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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2507.09716 |
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| _version_ | 1866911053757022208 |
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| author | Mannucci, Mirco A. |
| author_facet | Mannucci, Mirco A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09716 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When the Weak Becomes Strong: Effective Observables via Time-Symmetric Quantum Selection Mannucci, Mirco A. Quantum Physics Computational Engineering, Finance, and Science 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. |
| title | When the Weak Becomes Strong: Effective Observables via Time-Symmetric Quantum Selection |
| topic | Quantum Physics Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2507.09716 |