Weak value beyond conditional expectation value of the pointer readings

Abstract

It is argued that a weak value of an observable is a robust property of a single pre-and postselected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affects other systems as if it were in an eigenstate with eigenvalue equal to the weak value. This differs significantly from the action of a system pre-selected only and possessing a numerically equal expectation value. The weak value has a physical meaning beyond a conditional average of a pointer in the weak measurement procedure. The difference between the weak value and the expectation value has been demonstrated on the example of photon polarization. In addition, the weak values for systems pre-and post-selected in mixed states are considered.

Double Slit with an Einstein–Podolsky–Rosen Pair

“…by computing the predictability. We also note that Alice and Bob may switch roles and achieve similar results; this fact is manifested in (27) by noting the expression is invariant under permutation of the two particles.…”

“…Moreover, (27) allows application of this complementarity relation to any experiment where a CV is subjected to a binary-outcome measurement: one should have it evolve in a manner analogous to propagation of the double-slit wavefunction to the far-field; afterwards, an interference pattern should be extracted, either an actual one or some analogue; and finally, computation of the envelope-based visibility allow finding the "θ" and consequentially the predictability, thus inferring the strength of entanglement.…”

“…This also allows a simple way for Alice to generate a purification of her state, using only the parameters of her system and the interference visibility she measures. To put it more precisely, the state of the form (5) where θ is given by (27), yields the same single-particle Wigner function for Alice as the state (20) considered throughout this section (a proof appears in the Appendix B 3). Thus, (27) allows Alice to utilize any of the results obtained in the previous section, e.g.…”

Anomalous values, Fisher information, and contextuality, in generalized quantum measurements

“…The outcome of a measurement carried out on a spin-1/2 particle can turn out to be 100 [1,2]. What is exactly measured in these procedures, and whether this carries physical meaning has been debated ever since the introduction of the concept of postselected values [3][4][5][6][7]. These anomalies emerge when an observable is measured through an indirect procedure, i.e.…”

Negation of photon loss provided by negative weak value

“…no operations/ losses). The weak values, 0 and 1, always satisfy such a definite relation with the probabilities [3], while it has been recently shown that the system with a weak value affects the other system as if it were in an eigenstate with eigenvalue equal to the weak value under the weak correlation [38]. In this sense the weak value of −1 has an important implication in relation to these definite weak values: −1 is the value which negates the definite value of 1 (probability 1) to be the definite value of 0 (probability 0).…”