Quantum Probability and the Born Ensemble
- URL: http://arxiv.org/abs/2308.07440v2
- Date: Fri, 15 Sep 2023 23:23:35 GMT
- Title: Quantum Probability and the Born Ensemble
- Authors: Themis Matsoukas
- Abstract summary: We define the probability to observe a state, classical or quantum, in proportion to the number of textitevents at that state--the number of ways a walker may materialize at a point of observation at time t.
The quantum process differs from its classical counterpart in that the quantum walker is a pair of qubits, each transmitted independently through all possible paths to a point of observation.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: We formulate a discrete two-state stochastic process with elementary rules
that give rise to Born statistics and reproduce the probabilities from the
Schr\"odinger equation under an associated Hamiltonian matrix, which we
identify. We define the probability to observe a state, classical or quantum,
in proportion to the number of \textit{events} at that state--number of ways a
walker may materialize at a point of observation at time t through a sequence
of transitions starting from known initial state at t=0. The quantum stochastic
process differs from its classical counterpart in that the quantum walker is a
pair of qubits, each transmitted independently through all possible paths to a
point of observation, and whose recombination may produce a positive or
negative event (classical events are never negative). We represent the state of
the walker via a square matrix of recombination events, show that the
indeterminacy of the qubit state amounts to rotations of this matrix, and show
that the Born rule counts the number qubits on this matrix that remain
invariant over a full rotation.
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