Content deleted Content added
Aram.harrow (talk | contribs) changed to more modern notation: S(A|B)_rho instead of S(rho | sigma). I've explained the advantages of this on the talk page. |
typo S(A) changed to S(B) |
||
Line 7:
Given a bipartite quantum state <math>\rho^{AB}</math>, the entropy of the entire system is <math>S(AB)_\rho \ \stackrel{\mathrm{def}}{=}\ S(\rho^{AB})</math>, and the entropies of the subsystems are <math>S(A)_\rho \ \stackrel{\mathrm{def}}{=}\ S(\rho^A) = S(\mathrm{tr}_B\rho^{AB})</math> and <math>S(B)_\rho</math>. The von Neumann entropy measures how uncertain we are about the value of the state; how much the state is a [[mixed state (physics)|mixed state]].
By analogy with the classical conditional entropy, one defines the conditional quantum entropy as <math>S(A|B)_\rho \ \stackrel{\mathrm{def}}{=}\ S(AB)_\rho - S(
An equivalent (and more intuitive) operational definition of the quantum conditional entropy (as a measure of the [[quantum communication]] cost or surplus when performing [[quantum state]] merging) was given by [[Michał Horodecki]], [[Jonathan Oppenheim]], and [[Andreas Winter]] in their paper "Quantum Information can be negative" [http://arxiv.org/abs/quant-ph/0505062].
| |||