# Fidelity and Concurrence of conjugated states

@article{Uhlmann1999FidelityAC, title={Fidelity and Concurrence of conjugated states}, author={Armin Uhlmann}, journal={Physical Review A}, year={1999}, volume={62}, pages={032307} }

We prove some properties of fidelity (transition probability) and concurrence, the latter defined by a straightforward extension of Wootters' notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on conjugated pairs of density operator. These functions turn out to be concave or convex roofs. Optimal decompositions are constructed. Some applications to two and tripartite systems illustrate the general theorems.

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## References

SHOWING 1-7 OF 7 REFERENCES

### Optimizing entropy relative to a channel or a subalgebra

- Mathematics
- 1997

After recalling definition, monotonicity, concavity, and continuity of a channel's entropy with respect to a state (finite dimensional cases only), I introduce the roof property, a convex analytic…

### On Bures Distance and *-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W*-Algebras

- Mathematics
- 2000

On a W*-algebra M, for given two positive linear forms ν,ρ∈ M+* and algebra elements a, b ∈ M, a variational expression for the Bures distance dB(νa, ϱb) between the inner derived positive linear…

### Book Reviews: Group Theory. And Its Application to the Quantum Mechanics of Atomic Spectra

- Physics
- 1959

### Convex Analysis

- Princeton University Press
- 1970

### The implementation of time reversal in the algebra of quantum fields is combined, by convention, with taking the Hermitian adjoint

### Independently this has been shown by Ch. A. Fuchs with other techniques

### Open Sys

- & Inf. Dyn. 5 209
- 1998