In  it was observed that asymptotic boundary conditions play an important role in the study of holographic entanglement beyond AdS/CFT. In particular, the Ryu-Takayanagi proposal must be modified for warped AdS 3 (WAdS 3) with Dirichlet boundary conditions. In this paper, we consider AdS 3 and WAdS 3 with Dirichlet-Neumann bound-ary conditions. The conjectured holographic duals are warped conformal field theories (WCFTs), featuring a Virasoro-Kac-Moody algebra. We provide a holographic calculation of the entanglement entropy and Rényi entropy using AdS 3 /WCFT and WAdS 3 /WCFT du-alities. Our bulk results are consistent with the WCFT results derived by Castro-Hofman-Iqbal using the Rindler method. Comparing with , we explicitly show that the holographic entanglement entropy is indeed affected by boundary conditions. Both results differ from the Ryu-Takayanagi proposal, indicating new relations between spacetime geometry and quantum entanglement for holographic dualities beyond AdS/CFT.
We solve the entanglement classification under stochastic local operations and classical communication
(SLOCC) for general n-qubit states. For two arbitrary pure n-qubit states connected via local operations,
we establish an equation between the two coefficient matrices associated with the states. The rank of the
coefficient matrix is preserved under SLOCC and gives rise to a simple way of partitioning all the pure
states of n qubits into different families of entanglement classes, as exemplified here. When applied to the
symmetric states, this approach reveals that all the Dicke states |l,n> with l=1,..., [n/2] are
inequivalent under SLOCC.
The quantitative adiabatic condition (QAC), or quantitative condition, is a
convenient (a priori) tool for estimating the adiabaticity of quantum evolutions.
However, the range of the applicability of QAC is not well understood. It has
been shown that QAC can become insufficient for guaranteeing the validity of
the adiabatic approximation, but under what conditions the QAC would become
necessary has become controversial. Furthermore, it is believed that the inability
for the QAC to reveal quantum adiabaticity is due to induced resonant transitions.
However, it is not clear how to quantify these transitions in general. Here
we present a progress to this problem by finding an exact relation that can reveal
how transition amplitudes are related to QAC directly. As a posteriori condition
for quantum adiabaticity, our result is universally applicable to any (nondegenerate)
quantum system and gives a clear picture on how QAC could
become insufficient or unnecessary for the adiabatic approximation, which is a
problem that has gained considerable interest in the literature in recent years
Consider an age-dependent, single-species branching process defined by a progeny number distribution, and a lifetime distribution associated with each independent particle. In this paper, we focus on the associated inverse problem where one wishes to formally solve for the progeny number distribution or the lifetime distribution that defines the Bellman-Harris branching process. We derive results for the existence and uniqueness (the identifiability) of these two distributions given one of two types of information: the extinction time probability of the entire process (extinction time distribution), or the distribution of the total number of particles at one fixed time. We demonstrate that perfect knowledge of the distribution of extinction times allows us to formally determine either the progeny number distribution or the lifetime distribution. Furthermore, we show that these constructions are unique. We then consider “data” consisting of a perfectly known total number distribution given at one specific time. For a process with known progeny number distribution and exponentially distributed lifetimes, we show that the rate parameter is identifiable. For general lifetime distributions, we also show that the progeny distribution is globally unique. Our results are presented through four theorems, each describing the constructions in the four distinct cases.
We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing Bayesian inference in function spaces. Such inference comes about naturally in the study of inverse problems of recovering continuous (infinite dimensional) coefficient functions from ordinary or partial differential equations, a problem which is typically ill-posed. Regularization of these problems using L2 function spaces (Tikhonov regularization) is equivalent to Bayesian probabilistic inference, using a Gaussian prior. The Bayesian interpretation of inverse problem regularization is useful since it allows one to quantify and characterize error and degree of precision in the solution of inverse problems, as well as examine assumptions made in solving the problem—namely whether the subjective choice of regularization is compatible with prior knowledge. Using path-integral formalism, Bayesian inference can be explored through various perturbative techniques, such as the semiclassical approximation, which we use in this manuscript. Perturbative path-integral approaches, while offering alternatives to computational approaches like Markov-Chain-Monte-Carlo (MCMC), also provide natural starting points for MCMC methods that can be used to refine approximations. In this manuscript, we illustrate a path-integral formulation for inverse problems and demonstrate it on an inverse problem in membrane biophysics as well as inverse problems in potential theories involving the Poisson equation.