the distinguishability of quantum systems in different states, and the general process of extracting classical information from quantum systems
Questions tagged [state-discrimination]
45 questions
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Probability of making an error in identifying quantum state
In my notes I have the following:
In a measurement described by POVM $\{\pî_j\}$, we associate $\pî_j$
with state $\rhô_j$, that is if outcome $j$ is obtained, we take this
to indicate that the state sent was $\rhô_j$.
The probability of making…
PhysicsQuestion
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Making an ambiguous and unambiguous state determinations together
Measurement operators for those that one creates for unambiguous state discrimination, $\Pi_0,~\Pi_1,~\Pi_?$, are such that
$\Pi_0 + \Pi_1 + \Pi_? = \mathbb{1}$ and the probabilities for a measurement click are
$p_i = \langle E_i | \Pi_i | E_i…
BeauGeste
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Show pretty good measurements give the error probability bound $P_e^{\rm PGM}\le\sum_{i\neq j}\sqrt{p_i p_j} F(\rho_i\rho_j)$
While reading some online lecture notes (Link to pdf) about state discrimination, I stumbled upon the following bound for the success probability of discriminating between a set of states $\rho_i$, with prior probabilities $p_i$, using the…
glS
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What is the value of average success probability in unambiguous state discrimination?
Unambiguous state discrimination, as outlined here starting at p. 421, introduces an average success probability $P = 1 - Q^{POVM}$ where $Q^{POVM}$ is the average failure probability. However, I fail to see the value in these quantities when trying…
BeauGeste
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How to understand the result of Scenario 3.1 in John Watrous' book?
In scenario 3.1, Bob's goal is to correctly determine the value stored in $\textbf{Y} $ using only the information from the observation of $\textbf{X}$. How to understand the claim that "The probability that Bob correctly identifies the value stored…
Michael.Andy
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