arXiv subjects

Yiqi Yu

Publications and source records attributed to Yiqi Yu.

2 recordsLinked to original sources

arXiv2025

Bayesian Interpretation of Husimi Function and Wehrl Entropy

Husimi function (Q-function) of a quantum state is the distribution function of the density operator in the coherent state representation. It is widely used in theoretical research, such as in quantum optics. The Wehrl entropy is the Shannon entropy of the Husimi function, and is non-zero even for pure states. This entropy has been extensively studied in mathematical physics. Recent research also suggests a significant connection between the Wehrl entropy and many-body quantum entanglement in spin systems. We investigate the statistical interpretation of the Husimi function and the Wehrl entropy, taking the system of $N$ spin-1/2 particles as an example. Due to the completeness of coherent states, the Husimi function and Wehrl entropy can be explained via the positive operator-valued measurement (POVM) theory, although the coherent states are not a set of orthonormal basis. Here, with the help of the Bayes' theorem, we provide an alternative probabilistic interpretation for the Husimi function and the Wehrl entropy. This interpretation is based on direct measurements of the system, and thus does not require the introduction of an ancillary system as in POVM theory. Moreover, under this interpretation the classical correspondences of the Husimi function and Wehrl entropy are just phase-space probability distribution function of $N$ classical tops, and its associated entropy, respectively. Therefore, this explanation contributes to a better understanding of the relationship between the Husimi function, Wehrl entropy, and classical-quantum correspondence. The generalization of this statistical interpretation to continuous-variable systems is also discussed.

quant-ph↗

arXiv2023

Wehrl Entropy and Entanglement Complexity of Quantum Spin Systems

The Wehrl entropy of a quantum state is the Shannon entropy of its coherent-state distribution function, and remains non-zero even for pure states. We investigate the relationship between this entropy and the many-particle quantum entanglement, for $N$ spin-1/2 particles. Explicitly, we numerically calculate the Wehrl entropy of various $N$-particle ($2\leq N\leq 20$) entangled pure states, with respect to the SU(2)$^{\otimes N}$ coherent states. Our results show that for the large-$N$ ($N\gtrsim 10$) systems the Wehrl entropy of the highly chaotic entangled states (e.g., $2^{-N/2}\sum_{s_1,s_2,...,s_N=\uparrow,\downarrow}|s_1,s_2,...,s_N\rangle e^{-i\phi_{s_1,s_2,...,s_N}}$, with $\phi_{s_1,s_2,...,s_N}$ being random angles) are substantially larger than that of the very regular entangled states (e.g., the Greenberger-Horne-Zeilinger state). Therefore, the Wehrl entropy can reflect the complexity of the quantum entanglement of many-body pure states, as proposed by A. Sugita (Jour. Phys. A 36, 9081 (2003)). In particular, the Wehrl entropy per particle (WEPP) can be used as a quantitative description of this entanglement complexity. Unlike other quantities used to evaluate this complexity (e.g., the degree of entanglement between a subsystem and the other particles), the WEPP does not necessitate the division of the total system into two subsystems. We further demonstrate that many-body pure entangled states can be classified into three types, based on the behavior of the WEPP in the limit $N \rightarrow \infty$: states approaching that of a maximally mixed state, those approaching completely separable pure states, and a third category lying between these two extremes. Each type exhibits fundamentally different entanglement complexity.

cond-mat.stat-mech↗