Related papers: Weak quasi-factorization for the Belavkin-Staszews…
It was recently noted that the entanglement entropy for a subsystem of a chaotic eigenstate exhibits an enhanced correction when the subsystem approaches a phase transition at half the total system size. This enhanced correction was derived…
We examine the entanglement entropy of the even half of a translationally invariant finite chain or lattice in its ground state. This entropy measures the entanglement between the even and odd halves (each forming a "comb" of $n/2$ sites)…
We propose an EPR inequality based on an entropic uncertainty relation for complementary continuous variable observables. This inequality is more sensitive than the previously established EPR inequality based on inferred variances, and…
This manuscript is a review of the main results obtained in a series of papers involving the present authors and their collaborator J.L. Cardy over the last two years. In our work we have developed and applied a new approach for the…
We give new combinatorial proofs of known almost-periodicity results for sumsets of sets with small doubling in the spirit of Croot and Sisask, whose almost-periodicity lemma has had far-reaching implications in additive combinatorics. We…
We identify the near-critical effective theory (EFT) for a wide class of low-temperature phase transitions found via holography. The EFT is of the semi-holographic type and describes both holographic Berezinskii-Kosterlitz-Thouless (BKT)…
We prove the existence of weak solution for a system of quasi-variational inequalities related to a switching problem with dynamic driven by operator associated with a semi-Dirichlet form and with measure data. We give a stochastic…
We give a new characterization of relative entropy, also known as the Kullback-Leibler divergence. We use a number of interesting categories related to probability theory. In particular, we consider a category FinStat where an object is a…
We present a family of correlations constraints that apply to all multipartite quantum systems of finite dimension. The size of this family is exponential in the number of subsystems. We obtain these relations by defining and investigating…
We consider two-body and quasi-two-body decays of the type $f_1 \to f_2 B$, where $f_1$ and $f_2$ are spin-1/2 fermions and $B$ a spin-0 or spin-1 boson. After recalling the non-covariant formalism for decay amplitudes, we derive the…
We review in this paper the research status on testing the completeness of Quantum mechanics in High Energy Physics, especially on the Bell Inequalities. We briefly introduce the basic idea of Einstein, Podolsky, and Rosen paradox and the…
Weak-strong uniqueness property in the class of finite energy weak solutions is established for two different compressible liquid crystal systems by the method of relative entropy. To overcome the difficulties caused by the molecular…
We extend the definition of the conditional min-entropy from bipartite quantum states to bipartite quantum channels. We show that many of the properties of the conditional min-entropy carry over to the extended version, including an…
In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure.
We explore consequences of a hyperbolic metric induced by the composition property of the Harvda-Charvat/Dar\'{o}czy/Cressie-Read/Tsallis entropy. We address the special case of systems described by small deviations of the non-extensive…
This paper classifies the factorizations of almost simple groups with a factor having at least two nonsolvable composition factors. This together with a previous classification result of the authors reduces the factorization problem of…
Among the many facets of quantum correlations, bound entanglement has remained one the most enigmatic phenomena, despite the fact that it was discovered in the early days of quantum information. Even its detection has proven to be…
A flow $(X,T)$ induces the flow $(2^X,T)$. Quasifactors are minimal subsystems of $(2^X, T)$ and hence orbit closures of almost periodic points for $(2^X, T)$. We study quasifactors via the almost periodic points for $(2^X,T)$.
The challenge of equality in the strong subadditivity inequality of entropy is approached via a general additivity of correlation information in terms of nonoverlapping clusters of subsystems in multipartite states (density operators). A…
The relative entropy of entanglement is defined in terms of the relative entropy between an entangled state and its closest separable state (CSS). Given a multipartite-state on the boundary of the set of separable states, we find a closed…