Quantum state tomography on closed timelike curves using weak measurements

TL;DR

This paper introduces a method combining state tomography and weak measurements to assign and verify quantum states on closed timelike curves, clarifying differences between Deutsch's and postselected teleportation models.

Contribution

It presents a novel operational approach to assign and verify quantum states on CTCs, enabling comparison between D-CTCs and P-CTCs models.

Findings

Successfully verifies D-CTC predictions

Operationally assigns states to P-CTCs

Analyzes states in temporal paradox scenarios

Abstract

Any given prescription of quantum time travel necessarily endows a Hilbert space to the chronology-violating (CV) system on the closed timelike curve (CTC). However, under the two foremost models, Deutsch's prescription (D-CTCs) and postselected teleportation (P-CTCs), the CV system is treated very differently: D-CTCs assign a definite form to the state on this system, while P-CTCs do not. To further explore this distinction, we present a methodology by which an operational notion of state may be assigned to their respective CV systems. This is accomplished via a conjunction of state tomography and weak measurements, with the latter being essential in leaving any notions of self-consistency intact. With this technique, we are able to verify the predictions of D-CTCs and, perhaps more significantly, operationally assign a state to the system on the P-CTC. We show that, for any given combination of chronology-respecting input and unitary interaction, it is always possible to recover the unique state on the P-CTC, and we provide a few specific examples in the context of select archetypal temporal paradoxes. We also demonstrate how this state may be derived from analysis of the P-CTC prescription itself, and we explore how it compares to its counterpart in the CV state predicted by D-CTCs.