicit dependence upon variances in observables. This error-disturbance relation shows improvement over the one provided by the Branciard inequality and the Ozawa inequality for some initial states and for particular class of joint measurements under consideration. We also prove a modified form of Ozawas error-disturbance relation. The later relation provides a tighter bound compared to the Ozawa and the Branciard inequalities for a small number of states.
In quantum physics, measurement error and disturbance were first naively thought to be simply constrained by the Heisenberg uncertainty relation. Later, more rigorous analysis showed that the error and disturbance satisfy more subtle inequalities. Sever
Conventionally, unknown quantum states are characterized using quantum-state tomography based on strong or weak measurements carried out on an ensemble of identically prepared systems. By contrast, the use of protective measurements offers the possibility of determining quantum states from a series of weak, long measurements performed on a single system. Because the fidelity of a protectively measured quantum state is determined by the amount of state disturbance incurred during each protective measurement, it is crucial that the initial quantum state of the system is disturbed as little as possible. Here we show how to systematically minimize the state disturbance in the course of a protective measurement, thus enabling the maximization of the fidelity of the quantum-state measurement. Our approach is based on a careful tuning of the time dependence of the measurement interaction and is shown to be dramatically more effective in reducing the state disturbance than the previously considered strategy of weakening the measurement strength and increasing the measurement time. We describe a method for designing the measurement interaction such that the state disturbance exhibits polynomial decay to arbitrary order in the inverse measurement time $1/T$. We also show how one can achieve even faster, subexponential decay, and we find that it represents the smallest possible state disturbance in a protective measurement. In this way, our results show how to optimally measure the state of a single quantum system using protective measurements.
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous measurements, and comparing the values of unmeasured observables is not necessarily meaningful according to quantum theory. To overcome these conceptual difficulties, we take a different approach and define error and disturbance in an operational manner. In particular, we formulate both in terms of the probability that one can successfully distinguish the actual measurement device from the relevant hypothetical ideal by any experimental test whatsoever. This definition itself does not rely on the formalism of quantum theory, avoiding many of the conceptual difficulties of usual definitions. We then derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems, as well as for the case of position and momentum. Our relations may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information about conjugate observables to the environment. We also show that Englerts wave-particle duality relation [PRL 77, 2154 (1996)] can be viewed as an error-disturbance uncertainty relation.
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