# Cryptographic Distinguishability Measures for Quantum-Mechanical States

@article{Fuchs1997CryptographicDM, title={Cryptographic Distinguishability Measures for Quantum-Mechanical States}, author={Christopher A. Fuchs and Jeroen van de Graaf}, journal={IEEE Trans. Inf. Theory}, year={1997}, volume={45}, pages={1216-1227} }

This paper, mostly expository in nature, surveys four measures of distinguishability for quantum-mechanical states. This is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography. Each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions: namely, the probability of an identification error, the Kolmogorov distance, the Bhattacharyya coefficient, and the Shannon (1948…

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## References

SHOWING 1-10 OF 29 REFERENCES

### Distinguishability and Accessible Information in Quantum Theory

- Computer Science
- 1996

This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states, and gives a way of expressing the problem so that it appears as algebraic as that of the problem of finding quantum distinguishability measures.

### Quantum memory in quantum cryptography

- Computer Science, Physics
- 1999

This work defines strong attacks of this type, and shows security against them, suggesting that quantum cryptography is secure, and suggests a new type of quantum key distribution scheme where quantum memories are used instead of quantum channels.

### Information Gain vs. State Disturbance in Quantum Theory

- Physics
- 1996

Several aspects of the information–disturbance principle are explored in an attempt to make it firmly quantitative and flesh out its significance for quantum theory as a whole.

### Parity bit in quantum cryptography.

- Computer Science, MathematicsPhysical review. A, Atomic, molecular, and optical physics
- 1996

This paper finds the measurement which provides the optimal mutual information about the parity bit and calculates that information, and proves that this information decreases exponentially with the length of the string in the case where the single bit states are almost fully overlapping.

### Protocols for secure computations

- Mathematics23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)
- 1982

The author gives a precise formulation of this general problem and describes three ways of solving it by use of one-way functions, which have applications to secret voting, private querying of database, oblivious negotiation, playing mental poker, etc.

### Quantum detection and estimation theory

- PhysicsProceedings of the IEEE
- 1978

This online revelation quantum detection and estimation theory can be one of the options to accompany you in imitation of having other time.

### Mathematical techniques for quantum communication theory

- Mathematics
- 1995

A statistically motivated derivation of the Bures-Uhlmann measure of distinguishability for density operators and a simplified proof of the Holevo upper bound to the mutual information of quantum communication channels are presented.

### Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians

- Physics, Education
- 1986

This book is a quantum mechanics text, written on the assumption that the purpose of learning quantum mechanics is to be able to understand the results of fundamental research into the constitution…

### The Structure and Interpretation of Quantum Mechanics

- Physics
- 1989

Preface Introduction. The Stern-Gerlach Experiment PART I THE STRUCTURE OF QUANTUM THEORY 1. Vector Spaces Vectors Operators Eigenvectors and Eigenvalues Inner Products of Vectors in R2 Complex…