Weak value

In quantum mechanics (and computation), a weak value is a quantity related to a shift of a measuring device's pointer when there is pre- and postselection. It should not be confused with a weak measurement, which is often defined in conjunction. The weak value was first defined by Yakir Aharonov, David Albert and Lev Vaidman, published in Physical Review Letters 1988, and is related to the two-state vector formalism.

There are many excellent review articles on weak values (see e.g. ) here we briefly cover the basics.

We will denote the initial state of a system as ${\displaystyle |\psi _{i}\rangle }$, while the final state of the system is denoted as ${\displaystyle |\psi _{f}\rangle }$. We will refer to the initial and final states of the system as the pre- and post-selected quantum mechanical states. With respect to these state the weak value of the observable ${\displaystyle A}$ is defined as:

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