A (2+1)-dimensional gapped quantum many-body system can have a topologically protected energy current at its edge. The magnitude of this is determined entirely by the temperature and chiral central charge, quantity associated with effective field theory We derive formula for charge that, akin to topological entanglement entropy, completely ground state wave function in bulk. According our formula, nonzero gives rise obstruction that prevents from being real valued any local product basis.

We prove that the quantum Gibbs states of spin systems above a certain threshold temperature are approximate Markov networks, meaning conditional mutual information decays rapidly with distance. demonstrate exponential decay for short-ranged interacting and power-law long-ranged systems. Consequently, we establish efficiency sampling algorithms, strong version area law, quasilocality effective Hamiltonians on subsystems, clustering theorem information, polynomial-time algorithm classical...

In Phys. Rev. Lett. 128, 176402 (2022), we argued that the chiral central charge---a topologically protected quantity characterizing edge theory of a gapped $(2+1)$-dimensional system---can be extracted from bulk by using an order parameter called modular commutator. this paper, reveal general properties commutator and strengthen its relationship with charge. First, identify connections between conditional mutual information, time reversal, flow. Second, prove, within framework entanglement...

We introduce the concepts of a symmetry-protected sign problem and magic to study complexity topological (SPT) phases matter. In particular, we say state has or magic, if finite-depth quantum circuits composed symmetric gates are unable transform into non-negative real wave function stabilizer state, respectively. prove that states belonging certain SPT have these properties, as result their anomalous symmetry action at boundary. For example, find one-dimensional <mml:math...

Telecloning is a protocol introduced by Murao et al. to distribute copies of an unknown quantum state many receivers in way that beats the trivial ``clone-and-teleport'' protocol. In last decade, new type teleportation called port-based teleportation, which receiver can recover without having actively perform correction operations, but simply looking at correct port, has been widely studied. this paper, we consider analog telecloning, where conventional replaced variant. To achieve this,...

A special feature of the ground state in a topologically ordered phase is existence large scale correlations depending only on topology regions. These can be detected by topological entanglement entropy or measure called irreducible correlation. We show that these two measures coincide for states obeying an area law and having zero-correlation length. Moreover, we provide operational meaning proving its equivalence to optimal rate particular class secret sharing protocols. This establishes...

In Phys. Rev. Lett. 128, 176402 (2022), we argued that the chiral central charge---a topologically protected quantity characterizing edge theory of a gapped $(2+1)$-dimensional system---can be extracted from bulk by using an order parameter called modular commutator. this paper, reveal general properties commutator and strengthen its relationship with charge. First, identify connections between conditional mutual information, time reversal, flow. Second, prove, within framework entanglement...

Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases. We study the conditions needed for two-dimensional trivial states to exhibit spurious contributions that contaminates topological entropy. show if state at boundary a subregion is stabilizer state, then it non-zero contribution region and only if, in non-trivial one-dimensional $G_1\times G_2$ symmetry-protected-topological (SPT) phase. However, we provide candidate but does not belong...

The resource theory of thermal operations, an established model for small-scale thermodynamics, provides extension equilibrium thermodynamics to nonequilibrium situations. On a lattice any dimension with translation-invariant local Hamiltonian, we identify large set states that can be reversibly converted and from the state operations small amount coherence. These are spatially ergodic states, i.e., have sharp statistics observable, mixtures such same thermodynamic potential. As intermediate...

For quantum spin systems in any spatial dimension with a local, translation-invariant Hamiltonian, we prove that asymptotic state convertibility from to another one by thermodynamically feasible class of dynamics, called thermal operations, is completely characterized the Kullback-Leibler (KL) divergence rate, if and spatially ergodic. Our proof consists two parts phrased terms branch information theory resource theory. First, states, for which min max R\'enyi divergences collapse...

Observational entropy - a quantity that unifies Boltzmann's entropy, Gibbs' von Neumann's macroscopic and the diagonal has recently been argued to play key role in modern formulation of statistical mechanics. Here, relying on algebraic techniques taken from Petz's theory sufficiency Levy-type concentration bound, we prove rigorous theorems showing how observational system undergoing unitary evolution chosen at random tends increase with overwhelming probability reach its maximum very...

Observational entropy—a quantity that unifies Boltzmann's entropy, Gibbs' von Neumann's macroscopic and the diagonal entropy—was recently argued to play a key role in modern formulation of statistical mechanics. Here, relying on algebraic techniques taken from Petz's theory sufficiency Lévy-type concentration bound, we prove rigorous theorems showing how observational entropy system undergoing unitary evolution chosen at random tends increase with overwhelming probability reach its maximum...

Anyonic systems are modeled by topologically protected Hilbert spaces which obey complex superselection rules restricting possible operations. These cannot be decomposed into tensor products of spatially localized subsystems, whereas the product structure is a foundation standard entanglement theory. We formulate bipartite theory for pure anyonic states and analyze its properties as nonlocal resource quantum information processing. introduce new measure, asymptotic entropy (AEE), show that...

We consider two-dimensional states of matter satisfying a uniform area law for entanglement. show that the topological entanglement entropy is equal to minimum relative distance from reduced state set thermal local models. The argument based on strong subadditivity quantum entropy. For with zero entropy, in particular, formula gives locality at boundary region as Hamiltonians. It also implies spectrum one-dimensional region.

Growth hormone (GH) regulates the proliferation and maturation of chondrocytes in epiphyseal growth plate, which a temporal dimension is superimposed on septal organization tissue. In this study we investigated vivo effects hypophysectomy (Hypox) injection GH into Hypox animals (Hypox + GH) proliferative activity plate chondrocytes. We assessed immunohistochemical expression proliferating cell nuclear antigen (PCNA) paraffin-embedded tissues, using monoclonal antibody PC 10 against PCNA...