The Relevance of Sequential Time

Hans Primas

Razieh Mohseninia, José Raúl González Alonso, Justin Dressel

Quasiprobability distributions for out-of-time-ordered correlators are a robust witness of information scrambling, being very relevant to the study of quantum many-body physics, but typically hard to measure. Here a dramatically simplified scheme is presented for the case of sequential qubit measurements, thus opening exciting opportunities.

Sherif Ayman Ali Ashry Ghoneim

Ilya Prigogine

Claudio Carmeli, Teiko Heinosaari, Alessandro Toigo

We present a unified treatment of sequential measurements of two conjugate observables. Our approach is to derive a mathematical structure theorem for all the relevant covariant instruments. As a consequence of this result, we show that every Weyl–Heisenberg covariant observable can be implemented as a sequential measurement of two conjugate observables. This method is applicable both in finite- and infinite-dimensional Hilbert spaces, therefore covering sequential spin component measurements as well as position-momentum sequential measurements.

Kieran Flatt, Stephen Mark Barnett, Sarah Croke

Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957)]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003)], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.