There has been alot of research in quantum computing as scientists are exploring various prospective implementations for quantum computers. One such method uses photons to entangle trapped ions, which serve as the qubits (see "Entanglement of single-atom quantum bits at a distance" by Moehring et all., Nature ). The basic idea is that you have two separated ions trapped in magnetic fields. The ions are simultaneously excited using very short laser pulses to a higher energy state--one with multiple decay modes to lower energy states. As the ions decay they each emit a photon with specific attributes (such as polarization) that correlate to the decay mode, i.e. the photons will be entangled with their respective ions from which they were emitted. The system can be tuned such that both ions emit at the same time. If the two emitted photons are allowed to interfere at a beamsplitter and then detected with a pair of photo-multiplier tube detectors, it projects the ions onto an entangled state as the wavefunction of the photon-ion system collapses. This is somewhat intuitive since the beamsplitter erases which-path information (e.g. was photon1 emitted from ion1 and reflected at the beamsplitter or was it emitted from ion2 and transmitted though the beamsplitter?). This indistinguishability of the emitted photons translates the photon-ion entanglement into an ion-ion entanglement, thus implementing a basic quantum computing operation.
SUPERLUMINAL COMMUNICATION THOUGHT EXPERIMENT
The proposed thought experiment uses the same experimental setup as described in the BACKGROUND section but with a few modifications. The idea is to send a bit of information from point A (at the transmitter) to point B (the receiver) in less time than it would take light to travel the distance in a vacuum and to do this by utilizing the nonlocal, instantaneous nature of the wavefunction collapse to reduce the required transit time.
At point A (x=0) we have a classical transmitter capable of transmitting an RF or light signal. At point B (x=D) we have the receiver, which consists of the trapped ions held in place by magnetic fields. At time t=0, the transmitter sends a bit of information and at the same time the receiver ions are excited, causing them to emit photons. Near the mid-point (slightly closer to the transmitter (at x=D/2-d) we have a device, let's call it a PMD (photon mixer/detector) for lack of a better name, which performs the photon mixing and detection as described in the BACKGROUND section above EXCEPT that it does this in response to a control signal from the transmitter. If the transmitter sends a "0" the photons are blocked by optical switches and are not allowed to enter the PMD, thus preventing mixing, detection, and so preventing ion entanglement. If instead, the transmitter sends a "1", the photons are allowed to enter the PMD via the optical switches and are mixed and detected, resulting in ion entanglement.
To summarize, if the transmitter sends a "0", the receiver ions will not become entangled and will exist in a separable state such as:
|state 1> = 1/2 ( |00> + |01> + |10> + |11>)
If the transmitter sends a "1", the ions will become entangled and will exist in the Bell state:
|state 2> = (1/sqrt(2)) |00> + |11> (or some other Bell state)
How would this achieve superluminal signaling? The ions are projected onto either |state 1> or |state 2> at time t=(D/2+d)/c which is approximately 1/2 the time light would take to tranverse the distance D (i.e. t=D/c). Here we assume d<<D. I also assume the wavefunction collapse is instantaneous (note: I use wavefunction collapse for illustration, there is no need to believe in the Copenhagen Interpretation for this to work--I know I don't). This seems to be supported by experiments that show EPR-like correlations are non-local. The transmitter and receiver must share a clock or have independent, but very accurate, clocks so that the receiver knows when the transmitter may send a bit, so that it can delay its ion state measurement until after (D/2+d)/c seconds. There would need to be some test to determine whether the resulting ion state is state1 or state2 but let's assume that test can be done quickly so we can neglect that time (the distance D can be arbitrarily large).
I've omitted several details to make the explanation simpler. Entanglement generation of the ions cannot be achieved every time it is attempted, there is only certain probability of it happening (which may be quite low). This could be overcome in principle(?) by using arrays/ensembles of the described system (all synchronized and transmitting the same bit value at the same bit-clock time) and detecting the bias toward the Bell state when "1" is transmitted. Since state1 and state2 differ in their probabilities of the component eigenstates, it seems that they should be distinguishable. e.g. state2 never exhibits the |01> result, so if we have a large array/ensemble of identical systems all transmitting the same bit-value, it seems to me that we can distinguish the resulting ion states.
I don't necessarily see anything that violates QM or S/G Relativity and do not see what would stop this from working in principle, so I am interested to get feedback.
I originally conceived of this thought experiment a couple of years ago and have been contemplating it ever since. I have recently become aware of a very similar idea that uses delayed choice entanglement and exhibits equally interesting questions on causality (see "Experimental delayed-choice entanglement swapping", by Xiao-song Ma et. al).