Related papers: On the sharpness of the zero-entropy-density conje…
Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
In our recent work we found a surprising breakdown of symmetry conservation: using standard numerical discretization with very high precision the computed numerical solutions corresponding to very nice initial data may converge to…
We study the geometric distribution of the relative entropy of a charged localised state in Quantum Field Theory. With respect to translations, the second derivative of the vacuum relative entropy is zero out of the charge localisation…
In a remarkable paper [Phys. Rev. Lett. 96, 100503 (2006)], Dimitri Gioev and Israel Klich conjectured an explicit formula for the leading asymptotic growth of the spatially bi-partite von-Neumann entanglement entropy of non-interacting…
We study the vacuum state of spin chains where each site carry an arbitrary representation. We prove that the string hypothesis, usually used to solve the Bethe ansatz equations, is valid for representations characterized by rectangular…
We consider Einstein gravity with positive cosmological constant coupled to matter in an asymptotically de Sitter universe with sphere boundary at timelike infinity. In this setting we show that, to one-loop order and at late time, the norm…
The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being…
It is known that the entropy of a block of spins of size $L$ embedded in an infinite pure critical spin chain diverges as the logarithm of $L$ with a prefactor fixed by the central charge of the corresponding conformal field theory. For a…
We derive an inequality relating the entropy difference between two quantum states to their trace norm distance, sharpening a well-known inequality due to M. Fannes. In our inequality, equality can be attained for every prescribed value of…
We study the asymptotic behavior of the emptiness formation probability for large spin strings in a translation invariant quasifree nonequilibrium steady state of the isotropic XY chain. Besides the overall exponential decay, we prove that,…
We study the entanglement entropies of an interval on the infinite line in the free fermionic spinless Schr\"odinger field theory at finite density and zero temperature, which is a non-relativistic model with Lifshitz exponent $z=2$. We…
Extending our results in "Entropy conjecture for continuous maps of nilmanifolds", to appear in Israel Jour. of Math., we confirm that Entropy Conjecture holds for every continuous self-map of a compact $K(\pi,1)$ manifold with the…
We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an $n$-partite system $A = (A_1, \ldots A_n)$ corresponds to the sum of the entropies of its parts $A_i$. The Asymptotic…
We compute the entropy of entanglement in the ground states of a general class of quantum spin-chain Hamiltonians - those that are related to quadratic forms of Fermi operators - between the first N spins and the rest of the system in the…
We consider nonequilibrium systems such as the Edwards-Anderson Ising spin glass at a temperature where, in equilibrium, there are presumed to be (two or many) broken symmetry pure states. Following a deep quench, we argue that as time goes…
We argue that any superconductor with magnetic impurities is gapless due to a Lifshitz tail in the density of states extending to zero energy. At low energy the density of states $\nu(E \to 0)$ remains finite. We show that fluctuations in…
In the tensionless limit of string theory on flat background all the massive tower of states gets squeezed to a common zero mass level and the free theory is described by an infinite amount of massless free fields with arbitrary integer…
It has been conjectured, on the basis of the gauge-gravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/ 4 pi in units of the Planck constant divided by the Boltzmann…
We show that on exceeding a certain degree of mixedness (as quantified by the von Neumann entropy), entangled states become useless for teleporatation. By increasing the dimension of the entangled systems, this entropy threshold can be made…