Impossible operations?

by Erik Aurell (KTH)

Thursday 13 Feb 2025, 13:00 → 15:00 Europe/Stockholm

AlbaNova C4:3059 - Café Planck (AlbaNova Main Building)

Aharonov [1] and Sorkin [2] and Vaidman [3] and others have pointed out that quantum measurements may lead to supraluminal signalling, unless additional restrictions are placed on the set of admissible operations. In Sorkin's example Alice and Charlie each have access to one qubit, and conduct experiments in  spatially separated regions of space-time. The qubit pair is initialized in state |00>, and Alice can, if she so decides, flip her qubit so that the state is |10>. In between Alice and Charlie is Bob who makes a non-complete measurement that the 2-qubit state is either in the pure state |+><+|, or in its complement. Under reasonable, or seemingly reasonable, assumptions, Bob can then determine whether Alice flipped her qubit or not.

I will go over some of these examples in detail, and then discuss a recently proposed way out which limits the kind of measurements that can be described as localized interactions with a probe [4]. Much of the material is taken from a  2021 Essay for the Mathematical Tripos at Cambridge University available on-line [5].

[1] Aharonov, Y. and Albert, D. Z. (1980). States and observables in relativistic quantum field theories, Phys. Rev. D 21, pp. 3316–3324

[2] Sorkin, R. D. (1993). Impossible measurements on quantum fields,
arXiv:gr-qc/9302018 

[3] Vaidman, L. (2003). Instantaneous measurement of nonlocal variables, Phys. Rev. Lett. 90, p. 010402

[4] Fewster, C. J. and Verch, R. (2020). Quantum fields and local measurements, Communications in Mathematical Physics 378, pp. 851–889

[5] van der Lugt, T. (2021). Relativistic limits on quantum operations, arXiv:2108.05904