Quantum systems usually travel a multitude of different paths when evolving through time from an initial to a final state. In general, the possible paths will depend on the future and past boundary conditions, as well as the system’s dynamics. We present a gedanken experiment where a single system apparently follows mutually exclusive paths simultaneously, each with probability one, depending on which measurement was performed. This experiment involves the measurement of observables that do not correspond to Hermitian operators. Our main result is a scheme for measuring these operators. The scheme is based on the erasure protocol [Brodutch and Cohen (Phys. Rev. Lett. 116:070404, 2016)] and allows a wide range of sequential measurements at both the weak and strong limits. At the weak limit the back action of the measurement cannot be used to account for the surprising behaviour and the resulting weak values provide a consistent yet strange account of the system’s past.
|Number of pages||15|
|Journal||Quantum Studies: Mathematics and Foundations|
|State||Published - 1 Apr 2017|
Bibliographical noteFunding Information:
We would like to thank Yakir Aharonov, Raymond Laflamme, Marco Piani and Lev Vaidman for their valuable input on this work. AB is supported by NSERC, Industry Canada and CIFAR. EC was supported in part by the Israel Science Foundation Grant No. 1311/14 and by ERC AdG NLST. AB is now at the University of Toronto’s Center for Quantum Information and Quantum Control.
© 2016, The Author(s).
- Hermitian Operator
- Projective Measurement
- Sequential Measurement
- Strong Measurement
- Weak Measurement