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AB, EPR and AC Conspiring to Preserve Causality Avshalom C. Elitzur avshalom.elitzur@weizmann.ac.il Shmuel Marcovitch shmuelma@post.tau.ac.il. Superposition Censorship. Bob. Alice. EPR source Which-path correlation. Interference in Terms of Spin Using Stern-Gehrlach Devices. SG (- x ).
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AB, EPR and AC Conspiring to Preserve CausalityAvshalom C. Elitzuravshalom.elitzur@weizmann.ac.il Shmuel Marcovitchshmuelma@post.tau.ac.il
Superposition Censorship Bob Alice EPR source Which-path correlation
Interference in Terms of SpinUsing Stern-Gehrlach Devices SG (-x) Interference key: z-spin SG (x) C D Aharonov and Vardi, PRD 20, 3213 (1979) SG (z) (Erasure of the x-spin measurement) Eigenstate of z-spin enters
SG (-x) SG (x) Superposition Censorship SG (z) SG (z) Bob Alice SG (x) EPR-Bohm source Spin correlation
AB-MZI D C Click always in C Click in either C or D Current only on left (or right) Current superposed
AB+EPR We neglect any phases due to interaction of the spin with the magnetic fields in the SG devices throughout D C Click in C Click in either C or D Current only on left (or right) Current superposed Bob Alice measures x spin does nothing EPR-Bohm source
“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 = fluxon = electron does nothing measures spin x Alice Bob Particle acquires 0 or AB phase, thus breaking the fluxon’s interference Particle does not measure the fluxon, which stays in superposition
Resolution: Aharonov-Casher effect25 years retrodiction.. D C Aharonov and Casher, PRL 53, 319 (1984) AC effect: It is the fluxon interference which shifts! In any case, clicks may equally appear in D Alice Bob measures spin x Fluxon acquires 0 or AC phase, in accordance with Bob’s particle’s location
Superposition of Macroscopic Clockwise/Anticlockwise Currents Van der Wal el. al, Science, 206, 773 (2000) Friedman et. al. Nature, 406, 43 (2000) 2D: Solenoid SQUID System is in ground state Josephson Junction removes degeneracy Macroscopic current ~A
Superposition of Macroscopic Clockwise/Anticlockwise Currents Superconducting layer Induced magnetic field? topological effect – electron can be very far! superposition remains Alice Bob Particle acquires /2 or -/2 AB phase, breaking the fluxon’s superposition. Fluxon is not effected by the electron and stays in superposition. measures spin x does nothing
electron near and fast Strong Impulsive Interaction → Back-reaction Furry and Ramsey, Phys. Rev. 118, 623 (1960) Bob’s particle changes the state of the flux even when not interfering Bob cannot distinguish between Alice’s two choices No paradox
Enter Protective Measurement 16 years retrodiction..Aharonov, Anandan and Vaidman, PRA 47, 4616 (1993) Classic trajectory! Protective Measurement Strong measurement Electron in superposition e Measuring charge
This is just what we have: Protective AB setting Flux remains superposed Even if Alice does nothing, Bob’s particle remains unentangled with flux, measuring the flux’s expectation value: 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 Back-reaction – when interaction is strong Flux expectation value – when measurement becomes protective
3Delectron spread in long wire Electron flux flux Electron