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Adiabatic Spin Manipulation in EPR Experiment

  1. Dec 14, 2008 #1
    What would happen if adiabatic processes were applied in the context of a long-distance EPR Experiment? As background for my questions, see EPR paradox, Incompleteness of quantum physics, and: Description of the paradox)

    In the context of the foregoing, please visualize two particles that are quantum entangled moving apart in opposite directions. (See also: Brief explanation of entanglement in terms of photons) At some distance from their common origin, Alice measures the spin of one of the particles and finds that the spin is in the up direction. If Bob were then to measure the spin of the second particle, he will find that its spin is in the down direction. As often as Alice and Bob wish to repeat this experiment, Bob will find that the spin of his particle is always opposite to that found by Alice.

    Now, my specific question:
    What would happen if Alice, instead of conducting an ideal measurement, adiabatically imposes a direction of spin on her particle?

    Aharonov and Rohrlich in their book "Quantum Paradoxes: Quantum Theory for the Perplexed" provided the following introductory description to this concept:
    "How do we eliminate quantum jumping? Consider a closed system in an eigenstate of Hf, a Hamiltonian with discrete, nondegenerate eigenvalues. If Hf does not depend on time, the system never jumps to another state. What if Hf does depend on time? It can depend on time. If we prepare the system in an eigenstate of Hf, and Hf changes quickly, the system may jump to another state. But let Hf change adiabatically (slowly); if Hf changes slowly enough, the system never jumps to another state. Instead of jumping, it adjusts itself to the changing Hamiltonian. The system behaves like a heavy weight hanging on a thin string. Pull the string quickly - it snaps and the weight falls. Pull the string slowly - the weight comes up with it." (See also the “Adiabatic Theorem”).

    Based on the foregoing, what happens if Alice adiabatically imposes the up direction of spin on her particle? Is it permissible to assume that the spin of Alice's particle will, at the end of this adiabatic process, always be found to be in the up direction when her ideal measurement is eventually made? If so, what would happen if intermittent ideal measurements be conducted on Alice’s particle as the adiabatic processes are applied? Would also be permissible to assume that the probability of finding the spin of Alice’s particle to be in the up direction would gradually increase? If so, could we also assume that Alice’s findings would directly correlate with the duration of the adiabatic processes that Alice applies prior to each of her intermediate ideal measurements?

    Are my assumptions reasonable to this point? If so, let’s now consider Bob’s particle. We know that Bob's particle was entangled with Alice's particle and, because of this entanglement; the spin of Bob's particle will (due to conservation of angular momentum) always be opposite to that found after Alice’s particle is measured. We also know that the purpose of an adiabatic process is to effect change without causing a state change. Accordingly, is it permissible to assume that at the end the adiabatic process that Alice uses to cause her particle to spin in the up direction, that Bob’s particle will still be entangled with Alice’s particle? If so, would it then be reasonable to assume that, for the same axes, the spin of Bob’s particle would always be in the down direction when Bob’s measurement is eventually made?

    If so, we might then ask: what would happen if Alice never makes an ideal measurement? Must Alice conduct an ideal measurement on her particle in order to “cause” the spin of Bob’s particle to be in the down direction when his measurement is made? It is my conjecture that such an ideal measurement by Alice is not required. If there is any flaw in my logic or the applicable physics to this point, please help me identify it.

    Previously, I speculated that the probability of finding the spin of Alice’s particle to be in the up direction would gradually increase as a function of the intensity and duration of the adiabatic processes that Alice applied prior to Alice making certain intermediate ideal measurements. In this context, we must again consider what happens to Bob’s particle. Here, as an extension of the foregoing, I would speculate, again assuming Bob’s particle has remained entangled with Alice’s particle, that any increase in the probability of finding the spin of Alice’s particle to be in the up direction would cause a corresponding increase in the probability of finding the spin of Bob's particle to be in the down direction; and that this finding would occur whether or not any ideal measurements were ever conducted by Alice on her particles. Your thoughts on this conjecture would be valued

    I have not yet found any experiment that even touch on these conjectures. Is anyone aware of any studies that I may have missed? If relevant experiments have not occurred, is there some reason that such experiments could not be made? If such experiments are not otherwise precluded, could the 18km EPR experiment described below be adopted for this purpose?

    In a paper titled “Space-like Separation in a Bell Test assuming Gravitationally Induced Collapses” (See: http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.2425v1.pdf) D. Salart et. al describes a Franson-type test of the Bell inequalities is described where “pairs of entangled photons traveling through optical fibers are sent to two receiving stations physically separated by 18 km with the source at the center”. According to the paper’s authors, 18km established a new distance record for this type of experiment. The paper concludes that “under the assumption that a quantum measurement is finished only once a gravity-induced state reduction has occurred, none of the many former Bell experiments involve space-like separation, that is space-like separation from the time the particle (here photons) enter their measuring apparatuses (here interferometers) until the time the measurement is finished. In this sense, our experiment is the first one with true space-like separation. The results confirm the nonlocal nature of quantum correlations.” It is not my desire to contest or defend the conclusions of this paper.

    However, I would very much like to know whether an experiment might be designed utilizing Salart’s 18km experimental setup wherein one of the photons would be adiabatically polarized. Can this be done?

    Billy T provided a hint that some interesting science might result when he wrote in this Forum (see: Simultaneous measurement on 1 photon): “Because the photon can whip around a drum inside an optical fiber, I suspect it could also pass thru a weak optically active crystal or solution - a very strong one is effectively a type of polarizer, so that will destroy the entanglement, I think. I have a sense something important is tied up in my question about what is the nature of "disentangling interactions" with matter. I bet "adiabatic" has something to do with the answer.” And, vanesch’s responding post seems to imply that, because the adiabatically manipulated photon would become increasingly entangled with the environmental means employed to alter its spin, the spin correlation between Alice’s and Bob’s photons, that in the EPE context has been found following Alice’s or Bob’s an ideal measurement, might be lost. I hope readers will comment on both Billy T’s and vanesch’s conjectures.

    In any event, I hope there will be some agreement that some test involving adiabatic manipulations in an EPR experiment might generate some interesting science. If so, how might this adiabatic polarization process be performed? Should it or should it not be done in the context of the 18km experiment described above? Is any reader aware of experimenters with the requisite capacity and potential interest? Any speculations on any of the above that anyone might wish to share would be very much appreciated.

    Thank you,

    Jon Trevathan
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  3. Dec 14, 2008 #2


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    There is no energy cost to photon spin, so all photon spin states are degenerate; hence the adiabatic theorem doesn't apply in this case.

    If you start with the typical entangled spin state of two photons, [itex]{1\over\sqrt2}(|{+}{-}\rangle-|{-}{+}\rangle)[/itex], and send one through some filters, you just apply whatever the corresponding one-photon operator is to this state.
  4. Dec 14, 2008 #3


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    I have a difficulty considering adiabatically forcing an up state. The reason is that, as you say yourself, adiabatic evolution is unitary. So if you start from two orthogonal states, you cannot adiabatically evolve them into one and the same state, because the unitary evolution conserves in-product. Hence the in product of the evolution from, say, down, should be orthogonal to the evolution of the up state.

    In other words, if < up | down > = 0, then if |final-up> = U |up > and |final-down> = U | down>, we must have that < final-up | final - down > = 0 so they cannot both be up-states.
  5. Dec 18, 2008 #4
    Dear Avodyne:

    Please consider the following papers:

    A paper by Valerio Scarani, et. al., titled “Four-photon correction in two-photon Bell experiments” describes how a “Fourier-transform-limited pulsed laser is used to create non-degenerate photon pairs at telecommunication wavelengths (1310 and 1550 nm) by parametric down-conversion in a non linear-crystal.” (See: http://arxiv.org/PS_cache/quant-ph/pdf/0407/0407189v2.pdf)

    A paper by I. Marcikic, et. al., titled “Distribution of time-bin entangled qubits over 50 km of optical fiber” describes an experiment in which a ”150 femtosecond laser pulse with a 710 nm wavelength and with a repetition rate of 75MHz is first sent through an unbalanced, bulk, Michelson interferometer with an optical path difference of Δr = 1.2 ns and then through a type I LBO (lithium triborate) non-linear crystal where collinear non-degenerate photon pairs at 1.3 and 1.55 μm wavelength can be created by SPDC. The pump beam is then removed with a silicon filter and the pairs are coupled into an optical fiber. The photons are separated with a wavelength-division-multiplexer, the 1.3 μm photon is sent through 25.3 km of standard optical fiber (SOF) to Alice and the 1.55 μm photon through 25.3 km of dispersion shifted fiber (DSF) to Bob [15]. (See: http://arxiv.org/PS_cache/quant-ph/pdf/0404/0404124v1.pdf)

    A paper by Friedrich König, et. al., titled “Efficient and spectrally bright source of polarization-entangled photons” demonstrates “an efficient fiber-coupled source of nondegenerate polarization-entangled photons at 795 and 1609 nm using bidirectionally pumped parametric down-conversion in bulk periodically poled lithium niobate. The single-mode source has an inferred bandwidth of 50GHz and a spectral brightness of 300 pairs/s/GHz/mW of pump power that is suitable for narrowband applications such as entanglement transfer from photonic to atomic qubits.” The authors conclude that their methodology yields “a photonic source of polarization entanglement suitable for entanglement transfer to atoms via direct atomic excitations which have bandwidths of tens of MHz. The source could be used for testing long-distance teleportation schemes, in which the entanglement is stored in trapped-atom quantum memories [2]”. (See http://arxiv.org/PS_cache/quant-ph/pdf/0409/0409162v1.pdf)

    How might these studies impact your response to my post? Your comments on this and other questions I have raised would be appreciated.

    Sincerely yours,

    Jon Trevathan
  6. Dec 18, 2008 #5
    Dear Patrick (vanesch):

    I am having some difficulty reconciling your recent post and your 2005 post. If the entanglement between Alice’s and Bob’s photons is lost, which is what I thought you were saying in 2005, then it would seem that either Alice or Bob could adiabatically cause their photon to assume any arbitrary state.

    However, it is my belief that adiabatic processes may be applied by either Alice or Bob without causing the entanglement between their photons to be lost. If this belief is valid, which your recent post seems to support, I fully agree with your contention as follows:
    “if < up | down > = 0, then if |final-up> = U |up > and |final-down> = U | down>, we must have that < final-up | final - down > = 0 so they cannot both be up-states.”
    Accordingly, I have speculated that the adiabatic process that causes a state change to Alice’s particle will induce the corresponding state change to Bob’s particle that you indicate must occur.

    Your comments on this and the many other questions I posed in my post would be appreciated.

    Sincerely yours,

    Jon Trevathan
    Last edited: Dec 18, 2008
  7. Dec 18, 2008 #6


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    I'm not an expert on the experimental setups, but as far as I can tell, "nondegenerate" is used to mean that the two photons have different frequencies. The experimental procedures appear to produce a particular spin state, but, again as far as I can tell, the other spin states would have the same energy (= sum of the two individual photon energies).

    But I could certainly be wrong about this.
  8. Dec 19, 2008 #7


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    Assuming I understand your question and your definition of adiabatic (as being slow and small changes to a particle's state):

    Suppose you ran Alice's photon through a polarizing beam splitter (PBS) set at 30 degrees off the vertical, and then recombined the results into a beam in which the path taken cannot - in principle - be determined. Then you repeated that process at another PBS at 31 degrees, and so on. So I guess the question is: after a series of such manipulations, are Alice and Bob still entangled? Not knowing the answer to that, I would guess YES because: as long as the superposition remains in effect, there should be entanglement.
  9. Dec 22, 2008 #8
    First, I grateful for Dr. Chinese’s kind suggestions. If the procedures Dr. Chinese has proposed were applied, do the readers generally concur that the entanglement between Alice’s and Bob’s photons would be maintained? In the context of Dr. Chinese’s suggestion, could polarization-entangled photons be pre-selected such that the polarization of Alice’s photon was in the up direction and the polarization of Bob’s photon was in the down direction? If so, could the procedures suggested by Dr. Chinese be repeated to result in Alice’s photon being polarized in the down direction? If the entanglement between Alice's and Bob's particles are maintained, is my assumption reasonable that Bob’s photon, when tested, would be found to be polarized in the up direction; whether or not Alice’s photon is tested? If so, and if a large ensemble of pre-selected photons were subjected to intermediate testing by Bob, is it reasonable to assume that the polarization direction of Bob’s photon would be found to probabilistically evolve from the down direction to the up direction?

    Can the readers of this forum identify other processes that Alice might use to adiabatically impose an arbitrary direction of spin, polarization or other state on Bob’s particle while preserving the particles’ entanglement? How might the questions in my original post be answered, and an experiment set up, where entangled electrons, ions, or atoms were employed?
  10. Dec 24, 2008 #9
    Nicholas A. Peters, et. al., in their paper titled “Remote state preparation: arbitrary remote control of photon polarization” (http://arxiv.org/PS_cache/quant-ph/pdf/0503/0503062v2.pdf) make the following claim: “We experimentally demonstrate the first remote state preparation of arbitrary single-qubit states, encoded in the polarization of photons generated by spontaneous parametric downconversion. Utilizing degenerate and nondegenerate wavelength entangled sources, we remotely prepare arbitrary states at two wavelengths.

    I would be very grateful if the readers of this forum would comment on this paper.

    Thank you.
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