Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSum uncertainty relations for arbitrary $N$ incompatible observables
86
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty relations are explicitly derived. These bounds are shown to be tighter than the ones such as derived from the uncertainty inequality for two observables [Phys. Rev. Lett. 113, 260401 (2014)]. Detailed examples are presented to compare among our results with some existing ones.
rate research
Read More
We study a generalization of the Wigner function to arbitrary tuples of hermitian operators. We show that for any collection of hermitian operators A1...An , and any quantum state there is a unique joint distribution on R^n, with the property that the marginals of all linear combinations of the operators coincide with their quantum counterpart. In other words, we consider the inverse Radon transform of the exact quantum probability distributions of all linear combinations. We call it the Wigner distribution, because for position and momentum this property defines the standard Wigner function. We discuss the application to finite dimensional systems, establish many basic properties and illustrate these by examples. The properties include the support, the location of singularities, positivity, the behavior under symmetry groups, and informational completeness.
Uncertainty principle plays a vital role in quantum physics. The Wigner-Yanase skew information characterizes the uncertainty of an observable with respect to the measured state. We generalize the uncertainty relations for two quantum channels to arbitrary N quantum channels based on Wigner-Yanase skew information. We illustrate that these uncertainty inequalities are tighter than the existing ones by detailed examples. Especially, we also discuss the uncertainty relations for N unitary channels, which could be regarded as variance-based sum uncertainty relations with respect to any pure state.
Being one of the centroidal concepts in quantum theory, the fundamental constraint imposed by Heisenberg uncertainty relations has always been a subject of immense attention and challenging in the context of joint measurements of general quantum mechanical observables. In particular, the recent extension of the original uncertainty relations has grabbed a distinct research focus and set a new ascendent target in quantum mechanics and quantum information processing. In the present work we explore the joint measurements of three incompatible observables, following the basic idea of a newly proposed error trade-off relation. In comparison to the counterpart of two incompatible observables, the joint measurements of three incompatible observables are more complex and of more primal interest in understanding quantum mechanical measurements. Attributed to the pristine idea proposed by Heisenberg in 1927, we develop the error trade-off relations for compatible observables to categorically approximate the three incompatible observables. Implementing these relations we demonstrate the first experimental witness of the joint measurements for three incompatible observables using a single ultracold $^{40}Ca^{+}$ ion in a harmonic potential. We anticipate that our inquisition would be of vital importance for quantum precision measurement and other allied quantum information technologies.
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.
A new lower boundary for the product of variances of two observables is obtained in the case, when these observables are entangled with the third one. This boundary can be higher than the Robertson--Schrodinger one. The special case of the two-dimensional pure Gaussian state is considered as an example.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
