© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1805.10202

Potent Value and Potent Operator with Pre- and Post-selected Quantum Systems

Arun Kumar Pati

Published May 25, 2018• 0 citations

Abstract

We introduce a novel concept which we call as potent value of system observable for pre- and post-selected quantum states. This describes, in general, how a quantum system affects the state of the apparatus during the time between two strong measurements corresponding to pre- and post-selections. The potent value can be realized for any interaction strength and for arbitrary coupling between the system and the apparatus observables. Most importantly, potent values generalize and unify the notion of the weak values and modular values of observables in quantum theory. Furthermore, we define a potent operator which describes the action of one system on the another and show that superposition of time-evolutions and time-translation machines are potent operators. These concepts may find useful applications in quantum information processing and can lead to technological benefits.

DOI: 10.48550/arxiv.1805.10202

Related papers

Unusual Interactions of Pre-and-Post-Selected Particles

Yakir Aharonov, Eliahu Cohen, Shay Ben-Moshe

Weak value is increasingly acknowledged as an important research tool for probing quantum pre- and post-selected ensembles, where some extraordinary phenomena occur. We generalize this concept into the broader notion of “weak potential” which enables predicting the interactions between particles when one of them is pre-/post-selected and the interaction potential is small. A harmonic oscillator is considered, undergoing weak position and momentum measurements between strong position measurement, and shown to possess peculiar physical properties, affecting the momentum rather than the position of another oscillator interacting with it.

EPJ Web of Conferences•Jan 1, 2014•19 citations

Unusual Interaction of a Pre-and-Post-Selected Particle

Yakir Aharonov, Eliahu Cohen, Shay Ben-Moshe

Weak value is increasingly acknowledged as an important research tool for probing quantum pre- and post-selected ensembles, where some extraordinary phenomena occur. We generalize this concept to the broader notion of "weak potential" which enables predicting the interactions between particles when one of them is pre-/post-selected and the interaction potential is small. A harmonic oscillator is considered, undergoing weak position and momentum measurements between strong position measurement, and shown to possess peculiar physical properties, affecting the momentum rather than the position of another oscillator interacting with it.

arXiv:1208.3203•Aug 15, 2012•3 citations

On the Two-State Vector Reformulation of Quantum Mechanics

Yakir Aharonov, Lev Vaidman A

A description of quantum systems at the time interval between two successive measurements is presented. Two wave functions, the first pre-selected by the initial measurement and the second post-selected by the final measurement describe quantum systems at a single time. It is shown how this approach leads to a new concept: a weak value of an observable. Weak values represent novel characteristics of quantum systems between two measurements. They are outcomes of a standard measuring procedure that fulfills certain requirements of “weakness”. We call it weak measurement . Physical meaning and underlying mathematical structure of weak measurements are explored.

Physica Scripta•Jan 1, 1998•19 citations

Modular Values and Weak Values of Quantum Observables

Yaron Kedem, Lev Vaidman A

The concept of a modular value of an observable of a pre- and postselected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an effective interaction when the coupling is weak, it describes a coupling of any strength but only to qubit meters. The generalization of the concept for a coupling of a composite system to a multiqubit meter provides an explanation of some current experiments.

arXiv:1007.5281•Physical Review Letters•Nov 30, 2010•72 citations

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

Mirco A. Mannucci

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.

arXiv:2507.09716•Jul 13, 2025•0 citations

WEAK MEASUREMENTS

J. G. Story, Nicholas W. M. Ritchie, Randall G. Hulet

A general description of weak measurements is presented. The “weak value” of an operator in pre- and post-selected systems is described both mathematically and using physical arguments. An optical experiment in which a measurement of a weak value has been realized is described. The possible use of pre- and post-selection as a means to amplify and detect weak effects is also discussed.

Modern Physics Letters B•Nov 10, 1991•11 citations

We introduce a novel concept which we call as potent value of system observable for pre- and post-selected quantum states. This describes, in general, how a quantum system affects the state of the apparatus during the time between two strong measurements corresponding to pre- and post-selections. The potent value can be realized for any interaction strength and for arbitrary coupling between the system and the apparatus observables. Most importantly, potent values generalize and unify the notion of the weak values and modular values of observables in quantum theory. Furthermore, we define a potent operator which describes the action of one system on the another and show that superposition of time-evolutions and time-translation machines are potent operators. These concepts may find useful applications in quantum information processing and can lead to technological benefits.

Weak value is increasingly acknowledged as an important research tool for probing quantum pre- and post-selected ensembles, where some extraordinary phenomena occur. We generalize this concept into the broader notion of “weak potential” which enables predicting the interactions between particles when one of them is pre-/post-selected and the interaction potential is small. A harmonic oscillator is considered, undergoing weak position and momentum measurements between strong position measurement, and shown to possess peculiar physical properties, affecting the momentum rather than the position of another oscillator interacting with it.

Weak value is increasingly acknowledged as an important research tool for probing quantum pre- and post-selected ensembles, where some extraordinary phenomena occur. We generalize this concept to the broader notion of "weak potential" which enables predicting the interactions between particles when one of them is pre-/post-selected and the interaction potential is small. A harmonic oscillator is considered, undergoing weak position and momentum measurements between strong position measurement, and shown to possess peculiar physical properties, affecting the momentum rather than the position of another oscillator interacting with it.

A description of quantum systems at the time interval between two successive measurements is presented. Two wave functions, the first pre-selected by the initial measurement and the second post-selected by the final measurement describe quantum systems at a single time. It is shown how this approach leads to a new concept: a weak value of an observable. Weak values represent novel characteristics of quantum systems between two measurements. They are outcomes of a standard measuring procedure that fulfills certain requirements of “weakness”. We call it weak measurement . Physical meaning and underlying mathematical structure of weak measurements are explored.

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.