2024/09/06 by Patryk Michalski, Michalski, Patryk, Andrzej Dragan +1
Computer Science · #Art #Classical mechanics #Computability, Logic, AI Algorithms #FOS: Physical sciences #Formalism (music) #Literature #Physics #Quantum Physics (quant-ph) #State vector #Theoretical physics
paper · pdf · doi:10.48550/arxiv.2409.04396
openalex publication_date 2024/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The two-state vector formalism of quantum mechanics is a time-symmetrized approach to standard quantum theory. In our work, we aim to establish rigorous foundations for the future investigation within this formalism. We introduce the concept of a story - a compatible pair consisting of a two-state vector and an ideal measurement. Using this concept, we examine the structure of the space comprising all two-state vectors. We analyze the problem of distinguishability and confirm that some pairs of two-state vectors or their statistical mixtures cannot be physically distinguished. In particular, we discuss an example of a two-state vector that is indistinguishable from a statistical mixture of separable two-state vectors and provide an example of a two-state vector that can be distinguished from every such mixture. This leads us to formulate the definition of a strictly non-separable two-state vector as a genuine manifestation of entanglement between the past and the future.