Average entropy of a subsystem.

@article{Page1993AverageEO,
  title={Average entropy of a subsystem.},
  author={Page},
  journal={Physical review letters},
  year={1993},
  volume={71 9},
  pages={
          1291-1294
        }
}
  • Page
  • Published 7 May 1993
  • Mathematics
  • Physical review letters
If a quantum system of Hilbert space dimension mn is in a random pure state, the average entropy of a subsystem of dimension m\ensuremath{\le}n is conjectured to be ${\mathit{S}}_{\mathit{m},\mathit{n}}$= ${\mathit{S}}_{\mathit{k}=\mathit{n}+1}^{\mathit{mn}}$ 1/k-m-1/2n and is shown to be \ensuremath{\simeq}lnm-m/2n for 1\ensuremath{\ll}m\ensuremath{\le}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. 
Typical entropy of a subsystem: Page curve and its variance.
TLDR
For a system of non-interacting spins in a magnetic field, the thermal entropy arises as the typical entanglement entropy of a subsystem as well as the application to physical systems in an energy eigenstate.
Distinguishability of generic quantum states
Properties of random mixed states of dimension $N$ distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large $N$, due to the concentration of measure,
Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians.
TLDR
It is proved that in the limit in which the subsystem size is a vanishing fraction of the system size, the average entanglement entropy is maximal; i.e., typical eigenstates of such Hamiltonians exhibit eigenstate thermalization.
On the Geometric Probability of Entangled Mixed States
The state space of a composite quantum system, the set of density matrices P$$ \mathfrak{P} $$+, is decomposable into the space of separable states S$$ \mathfrak{S} $$+ and its complement, the space
Bounds on the entanglement entropy of droplet states in the XXZ spin chain
We consider a class of one-dimensional quantum spin systems on the finite lattice $\Lambda\subset\mathbb{Z}$, related to the XXZ spin chain in its Ising phase. It includes in particular the so-called
On the convergence of output sets of quantum channels
We study the asymptotic behavior of the output states of sequences of quantum channels. Under a natural assumption, we show that the output set converges to a compact convex set, clarifying and
Truncated Linear Statistics Associated with the Top Eigenvalues of Random Matrices
Given a certain invariant random matrix ensemble characterised by the joint probability distribution of eigenvalues $$P(\lambda _1,\ldots ,\lambda _N)$$P(λ1,…,λN), many important questions have been
Efficient decoding for the Hayden-Preskill protocol
TLDR
Two particular decoding procedures for reconstructing a quantum state from the Hawking radiation in the Hayden-Preskill thought experiment are presented, where the decay of out-of-time-order correlators (OTOCs) guarantees faithful state recovery.
Flavored N$$ \mathcal{N} $$ = 4 SYM — a highly entangled quantum liquid
A bstractWe study N$$ \mathcal{N} $$ = 4 SYM theory coupled to fundamental N$$ \mathcal{N} $$ = 2 hypermultiplets in a state of finite charge density. The setup can be described holographically as a
Renyi entropy of chaotic eigenstates.
Using arguments built on ergodicity, we derive an analytical expression for the Renyi entanglement entropies which, we conjecture, applies to the finite-energy density eigenstates of chaotic
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 15 REFERENCES
Average quantal behavior and thermodynamic isolation
We study the thermodynamic concept of isolation. The causal motion of a system that models a thermodynamic “universe” but nevertheless couples to a surround is reconciled with an increase of
Black hole information
Hawking's 1974 calculation of thermal emission from a classical black hole led to his 1976 proposal that information may be lost from our universe as a pure quantum state collapses gravitationally
Mathematical Methods in Physics
Volume II J. S. R. Chisholm and Rosa M. Morris Amsterdam: North-Holland. 1964 Pp. xviii + 717. Price 72s. This book is a valuable addition to an ever-growing collection of mathematical texts written
Phys
  • 19, 1028 (1978); cf. E. Lubkin and T. Lubkin, ”Average Quantal Behavior and Thermodynamic Isolation,” University of Wisconsin- Milwaukee preprint WISC-MILW-92-TH-12
  • 1992
Ann. Phys
  • Ann. Phys
  • 1988
Black Hole Information” (University of Alberta report Alberta- Thy-23-93
  • hep-th/9305040), to be published in Proceedings of the 5th Canadian Conference on General Relativity and Relativistic Astrophysics, University of Waterloo, 13–15 May, 1993, edited by R. B. Mann and R. G. McLenaghan
  • 1994
Information in Black Hole Radiation ” ( University of Alberta report AlbertaThy2493 , hepth / 9306083 ) , submitted to
  • Black Hole Information ” ( University of Alberta report AlbertaThy2393 , hepth / 9305040 ) , to be published in Proceedings of the 5 th Canadian Conference on General Relativity and Relativistic Astrophysics
  • 1994
Black Hole InformationUniversity of Alberta report Alberta- Thy-23-93, hep-th/9305040), to be
  • Proceedings of the 5th Canadian Conference on General Relativity and Relativistic Astrophysics
  • 1993
Commun
  • Math. Phys. 18, 160
  • 1970
Commun. Math. Phys
  • Commun. Math. Phys
  • 1970
...
1
2
...