Zixuan He

From phase-space entropy to coherent-state error: mode-uniform Rényi–Wehrl stability

Abstract When can a quantum optical source be replaced by a coherent state with controlled error in every subsequent experiment? We turn its Husimi phase-space entropy excess into an error bound for the entire quantum state. For every fixed Rényi order $p>0$ and every density ope...

Exact Hausdorff measure of SLE boundary contacts

The dimension of a random fractal specifies its scaling exponent; a finite, nonzero measure requires a finer calibration. We determine this calibration for the boundary contacts of chordal SLEκ, 4 < κ < 8. With δ = 2 − 8/κ and β = 8/κ − 1, the exact Hausdorff gauge is h(r) = rδ[l...

The active entropy photon-number inequality: exact Gaussian-channel minima and rigidity of near-optimal inputs

Abstract How much does a nearly minimal output entropy reveal about the quantum states entering an amplifier? We prove the active entropy photon-number inequality for two independent multimode inputs, each with arbitrary internal correlations, and characterise every equality case...

Sidorenko's property and edge retention in deep lower tails

When a random network contains very few copies of a given pattern, how many connections can its most likely configuration retain? For bipartite patterns, we prove that homogeneous minimization at every lower-tail threshold is equivalent to Sidorenko's property, for both Bernoulli...

Uniform Wehrl stability across all bosonic mode numbers: total entropy deficit controls full trace-norm distance to coherent states

Quantitative Wehrl stability is known at each fixed number of bosonic modes; the multimode results reviewed here allow dimension dependence. We prove a full-state stability theorem with one constant that works simultaneously for every finite mode count. For every $m$-mode bosonic...

Finite models of quantum light that preserve Wigner positivity and the energy budget

The state space of quantum light contains infinitely many photon-number levels, whereas numerical models usually retain only finitely many. Direct truncation can introduce Wigner negativity into an initially Wigner-positive state. We prove that every Wigner-positive state of fini...

Distinct stability laws for Wigner entropy and non-Gaussian structure

Proximity to the vacuum need not stabilise phase-space entropy. We construct Wigner-positive states whose total mean photon number and trace distance from vacuum vanish as the mode number $m$ grows, while their Shannon entropy deficit diverges. Their distance from the Gaussian co...

Distinct stability laws for Wigner entropy and non-Gaussian structure

Proximity to the vacuum need not stabilise phase-space entropy. We construct Wigner-positive states whose total mean photon number and trace distance from vacuum vanish as the mode number $m$ grows, while their Shannon entropy deficit diverges. Their distance from the Gaussian co...

Wigner entropy below vacuum: physical counterexamples and stability limits

Positive Wigner functions can have less Shannon entropy than the vacuum, even arbitrarily close to the vacuum state. We construct physical counterexamples and identify the competition that controls their entropy: the relative entropy to the vacuum phase-space density can exceed t...