
Omer and Nick's JJCCTT Device for FTL Signaling 
JJCCTT Device for FTL Signaling
Bell's Theorem proves that quantum reality must be nonlocal.
Belfastborn physicist John Stewart Bell based his important proof about reality on the EPR Device (named after
Einstein, Podolsky and Rosen) which uses TWO ENTANGLED PHOTONS whose wave function
ψ can be written:
ψ (EPR) = 1/√2 ( HH> + VV> ) (EQ1)
Bell showed (and
John Clauser subsequently measured) that this quantum wave function's statistical predictions exceed any result that any merely local reality is able to muster. Thus quantum reality is nonlocal.
Later
Greenberger, Horne and Zeilinger used THREE ENTANGLED PHOTONS described by the GHZ wave function:
ψ (GHZ) = 1/√2 ( HHH> + VVV> ) (EQ2)
to prove a "Bell's Theorem without Inequalities". GHZ showed from EQ 2 that a local reality predicts a certain result will never happen, while quantum mechanics says that this same result must always happen. Since quantum mechanics gives the correct prediction, one measurement suffices to prove that quantum reality is nonlocal.
In recognition of GHZ's concise proof, the quantum state described by EQ 2 is usually called a "GHZ state".
Recently,
Omer Dickstein, a physics student at
Jerusalem College of Technology, proposed to exploit the nonlocality exhibited by FOUR ENTANGLED PHOTONS for fasterthanlight signaling. His wave function just adds one more photon to the GHZ state:
ψ (GHZ + 1) = 1/√2 ( HHHH> + VVVV> ) (EQ3)
As a place holder I have tentatively called EQ 3 the "GHZ plus one" state. How this state will eventually be designated will depend on what we learn from temporarily construing it as the core ingredient of an FTL signaling machine  the socalled JJCCTT Device where JJCCTT stands for "Joint JerusalemCalifornia Collaboration on Transluminal Telecommunication".
The state HHHH> represents the simultaneous emission of FOUR Horizontallypolarized photons, two of which are measured by Alice, and two of which are measured by Bob, each of whom possess two detectors that register "H" when accepting a Horizontal photon and "V" when accepting a Vertical photon.
The state VVVV> represents the simultaneous emission of FOUR Verticallypolarized photons, two of which go to Alice, and two of which go to Bob.
One nice thing about the JJCCTT situation is that, unlike the EPR situation where Alice and Bob possess only one detector each (hence can obtain only ONE BIT of information), in the JJCCTT situation both particles possess two detectors (hence each can potentially obtain TWO BITS of digital information. The JJCCTT Device represents, informationwise, a more broadband channel than its EPR competitor.
One might naively imagine that EQ 3 represents a situation in which the 4photon source emits EITHER a pulse of 4 Hphotons OR a pulse of 4 Vphotons but that is not the case at all. In this peculiar process (called "polarization entanglement") illegal for all except quantum systems, the source emits BOTH a quadruple of Hphotons and a quadruple of Vphotons AT THE SAME TIME.
You might think of EQ 3 as describing a kind of "fourphoton Schrödinger Cat state". When unlookedat, "this cat" is in a superposition of both a 4Hcat and 4Vcat. (4Hcat has four Hazel (yellowishbrown) feet and 4Vcat has four Vermilion (yellowishred) feet). Each foot simultaneously is both colors. That's when not looked at. But whenever it's looked at, whoever looks will always see this cat with each foot having the same color  either four Hazelcolored feet or four Vermilioncolored feet  no matter how far apart the cat's feet are. Bob and Alice might be 100 lightyears apart and this feetcoloring process will happen exactly the same way.
According to quantum mechanics, when this ambiguous pulse of 4light (quantum cat) encounters a detector, the detector "flips a coin" and randomly decides which one of these two possible polarizations it will "make real". Will it be the allHstate or the allVstate? It is important to understand that quantum theory tells us that this choice of what polarization will be recorded is made at the detector, not at the source.
Once this decision is made by one detector (we can never really identify which one), the other 3 detectors follow suit, so that each detector, no matter how far it might be separated from all the others, immediately comes to the same conclusion concerning which possible polarization state (H or V) it will also make real.
It is easy to see how this apparent instantaneous conspiracy between fardistant detectors to always record the same polarization, when up until the moment of choice both polarizations were actively possible, might embolden some physicists to attempt to exploit this system to send signals faster than light.
The configuration pictured above won't work as an FTL channel between Alice (the traditional sender) and Bob (the inevitable recipient), because EQ 3 allows only two elemental events to happen, either HHHH or VVVV, none of which are under the control of either Alice or Bob.
But here's how Omer from JCT in Jerusalem plans to change all that. We note that in the START STATE (pictured below), only two things ever happen to Alice and Bob. They either both receive 4 Hphotons. Or both receive 4 Vphotons. Bob always registers HH or VV in his two polarization detectors. And so does Alice. Never anything else.

START STATE: Only two events can happen, either HHHH or VVVV. 
In particular Bob never observes a "cross term" such as HV or VH, where one of his two detectors counts a Hphoton and the other counts a Vphoton.
If there were something Alice could do with her photons that would produce "cross terms" in Bob's results, then Alice would be able to send a message to Bob at superluminal speed.
The essence of the JJCCTT Project is to examine all the things that Alice can do to her 2 photons, while looking for effects that Alice's actions might have on Bob's 2photon cross terms.
Here's a hint about what Alice might do to induce crossterms into Bob's detectors.
Alice might decide, for instance, to "make real" states of Right and Left Circularly polarized light rather than H and V polarized light as in the START STATE. Alice can easily configure her two detectors (using a phase plate and a beam combiner) to register R and L light rather than H and V light.
If Alice's RandLmaking action causes any amount of R and L light to appear at either one of Bob's detectors, this will have drastic consequences. Because R light incident on an H/V detector (the kind Bob has deployed) will always produce a random mixture of H and V counts  that will certainly lead to cross terms in Bob's data. Likewise L light incident on Bob's detectors will inevitably produce cross terms via the same procedure.
The 2photon EPR situation offers some hope that this could happen, via
a process that Irwin Schrödinger dubbed "steering". Starting with EQ 1, which represents a perfect correlation of H and V photons between Alice and Bob, Alice can transform her detectors from the PlanePolarized basis H/V to the CircularlyPolarized Basis R/L, where R and L are Right and Leftcircularly polarized photons. This transformation turns EQ 1 into:
ψ (EPR) = 1/√2 ( RL> + LR> ) (EQ4)
One interpretation of EQ 4 is that by Alice's choice to measure R/L polarization rather than H/V polarization, she was able to "steer" Bob's distant photons from a mixture of the H/V eigenstates into a mixture of the R/L eigenstates.
Can the same "steering mechanism" that works for the EPR state work its magic on the GHZ +1 state? If Alice can steer even the tiniest fraction of Bob's H/V photons into a R state and/or a L state, then transluminal signaling will be accomplished via the instant appearance of cross terms {of the form HV or VH) in Bob's two HV detectors.
Any physicist familiar with purported FTL signaling schemes will reflexively credit such a vaguely plausible argument as no more than a hopeful conjecture. And will suspend judgement until seeing some actual calculations. Omer at Jerusalem Center for Technology and Nick at Quantum Tantra Ashram in California are currently calculating the 16term quantum correlation matrix that encodes the full behavior of the JJCCTT device for whatever detector choices Alice can make to try to signal Bob. These are very elementary calculations. But it is easy to make mistakes.
For the record: It was Omer who suggested that the GHZ + 1 system might be a promising candidate for FTL signaling. And it was Omer who proposed that Alicecontrollable crossterms in Bob's HV detectors might function as an FTL signal. And it was Nick who suggested that Alice might use Schrödinger "steering" to remotely create crossterms in Bob's HV detectors. And Nick did the graphics.
RESULTS: Omer calculated the correlation matrix for the case where Alice chooses to measure R and L photons rather than H and V photons:

Now eight events can happen, but none produces Bob's HV or VH cross terms. 
Next Omer considered rotating both Alice's detectors by 45 degrees so that Alice registers Diagonal (D) and Slant (S) polarized photons instead of H and V.

Again eight events can happen, but none produces Bob's HV or VH cross terms. 
Neither of these two efforts on Alice's part succeeds in producing cross terms in Bob's detectors. And indeed a more general calculation that allows Alice to effect any possible combination of rotation and phase change in her detectors gives the same result. Nothing that Alice can do will produce an FTL signal in Bob's detector.
So the JJCCTT proposal fails as an FTL signaling device.
"Science is great, but it’s lowyield. Most experiments fail. That doesn’t mean the challenge isn’t worth it, but we can’t expect every dollar to turn a positive result. Most of the things you try don’t work out — that’s just the nature of the process. Rather than merely avoiding failure, we need to court truth."  Ferric Fang, microbiologist
Citing the
FTL signaling Impossibility proofs of Philippe Eberhard and
many others, it would be easy to have anticipated our negative result, These wellknown impossibility proofs state, in essence, that 1. YES, quantum Theory is nonlocal (by inspection); 2. YES, quantum Reality is nonlocal (proved by John Bell) but; 3. NO, the quantum Facts are as local as can be.
Despite the FTL nature of the Theory that represents the World, despite the FTL nature of the Reality which underlies the World, the World Herself displays not a speck of evidence for any FTL connections.
I wish to thank Omer at JCT for proposing this project and I appreciate the fun we had doing these calculations. But now, as in so many other encounters with quantum reality, we end up where we started, back home again at
Physics for Beginners.

Omer and Nick: two collaborators separated by 10 time zones. 