AB, EPR and AC Conspiring to Preserve Causality Avshalom C. Elitzur Shmuel Marcovitch

EPR source Which-path correlation Superposition Censorship Alice Bob

Interference in Terms of Spin Using Stern-Gehrlach Devices D C Eigenstate of z-spin enters SG (x) SG (z) SG (-x) (Erasure of the x-spin measurement) Interference key: z-spin Aharonov and Vardi, PRD 20, 3213 (1979)

SG (z) Alice Superposition Censorship SG (x) SG (z) SG (-x) SG (x) Bob EPR-Bohm source Spin correlation

AB-MZI D C Click in either C or D Click always in C Current superposed Current only on left (or right)

D C Alice Bob does nothing Click in either C or D measures x spin Click in C Current superposed Current only on left (or right) EPR-Bohm source AB+EPR We neglect any phases due to interaction of the spin with the magnetic fields in the SG devices throughout

“Cat State” of a Current too gedankenly? C D

Let’s Go 2-Dimensional Superconductor setting Quantum mechanical flux in discrete units

Flux Interference Josephson Arrays, Elion et. al, PRL 71, 2311, 1993 Bob Alice = fluxon does nothing Particle acquires 0 or  AB phase, thus breaking the fluxon’s interference measures spin x Particle does not measure the fluxon, which stays in superposition = electron

Resolution: Aharonov-Casher effect 25 years retrodiction.. Bob Alice measures spin x Fluxon acquires 0 or  AC phase, in accordance with Bob’s particle’s location AC effect: It is the fluxon interference which shifts! D C In any case, clicks may equally appear in D Aharonov and Casher, PRL 53, 319 (1984)

2D: Solenoid  SQUID Macroscopic current ~  A Josephson Junction removes degeneracy Superposition of Macroscopic Clockwise/Anticlockwise Currents Van der Wal el. al, Science, 206, 773 (2000) Friedman et. al. Nature, 406, 43 (2000) System is in ground state

Superconducting layer Bob Alice does nothing Particle acquires  /2 or -  /2 AB phase, breaking the fluxon’s superposition. measures spin x Fluxon is not effected by the electron and stays in superposition. Superposition of Macroscopic Clockwise/Anticlockwise Currents Induced magnetic field? topological effect – electron can be very far! superposition remains

AC cannot help ?

Strong Impulsive Interaction → Back-reaction Furry and Ramsey, Phys. Rev. 118, 623 (1960)  Bob cannot distinguish between Alice’s two choices Bob’s particle changes the state of the flux even when not interfering electron near and fast  No paradox

What if interaction is adiabatic?

Enter Protective Measurement 16 years retrodiction.. Aharonov, Anandan and Vaidman, PRA 47, 4616 (1993) Electron in superposition Classic trajectory! Strong measurement Protective Measurement Measuring charge e

This is just what we have: Protective AB setting measuring the flux’s expectation value: Flux remains superposed Even if Alice does nothing, Bob’s particle remains unentangled with flux, 0  No AB phase  No paradox

Conclusions AB bears on QM fundamentals: causality, nonlocality, adiabaticy Flux Interference: Causality protected by AB+AC electrons and fluxons interact topologically Flux Superposition: Causality protected by Flux expectation value – when measurement becomes protective Back-reaction – when interaction is strong

3D electron spread in long wire flux Electron