Operational formulation of weak values without probe systems

Abstract

Weak values are the fundamental values for observables in a pre- and post-selected system. Weak values are typically measured by weak measurement, in which weak values appear in the change of not the pre- and post-selected system but the probe system. This indirect characteristic of weak measurement obscures the meaning of weak values for the pre- and post-selected system, in contrast to conventional physical quantities, which have a clear operational meaning. In this study, we operationally formulate weak values as the sensitivity of post-selection probability amplitude to small transformation in a pre- and post-selected system. This formulation of weak values, which is free from the concept of probe shift assumed in weak measurement, gives a direct interpretation of strange weak values for the pre- and post-selected system. We further explain that this formulation can simplify weak-value measurement experiments because no probe system is required.

13 pages, 7 figures

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Cited by in corpus (6)

• Progress and Perspectives on Weak-value Amplification
• Complex counterpart of variance in quantum measurements for pre- and post-selected systems
• Weak value amplification and the lifetime of decaying particle
• Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation
• No-go result for quantum postselection measurements of rank-m degenerate subspace
• Quantum Resonance viewed as Weak Measurement