Asymptotic redundancies for universal quantum coding
@article{Krattenthaler1996AsymptoticRF,
title={Asymptotic redundancies for universal quantum coding},
author={Christian Krattenthaler and Paul B. Slater},
journal={IEEE Trans. Inf. Theory},
year={1996},
volume={46},
pages={801-819}
}Clarke and Barren (1990, 1994, 1995) have shown that the Jeffreys' invariant prior of Bayesian theory yields the common asymptotic (minimax and maximin) redundancy of universal data compression in a parametric setting. We seek a possible analog of this result for the two-level quantum systems. We restrict our considerations to prior probability distributions belonging to a certain one-parameter family, q/sub u/,-/spl infin/<u<1. Within this setting, we are able to compute exact redundancy…
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References
SHOWING 1-10 OF 74 REFERENCES
LETTER TO THE EDITOR: The quantum Jeffreys' prior/Bures metric volume element for squeezed thermal states and a universal coding conjecture
- Physics
- 1996
Clarke and Barron have recently established that the (classical) Jeffreys' prior yields universal codes - ones which do relatively well (in the sense of relative entropy) no matter what the true…
Jeffreys' prior is asymptotically least favorable under entropy risk
- Computer Science
- 1992
A general minimax result for relative entropy
- Computer ScienceIEEE Trans. Inf. Theory
- 1997
It is shown that the minimax and maximin values of this game are always equal, and there is always a minimax strategy in the closure of the set of all Bayes strategies.
Geometry of canonical correlation on the state space of a quantum system
- Mathematics
- 1994
A Riemannian metric is defined on the state space of a finite quantum system by the canonical correlation (or Kubo–Mori/Bogoliubov scalar product). This metric is infinitesimally induced by the…
Good quantum error-correcting codes exist.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1996
The techniques investigated in this paper can be extended so as to reduce the accuracy required for factorization of numbers large enough to be difficult on conventional computers appears to be closer to one part in billions.
Universal noiseless coding
- Computer ScienceIEEE Trans. Inf. Theory
- 1973
This paper considers noiseless coding for sources with unknown parameters, primarily in terms of variable-length coding, with performance measured as a function of the coding redundancy relative to the per-letter conditional source entropy given the unknown parameter.
LETTER TO THE EDITOR: Quantum Fisher - Bures information of two-level systems and a three-level extension
- Physics
- 1996
Braunstein and Caves have recently demonstrated that the Bures metric on the mixed quantum states is equivalent - up to a proportionality factor of four - to the statistical distinguishability or…
Schumacher's quantum data compression as a quantum computation.
- Computer SciencePhysical review. A, Atomic, molecular, and optical physics
- 1996
An explicit algorithm for performing Schumacher's noiseless compression of quantum bits is given, based on a combinatorial expression for a particular bijection among binary strings, expressed in a high-level pseudocode language.
Information-theoretic asymptotics of Bayes methods
- Computer ScienceIEEE Trans. Inf. Theory
- 1990
The authors examine the relative entropy distance D/sub n/ between the true density and the Bayesian density and show that the asymptotic distance is (d/2)(log n)+c, where d is the dimension of the parameter vector.
Applications of quantum and classical Fisher information to two-level complex and quaternionic and three-level complex systems
- Computer Science
- 1996
In the Bayesian theory of statistical inference, one can employ the square root of the determinant of an n×n Fisher information matrix as a reparametrization‐invariant prior (generally unnormalized) measure over an n‐dimensional family (Riemannian manifold) of probability distributions.