arXiv subjects

Jiamei Wang

Publications and source records attributed to Jiamei Wang.

3 recordsLinked to original sources

arXiv2022

Probability density functions of quantum mechanical observable uncertainties

We study the uncertainties of quantum mechanical observables, quantified by the standard deviation (square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions (PDFs) of the uncertainties of arbitrary qubit observables. Based on these PDFs, the uncertainty regions of the observables are characterized by the supports of the PDFs. The state-independent uncertainty relations are then transformed into the optimization problems over uncertainty regions, which opens a new vista for studying state independent uncertainty relations. Our results may be generalized to multiple observable case in higher dimensional spaces.

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arXiv2018

Average of uncertainty-product for bounded observables

The goal of this paper is to calculate exactly the average of uncertainty-product of two bounded observables and to establish its typicality over the whole set of finite dimensional quantum pure states. Here we use the uniform ensembles of pure and isospectral states as well as the states distributed uniformly according to the measure induced by the Hilbert-Schmidt norm. Firstly, we investigate the average uncertainty of an observable over isospectral density matrices. By letting the isospectral density matrices be of rank-one, we get the average uncertainty of an observable restricted to pure quantum states. These results can help us check how large the gap is between the uncertainty-product and any obtained lower bounds about the uncertainty-product. Although our method in the present paper cannot give a tighter lower bound of uncertainty-product for bounded observables, it can help us drop any one that is not tighter than the known one substantially.

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arXiv2018

Spectral density of mixtures of random density matrices for qubits

We derive the spectral density of the equiprobable mixture of two random density matrices of a two-level quantum system. We also work out the spectral density of mixture under the so-called quantum addition rule. We use the spectral densities to calculate the average entropy of mixtures of random density matrices, and show that the average entropy of the arithmetic-mean-state of $n$ qubit density matrices randomly chosen from the Hilbert-Schmidt ensemble is never decreasing with the number $n$. We also get the exact value of the average squared fidelity. Some conjectures and open problems related to von Neumann entropy are also proposed.

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