Wednesday, April 21, 2021

TIBET: A New Superluminal Signaling Scheme

  • The Way to Shambhala by Nicholas Roerich

     Near the First of April of this year I received an eMail from my physicist friend Demetrios Kalamidas proposing an original new way to use quantum entanglement to send signals faster-than-light. Kalamidas and I have a long history in which he proposes such a scheme, I try to understand, clarify, simplify it, give it a cute acronym and then work together with him to eventually refute it. Previous Kalamidas FTL proposals have included KISS (Kalamidas Instant Signaling System), TKO (The Kalamidas Option) and KHAN (Kalamidas-Herbert Augmented Nearness)

    Kalamidas's latest scheme I call TIBET for "TIme-Bin-Entangled Telegraphy".

    All of these schemes involve Alice and Bob receiving a series of photon pairs--one photon going to Alice, the other to Bob. These two photons are emitted from a source S located somewhere between Alice and Bob and are characterized by one or more of their properties P being "quantum-entangled". Entanglement means that, before measurement, neither Bob's property P, nor Alice's property P possesses a definite value but, in the quantum representation at least, the value of Bob's property P appears to depend on how Alice choses to measure her property P, and vice versa. Seemingly then, quantum entanglement appears to permit superluminal signaling resulting from, say, Alice's choice of how she measures P.
    However, a proof due to Philippe Eberhard (no-signaling theorem) shows that no way of making measurements on an entangled system can produce such distant instantaneous effects. The gist of Eberhard's Proof is that the intrinsic randomness that characterizes every quantum measurement destroys any coded pattern Alice attempts to impose. Another limit to Entanglement Telegraphy is the Holevo Bound which limits the amount of classical information one can extract from a quantum system. The polarization state of a single photon, for instance, encodes an infinite amount of quantum information, corresponding to the infinite number of directions an arrow can point on the Bloch sphere. The amount of classical information that can be extracted from a polarized photon, however, is exactly one classical bit. The most you can learn about the polarization of a single photon is the answer to a single yes/no question. You can pick the question, the photon provides the answer but is irreversibly changed in the process of measurement.
    There is a sense in which my own FTL FLASH proposal was an unsuccessful attempt to violate the Holevo bound on the amount of classical information one is able to extract about the polarization state of a single photon. 

    Kalimidas's previous proposals involved either path-entangled or polarization-entangled photon pairs. His newest proposal uses time-bin-entangled photon pairs, which I had never heard of but which apparently have the potential to play an important role in future quantum communication systems.

    The source S emits a pair of photons, one to Alice, one to Bob. In the peculiar quantum manner, each photon is uncertain into which time bin it was emitted. Was it a Late Photon L or an Early Photon E? Until measurement, neither Alice, nor Bob knows the answer to this question. But one thing is certain (the essence of entanglement) whatever time bin Bob's photon is measured to be in, Alice's photon will be the same. In the pictured situation, both photons possess the same (Horizontal) polarization, symbolized by H.

    It must be understood that although there are two time bins in each pulse, there is only one photon which occupies both bins in a manner only possible in quantum mechanics before a measurement happens. If one could bring the two time bins together in some way, it would be possible to make the photon interfere with itself in a wavelike manner. The conventional way of achieving this superposition uses a pair of beam splitters to split the beam in two, delay one beam by a time equal to the pulse separation and then recombine the two beams.  I call this the Detour Method.
    Detour Method of combining time bins 
    The Detour Method takes in two input pulses Early (E) and Late (L) and transforms them into three output pulses, one of which is the desired Late pulse superposed with the delayed Early pulse (L/dE) The other two pulses are an undelayed Early pulse (E) and a delayed Late pulse (dL)

    Kalamidas could not find any way of using this Detour Method as an FTL signaling scheme so he devised another way of mixing the two time bins. 

    To keep the time bins separate, the coherence time of each pulse must be smaller than the pulse separation. But if one could increase the coherence times the pulses could be made to overlap. To achieve this kind of superposition, Kalamidas inserts a narrow-band interference filter in both Alice and Bob's photon channel. This I call the Expand Method because it mixes the two time bins by expanding their coherence length
    The Expand Method of combining time bins 

    Kalamidas calculates that when his Expand Method unites the L and E packets, that because they are now indistinguishable, Bob's entanglement with Alice is lost. And that what was once an entangled state is transformed into a product state.

    The Detour Method adds the L and E states and outputs the result into TWO MODES, the two outputs of the final beam splitter. Kalamidas's narrow-band filter unites the L and E states into ONE MODE, call it |C>, traveling in the same direction as the original L and E states but now coherently overlapping over a portion of their path.
    The action of Filter F applied to both Alice's and Bob's photon can be written:
              |EH(a)> + |LH(a)> --- F- --> |CH(a)> Alice's Photon     1)

              |EH(b)> + |LH(b)> --- F ---> |CH(b)>   Bob's Photon    2)

    As a result of filter F, at least part of the entangled wave function turns into an unentangled product state:

         |EH(a)>|EH(b)> + |LH(a)> |LH(b)> --- F --->
                                                            |CH(a)> |CH(b)>    3)
    In what follows we will consider only this part of the total wave function, regarding the non-overlapping portion of the filter-induced superposition as "noise".  Eq 3) describes the essence of the Kalamidas scheme: when both E and L photons have the same polarization (Horizontal in this case), the Filter transforms entangled states into an unentangled product state.

    The next stage in the Kalamidas scheme is to change the polarization of the Late photons from Horizontal to Vertical by quickly inserting a Late rotator H -->V in both Alice and Bob's beam. This Late rotation takes place before the filter, at a place in the system where the time bins are still cleanly separated.

    The main consequence of the Late rotation is that now the Early state and the Late state are no longer identical, so even after the Filter they remain entangled:
    |EH(a)>|EH(b)> + |LV(a)> |LV(b)> --- F --->
                                  |CH(a)>|CH(b)> + |CV(a)> |CV(b)>  4)
    The combination of a Late rotator plus a narrow-band filter has transformed the original time-bin entangled state into a polarization-entangled state. 

    Now comes the clever part. What happens to the superposition if Alice decides to turn off her late rotator but Bob continues to rotate his late state?
    |EH(a)>|EH(b)> + |LH(a)> |LV(b)> --- F --->
      |CH(a)>|CH(b)> + |CH(a)> |CV(b)> =
                |CH(a)> [|CH(b)> + |CV(b)>] =
                     |CH(a)> [ |(H + V) C(b)> ]                     5)

    The final state is again a product state and Bob's photon seems to be in a pure polarization state H + V which we call Diagonal polarization.

    An alternative way of considering this scheme due to Nick Herbert yields the same general result. Bob's photon is unpolarized when Alice inserts her rotator; Bob's photon is polarized when Alice withholds her Late rotation. Voila! An apparent viable and robust  superluminal signaling scheme!

    In Nick's version, Bob's photon is polarized when Alice withholds her Late rotation, but Bob's polarization depends on the phase of the Filter-induced Early/Late overlap:

    Bob's Polarization = H cosine (z) + i V sine (z) where z is some phase angle that depends on the nature of the filter but is constant for any given experimental run. Note  that Diagonal polarization does not appear in this derivation but when z = 45 degrees, Bob's photon is Right-circularly polarized (RCP).
    It took me some time and many false steps to understand this scheme and now that I do, I find that I cannot refute it, I will leave that task to others.
    Congratulations, Demetrios! They said it couldn't be done. And you did it! (At least provisionally)
    Kalamidas's handwritten notes on TIBET

    Demetrios Kalamidas emerging from the sea