Blind spots between quantum states

TL;DR

This paper investigates the phenomenon of blind spots in quantum state overlaps, revealing their generic occurrence, dependence on state components, and the effects of decoherence, with implications for quantum orthogonality and superpositions.

Contribution

It demonstrates that complete orthogonality points are common, analyzes how decoherence affects these blind spots, and explores their structure in superpositions of coherent states.

Findings

Complete orthogonality occurs at isolated points.

Decoherence quickly lifts correlation minima from zero.

Blind spots form a hexagonal lattice pattern in certain superpositions.

Abstract

The overlap of a large quantum state with its image, under tiny translations, oscillates swiftly. We here show that complete orthogonality occurs generically at isolated points. Decoherence, in the Markovian approximation, lifts the correlation minima from zero much more quickly than the Wigner function is smoothed into a positive phase space distribution. In the case of a superposition of coherent states, blind spots depend strongly on positions and amplitudes of the components, but they are only weakly affected by relative phases and the various degrees and directions of squeezing. The blind spots for coherent state triplets are special in that they lie close to an hexagonal lattice: Further superpositions of translated triplets, specified by nodes of one of the sublattices, are quasi-orthogonal to the original triplet and to any state, likewise constructed on the other sublattice.