In quantum mechanics, and especially quantum information and the study of open quantum systems, the trace distance T is a metric on the space of density matrices and gives a measure of the distinguishability between two states. It is the quantum generalization of the Kolmogorov distance for classical probability distributions. (Wikipedia)
Questions tagged [trace-distance]
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Is the trace distance upper bounded by the Euclidean distance?
Suppose we have two pure state $|\psi\rangle$ and $|\phi\rangle$.
I was wondering whether the statement:
$\||\psi\rangle\!\langle\psi|- |\phi\rangle\!\langle\phi|\|_{\rm tr}$ is at most the Euclidean distance between $|\psi\rangle$ and…
Zehong Fan
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