When the Weak Becomes Strong: Effective Observables via Time-Symmetric Quantum Selection

2025/07/13 by Mirco A. Mannucci, Mannucci, Mirco A. · 1 citation
Physics and Astronomy · Computer Science · #Quantum Mechanics and Applications #Quantum Information and Cryptography #Quantum Computing Algorithms and Architecture

paper · pdf · doi:10.48550/arxiv.2507.09716

Abstract

We investigate the sequential composition of weak values in the framework of time-symmetric quantum mechanics. Specifically, we consider a forward'' weak measurement from a preselected state \ketψ to a post-selected state \ketϕ, followed by a reverse'' weak measurement. We show that the product of these two weak values corresponds to the normalized expectation value of a strong, state-conditioned observable B = A P_ψA, where P_ψ= \ketψ\braψ is the projector onto the preselected state. Analyzing the structure of B, we demonstrate how it encodes interference information, particularly when \ketψ is a superposition rather than an eigenstate of A. This formulation extends naturally to mixed states by replacing P_ψ with a generic density matrix ρ, linking the construction to the formalism of generalized quantum measurements. We illustrate practical applications in quantum information, including state-specific error witnessing in quantum computing, and show how the phase of a weak value can be inferred via strong measurements in the pure-state case.

Citations

• The Two-State Vector Formalism of Qauntum Mechanics: an Updated Review

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