# Subjective nature of path information in quantum mechanics

## TL;DR

This paper explores how quantum mechanics challenges classical ideas about tracking a particle's origin, showing that even with full path information, a photon's origin cannot always be determined.

## Contribution

The study demonstrates that full path information does not guarantee a definite origin for photons in multi-source quantum experiments.

## Key findings

- Even with full path information, photon pairs cannot be assigned a definite origin.
- Grouping crystals differently leads to different interpretations of path information.
- The results challenge classical intuition about trajectory-based origin tracing.

## Abstract

Common sense suggests that a particle must have a definite origin if its full path information is available. In quantum mechanics, the knowledge of path information is captured through the well-established duality relation between path distinguishability and interference visibility. If visibility is zero, high path distinguishability can be achieved, which enables one to determine with high predictive power where the particle originates. We investigate the complementarity between path information and interference visibility through an experiment involving three sources emitting into identical modes. Our findings challenge the classical intuition that a particle can be traced back to its origin through its trajectory when full path information is available. By grouping the crystals in different ways, we demonstrate that it is impossible to ascribe a definite physical origin to the photon pair, even if the emission probability of one individual source is zero and full path information is available. Our results shed new light on the physical interpretation of probability assignment and path information beyond its mathematical meaning and show that the interpretation of path information in quantum mechanics is subjective.

In multi-path interference experiments, the different possibilities of partitioning reality into alternatives represented by probability amplitudes can lead to unexpected consequences. Here, the authors study the interplay between interference and which-source information in a frustrated SPDC system with three nonlinear crystals, showing that even in the case of full which-source information, it is impossible to ascribe a definite origin to photon pairs.