Further Proofs for the 1-Photon PathEntanglement Communications Scheme

The author had previously set out devices to communicate over space-like intervals, with a full proof for the 2‑photon device and only a partial proof for the 1-photon device. The 2-photon device exploits entangled pairs; the 1-photon device utilises path-entanglement. The 1-photon device is fully analysed, then similarities (and differences) are drawn to the 2-photon device to show the holes in the No-communications Theorem: the creation operators representing the sum of paths through the device can be mapped outside the device and quantum state reduction/measurement is a space-like operation. A common misconception on faux rank-3 systems made from rank-2 components is elucidated, avoiding the criticism and null result obtained by naively taking the partial trace.

Further Proofs for the 1-Photon PathEntanglement Communications Scheme

The author had previously set out devices to communicate over space-like intervals, with a full proof for the 2-photon device and only a partial proof for the 1-photon device. The 2-photon device exploits entangled pairs; the 1-photon device utilises path-entanglement. The 1-photon device is fully analysed, then similarities (and differences) are drawn to the 2-photon device to show the holes in the No-communications Theorem: the creation operators representing the sum of paths through the device can be mapped outside the device and quantum state reduction/measurement is a space-like operation. Furthermore, global phase factors indicating causal delay are removed by the operation anyway.

NUMERICAL SIMULATION OF QUANTUM STATE REDUCTION IN BOSE–EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS

Following an idea first proposed by Penrose in 1996 to explain the problem of quantum state reduction as a gravitational effect, Moroz, Penrose and Tod1 have shown that quantum state reduction due to gravitational interactions could take place in about one second for the case of 1011 nucleons. However, keeping 1011 nucleons together in a quantum macroscopic state does not appear to be feasible as yet. The closest physical system to such a situation is provided by Bose–Einstein condensates (BEC) with attractive interactions. We present numerical simulations of the Schrödinger–Newton equations, which show that an attractive BEC with 103 atoms would yield a decorrelation time of the order of 10-2 seconds. Hence, a "Penrose-like" reduction, induced by BEC attractive interaction instead of gravity, might be observable and possibly monitored in current BEC experiments with attractive interactions.