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Register a new userError-Disturbance Trade-off in Sequential Quantum Measurements
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We derive a state dependent error-disturbance trade-off based on a statistical distance in the sequential measurements of a pair of noncommutative observables and experimentally verify the relation with a photonic qubit system. We anticipate that this Letter may further stimulate the study on the quantum uncertainty principle and related applications in quantum measurements.
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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.
The quantification of the measurement uncertainty aspect of Heisenbergs Uncertainty Principle---that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two incompatible observables---has regained a lot of interest recently. Several approaches have been proposed and debated. In this paper we consider Ozawas definitions for inaccuracies (as root-mean-square errors) in approximate joint measurements, and study how these are constrained in different cases, whether one specifies certain properties of the approximations---namely their standard deviations and/or their bias---or not. Extending our previous work [C. Branciard, Proc. Natl. Acad. Sci. U.S.A. 110, 6742 (2013)], we derive new error-trade-off relations, which we prove to be tight for pure states. We show explicitly how all previously known relations for Ozawas inaccuracies follow from ours. While our relations are in general not tight for mixed states, we show how these can be strengthened and how tight relations can still be obtained in that case.
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
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.
Although Heisenbergs uncertainty principle is represented by a rigorously proven relation about intrinsic indeterminacy in quantum states, Heisenbergs error-disturbance relation (EDR) has been commonly believed as another aspect of the principle. However, recent developments of quantum measurement theory made Heisenbergs EDR testable to observe its violations. Here, we study the EDR for Stern-Gerlach measurements. In a previous report [arXiv:1910.07929], it has been pointed out that their EDR is close to the theoretical optimal. The present note reports that even the original Stern-Gerlach experiment in 1922, the available experimental data show, violates Heisenbergs EDR. The results suggest that Heisenbergs EDR is more ubiquitously violated than it has long been supposed.
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