Probability amplitude

Probability amplitude refers to a complex number assigned to each transition in quantum mechanics, with an absolute value between 0 and 1. It is considered more fundamental than the real probability that can be obtained from it, and the probability amplitude |〈x|ψ〉|2 does not directly give the probability of finding a quantum system at a specific position.From: The Quantum Phase Operator [2019], Reflections on probabilistic compared to quantum computational devices [2021], Quantum Mechanics for Thinkers [2019]

Experiments with Entangled Photons

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Published in Walter Fox Smith, Experimental Physics, 2020

Enrique J. Galvez

The measurement leaves the photons in the state where both are horizontally polarized. Analytically, it yields the final state multiplied by the probability amplitude of being in that state. The probability is the absolute value squared of the probability amplitude, which in the above case is 1/2. This is done without measuring the state of photon 2. It also brings the topic of non-locality, that a measurement on one particle instantaneously also projects the state of photon 2. We could have also obtained the joint probability by projecting the state of both photons. For example,PHH/ψ=H1H2ψ2=1/2PVV/ψ=1/2PHV/ψ=0PVH/ψ=0.

Reflections on probabilistic compared to quantum computational devices

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Published in International Journal of Parallel, Emergent and Distributed Systems, 2021

Giuseppe Corrente

A quantum Turing machine (QTM) [9], on a finite set Q of states and the finite alphabet Γ, is given by a transition function assigning a so-called amplitude (or probability amplitude), a complex number, the absolute value of which is in the interval [0, 1], to each transition. Furthermore, for each configuration c0 and all its successor configurations c1, … , ck the following sentence must be true:

Probability amplitude

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Experiments with Entangled Photons

Reflections on probabilistic compared to quantum computational devices