Positive conditional entropy of a state thus means the state cannot reach even the classical limit, while the negative conditional entropy provides for additional information.
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Alice has access to system A and Bob to system B . The conditional entropy measures the average uncertainty Bob has about Alice's state upon sampling from his own system.
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The negative conditional entropy is also known as the coherent information, and gives the additional number of bits above the classical limit that can be transmitted in a quantum dense coding protocol.
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An "'information diagram "'is a type of Venn diagram used in information theory to illustrate relationships among Shannon's basic entropy, joint entropy, conditional entropy and mutual information.
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Because entropy can be conditioned on a random variable or on that random variable being a certain value, care should be taken not to confuse these two definitions of conditional entropy, the former of which is in more common use.
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In information theory, the "'conditional entropy "'( or "'equivocation "') quantifies the amount of information needed to describe the outcome of a random variable Y given that the value of another random variable X is known.
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Conditional Entropy asks the question : " Given that I know a set of tags, how much uncertainty regarding the document set that I was referencing with those tags remains ? " The fact that this curve is strictly increasing suggests that the specificity of any given tag is decreasing.
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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 MichaB Horodecki, Jonathan Oppenheim, and Andreas Winter in their paper " Quantum Information can be negative ".
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Given discrete random variables X with Image \ mathcal X and Y with Image \ mathcal Y, the conditional entropy of Y given X is defined as : ( Intuitively, the following can be thought as the weighted sum of H ( Y | X = x ) for each possible value of x, using p ( x ) as the weights)
