Demetrius,

coherence time is a concept valid for huge number of photons not for individual photons. So the photons would stay in definate state after the filters.

Nothing that is described by electrodynamics, no matter quantum or classical, allows superluminal signaling.

I am wondering what they teach you in the City College of New York.

Plimak-- they apparently taught me what you have not been taught: that nonlocality arises from standard quantum mechanics and implies real superluminal influences (as shown by Bell); that there has been serious (published) criticism of the no-go proofs given thus far; they also taught me that "no FTL signaling" was built into the formalism of quantum electrodynamics as an axiom (called 'microcausality').......and that this was before the stunning EPR- type nonlocality experiments were conducted (so this axiom really does not have a strong empirical justification). But, you just decided to be sarcastic without any basis for being sarcastic and have provided ZERO justification for your claim and ZERO critique of any aspect of the super-simple mathematical description I presented.

@Demetrios Kalamidas

Sir,

I am being sarcastic because you amply deserve it. I know all you are talking about, and even - imagine! - wrote a couple of papers on the topic.

I provided zero justification because all you are talking about is in textbooks. Since you ask, here are a few points to start your education:

1. The so-called "quantum nonlocality" is about correlations, not signaling. All serious researchers mention this.

2. Macroscopic causality is a well established experimental fact. Microcausality at the level of Planck's length and time is indeed an axiom. Perhaps you would explain me how and where this is relevant to your MACROSCOPIC setup.

3. By mentioning "inbuilt microcausality" in ED you shoot yourself in the foot. How on earth would you expect a formal environment with "inbuilt microcausality" describe superluminal signaling? Before you even utter the word "superluminal", you have to generalize both classical and quantum electrodynamics. Please let me know if you succeed.

Best wishes

LP

Plimak--If you feel like it, read attached paper (by Kennedy), which is one of several, published by 'serious researchers', that cast 'serious' doubt on the no-go theorems that state that these correlations definitely preclude signaling. The nonrelativistic QM formalism generates nonlocality from the postulate of superposition, and this is prior to the added postulate of operators being strictly local (look in Kennedy for the details). So, the capacity for signaling is already allowed by QM, and then one has to add the postulate of local operators to prohibit it (and that is the circularity being alleged).

In nonrelativistic QM this is known as the 'tensor product representation' and in quantum field theory as 'microcausality'. Now, my scheme is based wholly on 'quantum indistinguishability', as expressed most clearly by Feynman: if you cannot know which possibility gave the final state, add together (coherently) all possibilities (with appropriate pre-factors) and square-------My scheme is based on this principle, which has not failed yet in any quantum mechanical context, and that is why it can also apply to my macroscopic setup, since the macroscopic contexts (switching HWPs) act upon microscopic quantum states.

I'll wait for an experiment.

Plimak--OK, good answer.

Now, I hope others will take on this question I posed, to see if my scheme is trivially flawed or perhaps may be of some interest.

I don't think that your synchronous switching will result in 1/√2(|HAHB>+|VAVB>), rather it will produce 1/2|HA+VA>|HB+VB>. The switch on Alice's side can act only on the A factor of the wave function, the switch on Bob's side only on the B side. So if you start with |HAHB>, Alice's switch turns that into 1/√2|HA+VA>|HB> and Bob's switch produces 1/2|HA+VA>|HB+VB>. You can have Bob's switch act first to have the intermediate state1/√2|HA>|HB+VB> and, after Alice's switch has acted, get again 1/2|HA+VA>|HB+VB>. Since the sequence of the switches does not matter, you'll also get the same final state if they act simultaneously.

Now the state 1/2|HA+VA>|HB+VB> is not distinguishable, by Bob, from 1/√2|HA>|HB+VB> .

Look up the FLASH protocol for a bit of historical interest.

Demetrius

can you tell how long is the coherence lenghts of a single photon? And how it depends on parameters?

Andrew: Thanks for your interest. I am in frequent discussions with Nick Herbert (FLASH); I also was hanging out with Terry Rudolph way back when I was in Vienna. I would enjoy any of your thoughts on this scheme.

Ilian: In SPDC (Spontaneous Parametric Down-Conversion) the created photons typically have a coherence time of about 100 femtoseconds, and these can be spectrally filtered to a coherence time of tens or hundreds of picoseconds.

Prof. Kassner: Thanks much again for your input! I will reply to your comment soon, after I think about how to respond.

Prof. Kassner,

I have to disagree with your assessment.

The two photons comprising each SPDC pair are created virtually simultaneously at a near point-like region within the SPDC source, meaning that the state of the left HWP encountered by an Alice photon will be the same as the state of the right HWP encountered by a Bob photon (provided, of course, that we are assuming equal flight paths)--This (first) crucial fact demands that the two resulting quantum states, of the Alice and Bob photons respectively, will be 100% correlated: |HH> or |VV>. I claim that it is impossible to know which of these possibilities 'occured' because the only detected SPDC photons are the ones that have been filtered to a coherence time much longer than the switching interval of the HWPs--Now, this (second) crucial fact seems to demand that we must superpose the two possibilities. Furthermore, please remember that the coherence time of the unfiltered photons that encounter the HWPs is much shorter than the switching interval, so they encounter a 'steady state' of either 'ON/ON' or 'OFF'/OFF; then they proceed to be filtered and we are left without the ability to discern what state they encountered. I cannot see how the HWPs, which are designed to implement "|H> to |V>" (when 'ON'), can create an (1/sqrt2)|H+V> single-photon state in the manner you suggest; but, that state is indeed created (I claim), on Bob's side, only when Alice keeps her HWP in the 'OFF' state.

So, it is the time uncertainty, introduced by spectral filtering, that creates indistinguishability regarding the |HH> or |VV> joint states (and thus a superposition of them). It is this same time uncertainty that projects a Bob photon onto the pure state (1/sqrt2)|H+V> when Alice has her HWP 'OFF': Alice knows that her photon will be |H> for sure, but the time uncertainty still makes it impossible for her, and Bob, to know what HWP state Bob's photon encountered, thus projecting onto the joint state |H>(1/sqrt2)|H+V>.

Dear Demetrios, could you please describe the measurement on the Bob side that would allow you to distinguish between the two possible states you propose. It seems to me that you can only do this if you take into account the result of a simultaneous measurement on the Alice side, but in this case you cannot talk about any FTL effect.

Hi Viktor,

Thanks for your important question.

Assume that Bob is equipped with a polarizing beam-splitter (PBS) that is configured to transmit (1/sqrt2)|H+V>=|+> photons and reflect (1/sqrt2)|H-V>=|-> photons.

If Alice has her HWP switching synchronously with Bob's HWP, for a batch of runs, then Bob receives photons in the mixed state 1/2(|H>

Hi Demetrios, thanks for the explanation!

Now I finally realized what your claims are :)

I am still trying to understand where does this asymmetry between the states |+> and |-> come from.

It seems intuitively to me that these states should be quite symmetric in respect to the |H> and |V> bias states, but here we see something different. Could you comment on this?

And another issue: do you see any realistic experimental implementation for such a quick HWP switch, or it remains purely theoretical, so we can only discuss a sort of Gedanken experiment?

Hi Viktor,

I am glad that I have managed to convey the true intent of this scheme and what it implies.......I don't think such scenarios with "temporally switching devices acting on quantum states" have been considered before! 'Time' is not an operator in quantum mechanics so, who knows, maybe strange things (like this) occur when time is incorporated in certain fashions.

Now, the reason we only get the |+> state and not the |-> state on Bob's side (when Alice has her HWP 'OFF') is because we have assumed (for simplicity) that the relative phase between the |HH> and |VV> joint states is '+', giving (1/sqrt2)(|HH>+|VV>); but, we can easily insert a variable phase-plate, in either mode (A or B), and create any relative phase we like.......if we chose the phase-plate setting for '-' then Bob would only get |-> photons. Remember, in the case wherein Alice keeps her HWP 'OFF', her photon states are always |H> and this state factors out, superposing the |H> and |V> states of Bob's photons according to whatever relative phase exists between modes A and B.

I used to work with ultrafast lasers and know of effects wherein intense 100 femtosecond pulses can induce transient birefringence in media like glass and water.......this transient polarizability is also an ultrafast process. So, we can conceivably have a 'pump-probe' setup that implements the polarization rotations with sub-picosecond response! For sure regular Pockels cells would not be sufficient.

@Kalamidas: " I cannot see how the HWPs, which are designed to implement "|H> to |V>" (when 'ON'), can create an (1/sqrt2)|H+V> single-photon state in the manner you suggest; but, that state is indeed created (I claim), on Bob's side, only when Alice keeps her HWP in the 'OFF' state."

If the HWP on Bob's side can create that state when Alice keeps her HWP in the 'OFF' state, it can also do so when Alice keeps her HWP in the 'ON' state. The HWPs are local devices, and each acts only on one photon subspace. The photons are created in a product state and acting by devices on either side, they will stay in a product state. Entanglement will not be produced by two distant devices the way you suggest, no matter what time constraints you impose on the fields. You can switch entanglement from one partner of an already entangled state to another particle, but you will not produce entanglement from a product state via distant local operations.

But in fact, I think that your arrangement will not produce a superposition of |H> and |V> the way you suggest. In any case, whatever you do on one end, will not affect the property of the combined state to remain a product state.

@Kalamidas: I have looked at your recent paper on a quasi-Gedanken experiment challenging the no-signalling theorem. There you also conclude to a superposition of states in an illegitimate way, from the indistinguishability of the photon encountering a double-sided mirror (DSM) and a transparent phase plate (TPP).

In fact, you point out the problem with your result yourself -- your superposition produces a non-unitary tranformation of the state |ψR> under consideration, whereas application of either DSM or TPP alone gives a unitary transformation. Now, if your demon applies the unitary tranformations in fast alternation, the result of many such applications will still be a unitary transformation of |ψR>, so it cannot be the superposition that you indicate. It will be a state that is different from both |ψDSM> and |ψTPP> and this state will exhibit the fact that you cannot say that only one of the devices has been applied. But it will not be the superposition of states that you assume and which arises by a non-unitary transformation of |ψR>. It will simply be some different state that obtains by a unitary transfomation that could be calculated from the two transformations described via an analogue of the Trotter formula.

@Kalamidas: Having read the Kennedy paper that you were so friendly to attach in one of your answers, I must say that I find it absolutely unconvincing. A (failed) philosopher's attempt at mathematical rigor.

He attacks the tensor product representation of Hilbert spaces of combined systems and throughout a major part of the paper I was waiting for a counterexample, i.e. a combined system where the Hilbert space is not a tensor product of the Hilbert spaces of its two constituent systems. The counterexample never was given, nor a proof for his claim that this does not follow from von Neumann's axioms -- at least this should have been given. How on earth should an alternative construction of the Hilbert space of a combined system proceed?

Well, I think I can prove with one additional assumption beyond the von Neumann axioms that the Hilbert space of the combined system has to be the tensor product of the Hilbert spaces of its subsystems (or a direct sum of several tensor products in the case of Fock space). And I suspect that this assumption follows from the axioms, too...

Here goes. My assumption is that on each of the two subsystem Hilbert spaces there exists one Hermitian operator, let us call them A and B, so that A and B commute. We know from the axioms that the combined system also has a Hilbert space. The product AB must be Hermitian [(AB)+=(BA)+=A+B+=AB]. We know that Hermitian operators have a complete set of orthonormal eigenvectors, so the eigenvectors of AB constitute a basis of the Hilbert space of the combined system. But each product state of eigenstates of A and B is an eigenstate of AB (trivially). The converse is true in the nondegenerate case (as can be proved using the spectral representations of A and B). In the degenerate case, there are also eigenstates of AB that are not product states, but all eigenstates can be written as linear combinations of product states. So the combined Hilbert space has a basis consisting of product states, meaning it is the tensor product of the subsystem Hilbert spaces. Under the same assumptions obviously any psi-function can be written as a superposition of product states and this is not equivalent to a no-signalling condition.

So in order to have a Hilbert space of a combined system that is not the tensor product of the subsystem Hilbert spaces, we would have to require that no two Hermitian operators exist in the two subsystems that commute (a weird requirement). But what about the identity operators in the subsystems? They are Hermitean and they commute. Therefore, it seems that indeed we do not need anything beyond the von Neumann axioms to prove the tensor product representation.

Finally, the restricted action of the extension of an operator from the subsystem to the combined system has nothing to do with no signalling either. That is the standard way of mathematics to extend operators to a new domain. It is akin to saying that a real number in the complex plane is a number with imaginary part zero. (So a real number is extended to the complex plane...)

Anyway, it is easy to see that the circularity claimed by Kennedy does not hold. If assuming either the restricted action of the extension or the superposition of product states as psi-function were equivalent to a no-signalling condition, then no signalling should be possible given these premises. But they are not sufficient. If a non-unitary evolution in a subsystem is assumed, superluminal quantum signalling becomes indeed possible despite the satisfaction of the three conditions Kennedy mentions in his conclucion. So these conditions cannot be the reason for no signalling (or not the sole reason), because they are insufficient to guarantee it. And in particular, neither of these conditions can be "equivalent" to no-signalling. Some of them may be necessary (although that was not proven) but they are not sufficient and so the purported circularity is absent.

Hi Klaus.......many thanks for taking the time to think about the proposal and provide these detailed comments.......and for reading my paper and that of Kennedy!

First, let me try to respond to the issue below:

@Kalamidas: " I cannot see how the HWPs, which are designed to implement "|H> to |V>" (when 'ON'), can create an (1/sqrt2)|H+V> single-photon state in the manner you (K. Kassner) suggest; but, that state is indeed created (I claim), on Bob's side, only when Alice keeps her HWP in the 'OFF' state."

(K. Kassner) If the HWP on Bob's side can create that state when Alice keeps her HWP in the 'OFF' state, it can also do so when Alice keeps her HWP in the 'ON' state. The HWPs are local devices, and each acts only on one photon subspace. The photons are created in a product state and acting by devices on either side, they will stay in a product state. Entanglement will not be produced by two distant devices the way you suggest, no matter what time constraints you impose on the fields. You can switch entanglement from one partner of an already entangled state to another particle, but you will not produce entanglement from a product state via distant local operations.

The two HWPs are indeed local devices and the initial SPDC state is indeed a product state of polarization.......but there is entanglement in time and energy in the initial state that, I claim, is exploited so that this 'time-energy entanglement' is transferred to the polarization degree of freedom in the final state: By virtue of the two SPDC photons in each pair being created simultaneously (at random times) and their strict energy correlation (i.e., their energies must sum up to the singular energy of the pump), their spectral filtering at Alice's and Bob's sides creates uncertainty in their time-of-flight determination which, in turn, creates uncertainty in their polarization state via the switching HWPs. Specifically, only when Alice has her HWP 'OFF', does the (alleged) joint state take the form

(1/sqrt2)(|HH>+|HV>)=|H>(1/sqrt2)(|H>+|V>),

allowing the Alice state |H> to be factored out and causing the Bob state to be projected onto (1/sqrt2)(|H>+|V>).

So, the initial 'product state in polarization' is transformed into an 'entangled state of polarization' (or not, as shown by the product state above) by exploiting the initial time-energy entanglement via the manipulation of the two HWPs (as I describe). Therefore, we are not dealing with a situation where there is no entanglement at all and then, somehow, the local actions of Alice and Bob create entanglement (that is indeed impossible). Rather, we are dealing with a transfer of entanglement from the (initial) time-energy domain to the (final) polarization domain.

I will try to respond to your comments on my published paper and your criticism of Kennedy's paper in separate messages, so that I can think more carefully about what you have stated.

Hi Klaus,

Concerning my paper: The working principle of this current proposal derives from the 'gedanken' version of the paper; I presented it for discussion as a possible feasible alternative to the Demon's action described in the paper.

You state that I create an "illegitimate" superposition of the quantum states corresponding to the 'mirror' and 'phase plate' device-states; I believe that, at present, we cannot be sure of this illegitimacy unless a rigorous mathematical disproof emerges should one carry out the full multimode & time-dependent quantum-optical treatment of the setup or, if no mathematical disproof arises in such a treatment, the result must be determined experimentally. So far the heuristic principle of 'indistinguishability' has not failed to produce its predicted results in any quantum mechanical context. Importantly, in the case of my 'Switching Double-Slit' scenario, even you stated that you believe that the switching between the single slits would in fact result in a typical double-slit superposition state after the spectral filtering (temporal erasure mechanism).......the working principle is the same here (now extended to entangled states), but the implications in this current scenario are much more controversial. However, your guidance towards the Trotter product formula may be important and I have not considered it.......so I must study that.

Next I will think about your comments on Kennedy's paper.

I admit that I didn't read all the comments here, but superluminal communication is not only an impossibility of the QM. It is forbidden in our universe, because it would enable re-writing the past.

So, the question is, where is the mistake.

Here is the mistake: as the experiment is described, Alice and Bob don't get two pairs of photons, but 4 photons, i.e. two photons each. For obtaining the superposition (|2;H>Alice + |2;H>Bob) one doesn't use two pairs of photons comming after one another. Such two pairs give a product, not a superposition. For obtaining superposition one has to pass the U.V. beam through a beam-splitter, and each wave-packet has to be passed through a nonlinear crystal. In this way one gets (1/√2)( |1;H>|1;V>I + |1;H>|1;V>II), where the subscripts I and II mean crystal I and crystal II.

Unfortunately, even in this case the desired superluminal communication won't be possible. The Nature is terrible in defending her NO-GO laws. Alice couldn't superpose the state |1;H> comming from crystal I upon the |1;H> comming from crystal II - it's against unitarity.

Dear physicists, sometimes the mistake is under our nose, no need to search it with high phylosophy. A simple replacement of the symbol "×" by the symbol "+" and one gets miracles. (Satan hides in the details.)

So, we don't have here any chance for a Nobel prize.

Dear Demetrios, it seems to me that the most questionable in your proposal is your ability to ensure the "perfect switching synchronization" between the two space-like separated HWPs. Can you describe any possible synchronization mechanism? I could perhaps imagine a sort of coincidence scheme being able to do the job, but this would assume time-like separated HWPs and is something you are trying to avoid.

You hope to use such a perfect synchronization to produce the polarization entanglement, so the precision should at least match the temporal precision provided by the down-conversion process, which produce the time-energy entanglement. Providing such a precision with macroscopic means is quite challenging.

But I guess the first big challenge could be to show experimentally that your scheme even works for time-like separated HWPs, without any relation to FTL effect.

Hi Viktor,

Thanks for your continued interest.

For the detectors: We can arrange that the SPDC pair-production rate is low enough so that only one pair, at most, is produced, on average, per gating interval (the rate being determined by the pump intensity); this would allow the synchronization between the two detectors to be relaxed to, say, microseconds (not nanoseconds or picoseconds). The two photons in each pair are created simultaneously but at random times in this CW-pump scheme, so only sporadically will the gated synchronized detectors, that are assumed to be gating at regular intervals, detect a pair.

The devices that would implement the "switching half-wave plates" would have to be synchronized to within several tens of picoseconds, or even up to about one hundred picoseconds (since spectral 'notch' filtering can achieve coherence times of several hundred picoseconds in the case of typical SPDC photons). This level of synchronization can perhaps be achieved if these devices are 'activated' by femtosecond laser pulses split from a central femtosecond-laser source (typically producing 80-100 fs pulses). Now, because of the CW pump, there is 100% energy correlation between the two photons so that if one spectrally filtered photon is detected on the left, its partner will be detected on the right with certainty, so there is no need for coincidence counting.

As a first experimental test, one doesn't have to worry at all about spacelike separation, the setup can be on a tabletop with dimensions on the order of a meter. Why? Because the 'no signalling proofs' prohibit any quantum signaling (subluminal, luminal, or superluminal).......and the definition of 'quantum signaling' is that Bob knows what Alice has done solely on the results of his local measurement, without coincidence counting, postselection, and an ancillary classical-information signal.

Please re-read my latest response just above, I have made some changes since I first posted it.

Why are you talking now about sinchronization between two detectors? Do you really need something like that? What do you mean?

Hi Viktor,

This experiment makes the role of the detectors fuzzy: Do they need to be in place in order to induce the the irreversible amplification that causes the 'collapse' (projection) of the wave function? Or, does the projection happen right after the filtering, or even somewhere else, making the detectors superfluous? I have assumed, as a starting point, that the detectors are required, in which case their synchronization would allow each SPDC pair to be separately detected (on the left and right) thus reducing, I presume, the signal to noise ratio (for instance: if the detectors on the left and right were gating in an uncorrelated fashion, then many detected photons on the right would have 'unprojected' photons on the left, thus reducing the quality of the pure state that is alleged to occur on the right).