Questions tagged [probability]

For questions associated with the calculation of probability, expected value, variance, standard deviation, or similar statistical quantities.

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What is the probability $\Pr(\|U-I\|_{\rm op}<\varepsilon)$ of a Haar-random unitary being close to the identity?

If one generates an $n\times n$ Haar random unitary $U$, then clearly $\Pr(U=I)=0$. However, for every $\epsilon>0$, the probability $$\Pr(\|U-I\|_{\rm op}<\varepsilon)$$ should be positive. How ...
4
votes
0answers
52 views

In QAOA why do we need $m \log(m)$ repititions to get at least $F_{p}(\beta , \gamma) - 1$ with probability of $1 - 1/m$?

In the original QAOA paper from Farhi https://arxiv.org/pdf/1411.4028.pdf, it is stated in chapter 2 last paragraph (page 6) that: when measuring $F_{p}(\beta , \gamma)$ we get an outcome of at least ...
2
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What is the relation between density matrices and phase-space probability distributions?

According to its tag description, a density matrix is the quantum-mechanical analogue to a phase-space probability measure (probability distribution of position and momentum) in classical statistical ...
1
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46 views

Is this inequality related to time-energy uncertainty true or testable?

Background It is known: In all physical systems in which energy is bounded below, there is no self-adjoint observable that tracks the time parameter t. However I don't think this forbids any ...
0
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29 views

RAC for XOR functions

I need the optimal encoding protocol for 3 $\rightarrow$ 1 Classical RAC such that the receiver is able to retrieve any one of the initial bits, as well as the XOR combinations of those bits. ( If a, ...