Subjective nature of path information in quantum mechanics

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, a high path distinguishability can be obtained, which enables one with high predictive power to know where the particle comes from. Here we show that this perception of path information is problematic. We demonstrate the simultaneous observation of zero interference visibility and the complete absence of which-path information using a three-crystal interference setup. With a contradictory argument by grouping the crystals in different ways, we show 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 findings shed new light on the physical interpretation of probability assignment and path information beyond its mathematical meaning and reshape our understanding of the whole and part in the context of distinguishability.

Subjective Nature of Path Information in Quantum Mechanics

The paper explores the nuances and implications of which-path information within quantum mechanics, emphasizing its subjective nature. The primary objective of the study is to challenge the conventional understanding of particle path information when using a three-crystal interference setup. The authors argue that the traditional interpretation, which links clear path knowledge to high path distinguishability and low interference visibility, is incomplete.

Central to this paper is the duality relation (D^2 + V^2 \leq 1), illustrating the inverse relationship between path distinguishability (D) and interference visibility (V). This duality, initially established for systems such as the archetypical two-path interferometer, is extended here to a three-path system. The research introduces an experimental contradiction, demonstrating that assigning definite origins to photons in a three-path interference system is problematic, even in cases where theoretical calculations suggest such origins should exist.

The experimental setup in this paper involves a novel use of a three-crystal configuration where the relative phases between photon emissions from each crystal can be manipulated. The notable experimental results reveal that adjusting these phases can simultaneously lead to a scenario devoid of interference visibility and lacking definitive path information. This seemingly paradoxical result challenges the straightforward application of the complementarity principle.

When the authors group crystals in different configurations and interpret path information through these groupings, they find that interpretations are inconsistent with one another. For example, assigning path origins in certain groupings does not align with observations or expectations when crystals are grouped differently, leading to conflicting results within the same experimental framework.

The findings have significant implications for the theoretical interpretation of probability and path information in quantum systems. The study suggests that path information should not be seen as an absolute property intrinsic to the quantum system. Instead, it highlights the contextual nature of path information dependent on the framework chosen for interpretation.

Practically, these results invite further examination of the logical underpinnings of quantum mechanics, especially as they pertain to experiments involving multiple indistinguishable paths or particles. Theoretically, this work could revolutionize our understanding of quantum interference patterns, particularly in the context of multiparticle systems. It also poses profound questions about how quantum systems can or should be decomposed into distinguishable parts, thereby influencing the development of quantum information theory and application in quantum computing.

In conclusion, by demonstrating that the lack of interference does not necessarily correlate with definitive which-path information, this paper sheds new light on the versatile and often subjective nature of quantum information. Future experiments can build on these findings by further examining the configurations or introducing more variables, potentially unveiling even more intriguing aspects of path indistinguishability and quantum mechanics.