|Nick calculating the Kalamidas effect (NKE)|
Recently Demetrios Kalamidas, a young New York quantum-optics physicist, proposed an imaginative new superluminal signaling scheme--OKE (see also KISS and Demetrios! the Opera). The Kalamidas experiment proposes for Bob to send instant signals to Alice via the medium of a pair of path-entangled photons (A and B).
When Bob knows (from observation of his photon B) which path Alice's A photon took, then Alice cannot observe two-path interference. But if Bob can erase which-path information then, in principle, Alice can get her path-uncertain photon to interfere with itself.
Switching between these two options (knowledge of Alice's photon's path and erasure of that knowledge) Bob can instantly send a signal to Alice no matter how large the distance that separates them. So goes the argument for FTL signaling via quantum entanglement.
In my analysis of the Kalamidas experiment: NKE (caution: 2-MB pdf download), I consider three possible choices that Bob could make to either obtain or erase which-path info concerning Alice's photon A.
I call these three choices: 1. the Fock Choice; 2. the Frost choice and 3. the Kalamidas choice. The Fock choice preserves which-path info and both the Frost choice and the Kalamidas choice erase which-path info—but in two different ways.
The Frost-choice method for quantum-erasure of which-path info is well-known—scramble Bob's two paths in a beam splitter. This choice does indeed lead to interference of Alice's photons. But this interference is INVISIBLE because it is superposed with an exactly complementary anti-interference pattern, the sum of which produces a completely random signal at Alice's detectors. These two patterns (signal and anti-signal) can however be separated by a coincidence trigger from Bob that tells Alice which of Bob's two detectors fired. If detector B1 went off then Alice sees a signal; if detector B2 went off, then Alice sees an anti-signal.
So (making the Frost choice) Bob's erasure of which-path info does indeed produce interference at Alice's detectors but ALICE'S INTERFERENCE IS ENCRYPTED using a random key that Bob can only send by conventional slower-than-light methods. Hence the Frost choice fails as a superluminal signaling device.
What about the Kalamidas choice?
The gist of the Kalamidas experiment is the novel method he has invented for Bob to quantum-erase which-path info. In his original article: OKE = Original Kalamidas Experiment, Kalamidas demonstrates that his method leads to UNENCRYPTED INTERFERENCE at Alice's detectors. Hence it appears that Demetrios Kalamidas has devised a viable mechanism for sending signals faster-than-light. Furthermore all of the components of the Kalamidas device are available in most modern quantum-optics labs. No exotic processes needed—everything in principle is completely understood.
For his FTL machine, Kalamidas employs an unusual method for which-path erasure. Bob "ambiguifies" the number of photons in each of his two paths by mixing each photon (which is normally in a "Fock state" of definite photon number—either zero or one) with a state of uncertain photon number. In Kalamidas's original paper (OKE), he used for this number-uncertain state a truncated coherent state. In Nick's version of the Kalamidas experiment (NKE), I use a state |U> = x|0> + y|1> (which I call "gray light") as my number-uncertain input.
The beam-splitter math for the NKE experiment is simple but tedious—30 terms that must be carefully squared, added together and matched correctly with the right output detectors. The first time I carried out this calculation, I verified Kalamidas's claim: Bob, by his choice of what to measure could seemingly cause: 1. nothing to happen at Alice's detectors or 2. unencrypted interference to happen at Alice's detectors with a very large amplitude (when gray light parameters were maximized) of 25%.
I was happy to see this result. Not because I believed that I had verified FTL signaling. But because I believed that I had created a paradox (the Kalamidas-Herbert paradox?) which would be resolved in some clever way that might teach us something new about the subtleties of few-photon quantum physics.
I sent my results to Demetrios, who scrutinized them with a critical eye, eventually discovering a simple conceptual error that I had missed over and over again. It's easy to overlook your own mistakes—another good reason for peer review in science.
Correcting my mistake I recalculated and obtained Bob-induced interference at Alice's detectors. But this correctly calculated interference was completely encrypted—only visible (like the Frost choice) if Bob sends a coincidence-triggered decryption signal to Alice at slower-than-light speeds.
(Quoted from NKE): I wish to congratulate Demetrios Kalamidas for coming up with his imaginative new FTL scheme which gave me much pleasure and excitement to analyze. I would also like to thank him for correcting an error in my work which, up until his intervention, seemed to show confirmation of his FTL signaling claim. After his timely input, the present (presumably correct) calculation demonstrates a complete refutation of any FTL effect. However, the Kalamidas scheme of erasing which-path info by mixing Fock light with gray light is clever and may yet find new technical applications in areas other than superluminal communication technology.
|Sketch of the original Kalamidas experiment (OKE)|