Recognition: unknown
Average Entropy of a Subsystem
read the original abstract
If a quantum system of Hilbert space dimension $mn$ is in a random pure state, the average entropy of a subsystem of dimension $m\leq n$ is conjectured to be $S_{m,n}=\sum_{k=n+1}^{mn}\frac{1}{k}-\frac{m-1}{2n}$ and is shown to be $\simeq \ln m - \frac{m}{2n}$ for $1\ll m\leq n$. Thus there is less than one-half unit of information, on average, in the smaller subsystem of a total system in a random pure state.
This paper has not been read by Pith yet.
Forward citations
Cited by 8 Pith papers
-
Large $N$ factorization of families of tensor trace-invariants
Families of complex tensor trace-invariants with tree-like dominant pairings factorize at large N, allowing computation of typical multipartite Rényi entropies for uniform random states.
-
Quantum Maxwell Demon at the Black Hole Horizon: Thermodynamics, Information, and the Equivalence Principle
A quantum Maxwell demon near a black hole horizon loses some work extraction ability for external observers due to information inaccessibility but obeys local thermodynamics and preserves the equivalence principle for...
-
Typical entanglement entropy with charge conservation
Typical entanglement entropy with fixed global charge is given by the local thermal entropy at fixed charge density for both U(1) and SU(2) symmetries in the thermodynamic limit.
-
The Fate of Nucleated Black Holes in de Sitter Quantum Gravity
Nucleated maximal-mass black holes in de Sitter space undergo thermal Hawking evaporation in smooth quantum states and return fully to the empty de Sitter vacuum.
-
The Fate of Nucleated Black Holes in de Sitter Quantum Gravity
Nucleated black holes in de Sitter space evaporate via standard Hawking radiation back to the empty vacuum, rendering nucleation a temporary fluctuation.
-
Properties of tensorial free cumulants
The authors extend tensorial free cumulants to arbitrary orders, connect prior frameworks, and compute non-trivial examples for Gaussian tensors with structured covariances.
-
Eigenstate entanglement entropy in Bose-Hubbard models
The volume-law coefficient of eigenstate entanglement entropy in Bose-Hubbard models remains unchanged by on-site disorder, while the O(1) contribution depends on particle density and bosonic cutoff in conserving case...
-
Quantum chaotic systems: a random-matrix approach
Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.