Interpreting Quantum Interference Using a Berry’s Phase-like Quantity

Abstract

We show that quantum interference can be interpreted in terms of a phase invariant quantity, not unlike the Berry's phase. Under this interpretation, closed loops in time become fundamental quantum entities, and all quantum states become periodic. Decoherence is then seen to occur naturally as a consequence. This formalism, although counterintuitive, provides another useful way of assigning meaning to quantum probabilities and quasi-probabilities.

Quantum Interference and Many Worlds: A New Family of Classical Analogies

“…It was recently shown that QI can be understood heuristically as a quasi-probability effect as opposed to being interference in the traditional sense [11]. Surprisingly, this interpretation requires one to think of closed loops in time (represented by products of probability amplitudes) as fundamental quantum entities, much as we think of state vectors normally.…”

“…We will calculate the probability P f i for the |i → |f transition two ways: the traditional way, and by the method suggested in [11].…”

“…2. Following [11], we can also find P f i by enumerating all possible closed loops that contain |i and |f . For each, we write down an amplitude; there are four such amplitudes, and P f i is then the sum of these amplitudes:…”

“…This sort of construction is obviously inspired by Berry's geometric phase [17], in which parametric Hamiltonians H(λ) acquire a gauge-invariant phase factor when λ evolves and returns to its starting value. Indeed, the work in [11] had its genesis in a simple question: "Can Berry's geometric phase be used to interpret quantum interference?" In [11], the parameter λ is considered to be time itself, although this need not be the case.…”

“…Indeed, the work in [11] had its genesis in a simple question: "Can Berry's geometric phase be used to interpret quantum interference?" In [11], the parameter λ is considered to be time itself, although this need not be the case.…”