TIBET: A New Superluminal Signaling Scheme

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  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
  

  
  

First Physics-based Restriction on Local Psychic Powers

Nick Herbert devises an important new restriction on local psychic powers.

FIRST PHYSICS-BASED RESTRICTION ON LOCAL PSYCHIC POWERS

Personal experience, scientific research and the occasional spectacular phenomenon (a flying monk from Cupertino, for instance) seem to demonstrate the real existence of psychic powers, but our theoretical understanding and extension of such powers seems not to have advanced at all. Most limiting is the fact that we possess no confident scientific understanding of ordinary consciousness let alone its paranormal extensions. Much to be desired would be the application of the methods of our dazzlingly successful physical sciences to some of the problems of mind. That is what I have done, in a small way, in an article soon to appear in the journal Activitas Nervosa Superior (online version here) as part of a Festschrift in honor of Berkeley physicist Henry Pierce Stapp.

On the other hand, the moderators of the Cornell University Physics arXiv, which I scan daily, looking for innovations in quantum physics, have declined to list this article on the grounds that "your submission is not of plausible interest for arXiv." My guess is that the mere mention of "psychic powers" in a physics paper caused some old fuddy duddy at arXiv to lose his lunch.

From the great variety of possible psychic powers I chose extrasensory perception, the alleged ability of a psychically gifted human being to correctly guess, with odds better than chance, the outcome of a sequence of symbols generated by a random process. To simplify the discussion, I limit the choice of target symbols to two, which could be zero/one, black/red, heads/tails or even/odd. And the random process is designed to make each of these two symbols appear with 50/50 probability. The "power" of a psychic faced with such a task is defined by the percentage of correct guesses that consistently exceed 50%. On this scale a perfect score would be "50".

Once we find a high-scoring psychic let's now confront him or her with two different kinds of tasks which I will describe as classical ignorance and quantum ignorance.

Classical ignorance; result exists before guess and is governed by classical randomness

 In the case of classical ignorance, the target symbol exists before the psychic makes his guess. As in the turning over of a top card -- the card was definitely"black" or "red" but its value was hidden from ordinary perception.

Quantum ignorance: result does not exist before guess and is governed by quantum randomness

 In the case of quantum ignorance, the target symbol is produced only after the guess and is governed by quantum randomness -- the basic uncertainty that governs every quantum transition in the Universe. In the example above, the blue cylinder shoots a single photon at a half-silvered mirror. Whether the mirror deflects the photon forward into red photon detector #1 or sideways into red photon detector #2 is determined by an uncertainty so fundamental that some physicists have joked that not even God can say which path that single photon will take.

Now the question I ask about psychic powers is this: Which kind of ignorance does the psychic find easier for his extrasensory powers to overcome -- classical or quantum uncertainty?

Since we know absolutely nothing about how psychic powers operate, we are free to let our imaginations run wild. Perhaps, for instance, quantum uncertainty is somehow "softer" and more "mindlike" than classical uncertainty so the psychic will score higher on the quantum task. On the other hand, if it is true that not even God can predict the outcome of a quantum-random event, then the psychic must necessarily score higher on the classical task.

Via a digression into the topic of faster-than-light (FTL) signaling schemes, I answer the question of whether a psychic can score better against classical or against quantum ignorance.

For longer than I can remember, I have been curious about superluminal signaling schemes and have invented several devices tagged with unusual acronyms: QUIK, FLASH, ETCALLHOME and many others, and I was much involved in the refutation of Demetrios Kalamidas's ingenious KISS scheme. The detailed refutation of each of these proposals led to a slightly deeper understanding of the foundations of quantum theory. And in the case of the refutation of FLASH, resulted in the discovery of the quantum no-cloning rule. 

Each of these proposed FTL signaling devices invokes the strange situation of quantum entanglement in which two photons A and B, separated by a great distance, nonetheless appear to act as though they were a single entity. In the usual setup, photon A is sent to Alice and photon B is sent to Bob. In the math it looks as though what Alice chooses to measure on her photon A seems to instantly affect what Bob will measure on his photon B. Irish physicist John Bell proved in 1964 that any model of reality that correctly describes quantum entanglement must necessarily be non-local, that is, something must be going on that is faster than light. Bell's theorem proves that deep reality must be faster than light. But we humans cannot observe deep reality, only its surface consequences; and these surface consequences always appear to obey the Einstein speed limit.

Indeed, a result proved by Philippe Eberhard, a colleague of Henry Stapp's at Berkeley, shows that any ordinary measurements performed by Alice will have no measurable effect at Bob's receiving site. Eberhard's Proof demonstrates that superluminal signaling using Alice/Bob quantum entanglement is impossible.

Alice and Bob each receive one member of a pair of entangled photons. Is there anything they can do that would allow Alice to send an FTL message that Bob could decode?

To get around the roadblock of Eberhard's Proof, one might consider using a clever and subtle measurement process that evades the proof's assumptions. The hope of devising some unconventional measurement scheme lies behind the KISS, FLASH, QUIK, etc. schemes mentioned above. None of these measurement schemes, however, is bizarre enough to evade Eberhard's sturdy proof of the impossibility of using quantum entanglement for superluminal signaling.

But what about going beyond physics into the realm of psychic powers?

That's what I have done in my recent paper. In my setup, Alice sends Bob a Morse Code signal which he receives as two kinds of ignorance. a dot is encoded as a situation of classical ignorance. And a dash is encoded as a situation of quantum ignorance. Alice sends each symbol as a bunch of N photons that appear at Bob's site to possess the same kind of ignorance, that is, all N photons in a bunch are either all classically or all quantum uncertain.

Upon receiving Alice's message, Bob applies his psychic powers to try to guess the outcome of his measuring a particular bunch of N photons. If Bob's psychic power works better for one kind of ignorance rather than another, then Bob can successfully decode Alice's message as a series of dots and dashes.

This method of signaling faster than light evades Eberhard's Proof because it does not use conventional physical measurements, but measurements of an entirely non-physical kind.

The acronym for my scheme, by the way, is GUESS = Going Unphysical Enables Superluminal Signaling.

However, an easy way to outlaw superluminal signaling of the GUESS kind is to demand that a psychic's ability to guess a quantum random sequence must be exactly equal to his ability to guess a classical random sequence.

This result I call "Nick's restriction". The journal referees made me call it something else but in my blog I can call it anything I want. And so can you.

One beauty of Nick's restriction is that it can be experimentally tested. All one needs to do is find a reliable psychic and to devise a robust on-demand source of quantum randomness.

A further beauty of Nick's restriction is that it cannot fail. If measurement does show the expected result: that a psychic possesses identical powers of guessing quantum or classical random sequences, then Nick's restriction will take its rightful place as one of the solid cornerstone truths of a modern psychic science.

But what if Nick's restriction is false? What if psychic researchers measure a consistent difference between a psychic's ability to fathom one kind of ignorance rather than another?

Why that's even better. For then we will be able to use quantum entanglement to send signals faster than light.

A basic new law of psychic phenomena? Or an easy FTL communication scheme?

On the question of the practical usefulness of Nick's restriction, we simply can't lose.

Does Doc Brown's psychic power amplifier obey Nick's restriction or not?