arXiv subjects

Hassan Nasreddine

Publications and source records attributed to Hassan Nasreddine.

5 recordsLinked to original sources

arXiv2026

Energy-Constrained Commutator Variance for Weyl Pairs

Let $W$ be a representation of the Weyl relations on a separable Hilbert space and write $\mathcal R_W(K)=\{W(f):f\in K\}''$. If the symplectic pairing of $K_1$ and $K_2$ is nonzero, there is a self-adjoint unitary $B\in\mathcal R_W(K_2)$ such that, for every normal state $ρ$, one can choose a self-adjoint unitary $A_ρ\in\mathcal R_W(K_1)$ with $\operatorname{Var}_ρ(-i[A_ρ,B])=4$. Hence the optimized mean-input-energy-constrained coefficient equals $4$ at every admissible energy threshold. For the fixed trigonometric Weyl witness $h$, an exact identity for $4-h^2$ reduces the deficit to a phase-fixed problem for commuting squared Weyl translations. For the one-mode quadratic energy $G_M=\frac12 R^TMR-\frac12\sqrt{\det M}$, with $M>0$ and $u^TΩv=π$, we prove $4-γ_{G_M,E}(h)=\frac{u^TMu+v^TMv+2π\sqrt{\det M}}{4E}+O(E^{-2})$. The lower bound holds over all normal states satisfying the mean-energy constraint, and a localized Zak construction attains the same coefficient. For $G=dΓ(H_1)$ and witness directions $u,v\in\operatorname{dom}H_1^{1/2}$, the fixed-witness deficit is $Θ(E^{-1})$ whenever at least one direction lies outside $\ker H_1$; if both directions are zero modes, the constrained supremum equals the endpoint at every positive threshold.

quant-ph↗

arXiv2026

Essential Duality and Quantitative Channel Composability in Algebraic Quantum Field Theory

Let $O\mapsto A(O)$ be a local Haag--Kastler net and let $A^d(O)=A(O')'$ be its dual net. Normal unital completely positive maps on $B(H)$ that fix $A(O')$ pointwise are exactly the channels with Kraus operators in $A^d(O)$. Thus Haag duality at $O$ is equivalent to equality with the $A(O)$-inner channels, while essential duality is equivalent to order-independence of the corresponding causal-complement channel classes at spacelike separation. For self-adjoint generators $a\in M$ and $b\in N$, the small-parameter order defect has coefficient $\operatorname{diam}σ(-i[a,b])$. Uniform optimization gives $Γ(M,N)=2Δ_{\mathrm{sa}}(M,N)$, and reversible inner-channel cb balls recover the same invariant through $\lim_{\varepsilon\downarrow0}Ω^{\mathrm{rev}}_\varepsilon(M,N)/\varepsilon^2=Γ(M,N)/4$. The full inner-channel class admits a normalized coefficient with the same commutativity zero set. With a positive reference observable $G$, the mean-input-energy-constrained coefficient $Γ_{G,E}$ has the same zero criterion and increases to $Γ$ as $E\to\infty$, while no model-independent recovery rate follows from the general von Neumann-algebraic hypotheses. For bosonic second-quantization nets the spacelike defect is either $0$ or $4$; generalized free-field examples realize both branches. In the translation-covariant case with positive one-particle time generator, failure of essential duality admits extremal bounded witness flows that are energy-limited relative to the second-quantized time-translation energy.

quant-ph↗

arXiv2026

Sharp Entropy Cost of Coherent Leakage Across a Block Decomposition

Let $\mathcal{H}=P\mathcal{H}\oplus Q\mathcal{H}$ and let $Πρ=PρP\oplus QρQ$ be the two-block pinching of a density matrix. Write $A=PρP$, $B=PρQ$, and $C=QρQ$. We study the block-coherence entropy $D(ρ\|Πρ)$, the relative-entropy cost of removing cross-block coherence. First, we prove a midpoint Bogoliubov--Kubo--Mori coercivity estimate, giving the operator-kernel lower bound $D(ρ\|Πρ)\ge \operatorname{Tr}[B^*Ω^{-1}_{A,C}(B)]$ for strictly positive diagonal blocks. The proof uses the block-sign involution $U=P-Q$ to obtain a sign-symmetric midpoint lower bound for the BKM Hessian. Second, we determine the exact minimum in the associated constrained entropy-minimization problem: at fixed protected-sector floor, leakage mass, and quadratic coherence, the minimum can be achieved by a single active two-level block, independently of the ambient dimension. Third, under a uniform floor $A\ge a_0P$ and $0<\varepsilon_Q\le a_0/2$, we obtain the logarithmic boundary law $D(ρ\|Πρ)\ge \|B\|_F^2\log(a_0/\varepsilon_Q)$, showing that the lower-bound coefficient multiplying the quadratic coherence diverges logarithmically as leakage mass tends to zero. As a finite-dimensional application, the estimates give an entropy certificate for coherent leakage from a protected subspace: $PρQ$ measures protected--leakage coherence, and the constrained entropy minimum is attained by a state supported on a single effective two-level transition. The BKM estimate also yields a dissipation lower bound along an idealized uniform block-dephasing orbit. Finally, the midpoint mechanism extends to finite-dimensional trace-preserving $\mathbb{Z}_2$-graded automorphisms and bounded finite-trace semifinite corners.

quant-ph↗

arXiv2026

Entropy Moduli and Support-Sensitive BKM Coercivity for Rank-Deficient Non-Commutative Markov Semigroups

We study entropy--coherence relations near rank-deficient support boundaries in finite-dimensional quantum systems. For block-diagonal reference states, we establish support-sensitive coercivity estimates showing that the entropy cost of cross-boundary coherence acquires a logarithmic enhancement as the population scale approaches the support boundary. Combined with finite-time entropy bounds, these estimates yield conditional entropy--activation bounds with a logarithmic correction factor of order $e^{-αt}(1+αt)^{-1/2}$ in coherence-dominant regimes. The analysis proceeds through pinching reductions and effective $2\times2$ Bogoliubov--Kubo--Mori (BKM) estimates adapted to the coherence--population structure. We further apply the framework to Davies semigroups under additional secular decoupling and population-rate assumptions. The resulting statements provide conditional certification bounds near rank-deficient stationary states, rather than general mixing-time or convergence-rate estimates.

quant-ph↗

arXiv2026

Quadratic Stability of Entropy Minimizers under Block-Separable Convex Constraints

We investigate entropy minimization problems for quantum states subject to convex block-separable constraints. Our principal result is a quantitative stability theorem: under a natural confining (fixed-support) hypothesis, if a state has entropy within ε of the minimum permitted by the constraint, then it must lie within O(ε^{1/2}) in trace norm of the set of entropy minimizers. We show that this rate is optimal and cannot be improved uniformly. The analysis is entirely finite-dimensional and exploits the block-separable structure of the constraint set, which induces a natural decomposition of entropy into a marginal (classical) component and conditional (internal) components. Quadratic stability emerges from the curvature of Shannon entropy on the marginal polytope and of von Neumann entropy on the constrained block states, yielding explicit stability constants determined by the geometry of the constraint. We further demonstrate that this stability phenomenon cannot be derived from Pinsker-type inequalities or standard entropy continuity bounds, since no reference state is fixed a priori and the entropy minimizer arises intrinsically from the constraint geometry. The framework is abstract and independent of any arithmetic input, and provides a general quadratic stability principle for entropy minimization under structured convex constraints.

quant-ph↗