907 research outputs found
No Simple Dual to the Causal Holographic Information?
In AdS/CFT, the fine grained entropy of a boundary region is dual to the area
of an extremal surface X in the bulk. It has been proposed that the area of a
certain 'causal surface' C - i.e. the 'causal holographic information' (CHI) -
corresponds to some coarse-grained entropy in the boundary theory. We construct
two kinds of counterexamples that rule out various possible duals, using (1)
vacuum rigidity and (2) thermal quenches. This includes the 'one-point entropy'
proposed by Kelly and Wall, and a large class of related procedures. Also, any
coarse-graining that fixes the geometry of the bulk 'causal wedge' bounded by
C, fails to reproduce CHI. This is in sharp contrast to the holographic
entanglement entropy, where the area of the extremal surface X measures the
same information that is found in the 'entanglement wedge' bounded by X.Comment: 21 pages, 5 figure
Postquantum Br\`{e}gman relative entropies and nonlinear resource theories
We introduce the family of postquantum Br\`{e}gman relative entropies, based
on nonlinear embeddings into reflexive Banach spaces (with examples given by
reflexive noncommutative Orlicz spaces over semi-finite W*-algebras,
nonassociative L spaces over semi-finite JBW-algebras, and noncommutative
L spaces over arbitrary W*-algebras). This allows us to define a class of
geometric categories for nonlinear postquantum inference theory (providing an
extension of Chencov's approach to foundations of statistical inference), with
constrained maximisations of Br\`{e}gman relative entropies as morphisms and
nonlinear images of closed convex sets as objects. Further generalisation to a
framework for nonlinear convex operational theories is developed using a larger
class of morphisms, determined by Br\`{e}gman nonexpansive operations (which
provide a well-behaved family of Mielnik's nonlinear transmitters). As an
application, we derive a range of nonlinear postquantum resource theories
determined in terms of this class of operations.Comment: v2: several corrections and improvements, including an extension to
the postquantum (generally) and JBW-algebraic (specifically) cases, a section
on nonlinear resource theories, and more informative paper's titl
The Physical Basis of the Gibbs-von Neumann entropy
We develop the argument that the Gibbs-von Neumann entropy is the appropriate
statistical mechanical generalisation of the thermodynamic entropy, for
macroscopic and microscopic systems, whether in thermal equilibrium or not, as
a consequence of Hamiltonian dynamics. The mathematical treatment utilises well
known results [Gib02, Tol38, Weh78, Par89], but most importantly, incorporates
a variety of arguments on the phenomenological properties of thermal states
[Szi25, TQ63, HK65, GB91] and of statistical distributions[HG76, PW78, Len78].
This enables the identification of the canonical distribution as the unique
representation of thermal states without approximation or presupposing the
existence of an entropy function. The Gibbs-von Neumann entropy is then
derived, from arguments based solely on the addition of probabilities to
Hamiltonian dynamics.Comment: 42 pages, no figures (3rd version substantial revision and
simplification of central argument incorporating adiabatic availability and
passive distributions
Low dimensional manifolds for exact representation of open quantum systems
Weakly nonlinear degrees of freedom in dissipative quantum systems tend to
localize near manifolds of quasi-classical states. We present a family of
analytical and computational methods for deriving optimal unitary model
transformations based on representations of finite dimensional Lie groups. The
transformations are optimal in that they minimize the quantum relative entropy
distance between a given state and the quasi-classical manifold. This naturally
splits the description of quantum states into quasi-classical coordinates that
specify the nearest quasi-classical state and a transformed quantum state that
can be represented in fewer basis levels. We derive coupled equations of motion
for the coordinates and the transformed state and demonstrate how this can be
exploited for efficient numerical simulation. Our optimization objective
naturally quantifies the non-classicality of states occurring in some given
open system dynamics. This allows us to compare the intrinsic complexity of
different open quantum systems.Comment: Added section on semi-classical SR-latch, added summary of method,
revised structure of manuscrip
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