question: How is it possible for a particle which is quantumly entangled to another particle to "know" at FTL speed about a change happening to its twin?
comment: Here is an analogy: Rotate the tires on a bicycle so that the inner tube nozzles are aligned in some way, such as both of them pointing up. As you ride the bike around, you will have no idea where the nozzles are pointing because you can't see them as you ride. As soon as you stop the bike and measure one tire, you will immediately know which orientation the other nozzle has, without looking at it.
passages: BULLET::::3. Twin: It is possible to "entangle" two elementary particles and separate them by a significant distance, so that they have the same squared spin results if measured in parallel directions. This is a consequence of quantum entanglement, but full entanglement is not necessary for the "twin" axiom to hold (entanglement is sufficient but not necessary).
   Therefore, if the SPD detects no photons, it is not certain which state was sent. The error of guessing wrong is equal to the probability formula_46 that the formula_5 state was sent, which is 50% as it is assumed either state is equally likely to be sent, times the probability that a zero detection result can occur when the displaced state is formula_37. The probability of error formula_49 becomes,
   This establishes that the "k"-factor for observers moving directly apart (red shift) is the reciprocal of the "k"-factor for observers moving directly towards each other at the same speed (blue shift).
  
  Section::::The twins paradox.
  
  Consider, now, a fourth inertial observer Carol who travels from Dave to Alice at exactly the same speed as Bob travels from Alice to Dave. Carol's journey is timed such that she leaves Dave at exactly the same time as Bob arrives. Denote times recorded by Alice's, Bob's and Carol's clocks by formula_22.
   The delayed choice quantum eraser experiment performed by Marlan Scully involves pairs of entangled photons that are divided into "signal photons" and "idler photons", with the signal photons emerging from one of two locations and their position later measured as in the double-slit experiment. Depending on how the idler photon is measured, the experimenter can either learn which of the two locations the signal photon emerged from or "erase" that information. Even though the signal photons can be measured before the choice has been made about the idler photons, the choice seems to retroactively determine whether or not an interference pattern is observed when one correlates measurements of idler photons to the corresponding signal photons. However, since interference can only be observed after the idler photons are measured and they are correlated with the signal photons, there is no way for experimenters to tell what choice will be made in advance just by looking at the signal photons, only by gathering classical information from the entire system; thus causality is preserved.
   The feedback of the Donlinar receiver works by switching the displacement if there was a photon counted but before the next copy of the input state arrives. If no photons are detected, the displacement remains unchanged for the next arrival of a copy. For each no count result, it becomes more and more likely that the state copies are being displaced to vacuum and the certainty of the hypothesis increases. On the whole, the history of the detection results in conjunction with their corresponding displacements can give more and more complete information about the most likely identity of the input state.
   Another example can illustrate the potential error correction the feedback provides. Suppose the same setup as before, except that on the first detection trial no photons are detected, as is possible for the displaced formula_37 state. The receiver will not change the displacement, and the next copy of the input state will be again displaced to formula_37. However, two no count results in a row is unlikely given the formula_37 state entering the SPD. It is most likely on the second or third pass the SPD will detect a photon and switch the displacement, after which there will be no more photon counts. As before, each lack of counted photons after a displacement switch reinforces the hypothesis that the original guess was incorrect.
   The newly observed effect of two-photon emission from electrically driven semiconductors has been proposed as a basis for more efficient sources of entangled photon pairs. Other than SPDC-generated photon pairs, the photons of a semiconductor-emitted pair usually are not identical but have different energies. Until recently, within the constraints of quantum uncertainty, the pair of emitted photons were assumed to be co-located: they are born from the same location. However, a new nonlocalized mechanism for the production of correlated photon pairs in SPDC has highlighted that occasionally the individual photons that constitute the pair can be emitted from spatially separated points.
   The result of Alice's Bell measurement tells her which of the above four states the system is in. She can now send her result to Bob through a classical channel. Two classical bits can communicate which of the four results she obtained.
  
  After Bob receives the message from Alice, he will know which of the four states his particle is in. Using this information, he performs a unitary operation on his particle to transform it to the desired state formula_22:
   It turns out that the phases of the twin beams are quantum correlated as well, leading to entanglement, theoretically predicted in 1988. Below threshold, entanglement was measured for the first time in 1992, and in 2005 above threshold.
  
  Above threshold, the pump beam depletion makes it sensitive to the quantum phenomena happening inside the crystal. The first measurement of squeezing in the pump field after parametric interaction was done in 1997.
  
  It has been recently predicted that all three fields (pump, signal and idler) must be entangled, a prediction which was experimentally demonstrated by the same group.
   Detection of signal photons at "D" does not directly yield any which-path information. Detection of idler photons at "D" or "D", which provide which-path information, means that no interference pattern can be observed in the jointly detected subset of signal photons at "D". Likewise, detection of idler photons at "D" or "D", which do not provide which-path information, means that interference patterns "can" be observed in the jointly detected subset of signal photons at "D".
   Let clock K' be associated with the rocket that makes the trip.
  
  At the departure event both clocks are set to 0.
  
  Knowing that the clock "K" remains inertial (stationary), the total accumulated proper time Δ"τ" of clock K' will be given by the integral function of coordinate time Δ"t"
  
  where "v"("t") is the "coordinate velocity" of clock K' as a function of "t" according to clock "K", and, e.g. during phase 1, given by
  
  This integral can be calculated for the 6 phases:
   BULLET::::4. As a result of the measurement performed at location A, the EPR pair qubit at location B is in one of four possible states. Of these four possible states, one is identical to the original quantum state formula_1, and the other three are closely related. Which of these four possibilities actually obtained, is encoded in the two classical bits. Knowing this, the EPR pair qubit at location B is modified in one of three ways, or not at all, to result in a qubit identical to formula_1, the qubit that was chosen for teleportation.
   The total pattern of all signal photons at "D", whose entangled idlers went to multiple different detectors, will never show interference regardless of what happens to the idler photons. One can get an idea of how this works by looking at the graphs of "R", "R", "R", and "R", and observing that the peaks of "R" line up with the troughs of "R" (i.e. a π phase shift exists between the two interference fringes). "R" shows a single maximum, and "R", which is experimentally identical to "R" will show equivalent results. The entangled photons, as filtered with the help of the coincidence counter, are simulated in Fig. 5 to give a visual impression of the evidence available from the experiment. In D, the sum of all the correlated counts will not show interference. If all the photons that arrive at "D" were to be plotted on one graph, one would see only a bright central band.
   Now expand the situation to have one sentient being observing the device. Now, he too enters the indefinite state. His eyes, body, and brain are seeing both spins at the same time. The mind however, stochastically chooses one of the directions, and that is what the mind sees. When this observer goes over to the second detector, his body will see both results. His mind will choose the result that agrees with the first detector, and the observer will see the expected results. However, the observer's mind seeing one result does not directly affect the distant state - there is just no wave function in which the expected correlations do not exist. The true correlation only happens when he actually goes over to the second detector.
   BULLET::::2. At location A, a Bell measurement of the EPR pair qubit and the qubit to be teleported (the quantum state formula_1) is performed, yielding one of four measurement outcomes, which can be encoded in two classical bits of information. Both qubits at location A are then discarded.
  
  BULLET::::3. Using the classical channel, the two bits are sent from A to B. (This is the only potentially time-consuming step after step 1, due to speed-of-light considerations.)
   The question then becomes one of whether the expected correlations in results will appear: will the two particles behave in accordance with the laws of quantum mechanics? Let us denote by formula_118 the idea that the observer formula_119 (Alice) measures the state of the system formula_120 (Alice's particle).
  
  So, at time formula_43, Alice knows the value of formula_118: the spin of her particle, relative to herself. But, since the particles are in a singlet state, she knows that
   However, the interference pattern can only be seen retroactively once the idler photons have been detected and the experimenter has had information about them available, with the interference pattern being seen when the experimenter looks at particular "subsets" of signal photons that were matched with idlers that went to particular detectors.
   One common method involves Alice not using the noisy channel to transmit source states directly but instead preparing a large number of Bell states, sending half of each Bell pair to Bob. The result from transmission through the noisy channel is to create the mixed entangled state formula_13, so that Alice and Bob end up sharing formula_54 copies of formula_13. Alice and Bob then perform entanglement distillation, producing formula_56 almost perfectly entangled states from the mixed entangled states formula_13 by performing local unitary operations and measurements on the shared entangled pairs, coordinating their actions through classical messages, and sacrificing some of the entangled pairs to increase the purity of the remaining ones. Alice can now prepare an formula_56 qubit state and teleport it to Bob using the formula_56 Bell pairs which they share with high fidelity. What Alice and Bob have then effectively accomplished is having simulated a noiseless quantum channel using a noisy one, with the aid of local actions and classical communication.
   BULLET::::2. The current spin values of both entities originated within a single well-defined quantum event (wave function) at some earlier location in classical space and time.
  
  BULLET::::3. The originating wave function relates the two entities such a way that their net angular momentum must be zero, which in turn means that if and when they are detected experimentally, conservation of angular momentum will require their spins to be in full opposition (antiparallel).
   The total pattern of signal photons at the primary detector never shows interference (see Fig. 5), so "it is not possible to deduce what will happen to the idler photons by observing the signal photons alone". The delayed-choice quantum eraser does not communicate information in a retro-causal manner because it takes another signal, one which must arrive by a process that can go no faster than the speed of light, to sort the superimposed data in the signal photons into four streams that reflect the states of the idler photons at their four distinct detection screens.
   A very common misunderstanding about this experiment is that it may be used to communicate information instantaneously between two detectors. But you must take into consideration the above coincidence detector. The linear polarizer in the top path is effectively filtering out half the entangled photons, and via the coincidence detector, is filtering out the corresponding photons in the bottom path. The coincidence detectors can only communicate classically.
   In this case, the quantum network consists of many short distance links of perhaps tens or hundreds of kilometers. In the simplest case of a single repeater, two pairs of entangled qubits are established: formula_12 and formula_13 located at the sender and the repeater, and a second pair formula_14 and formula_15 located at the repeater and the receiver. These initial entangled qubits can be easily created, for example through parametric down conversion, with one qubit physically transmitted to an adjacent node. At this point, the repeater can perform a bell measurement on the qubits formula_13 and formula_14 thus teleporting the quantum state of formula_13 onto formula_15. This has the effect of "swapping" the entanglement such that formula_12 and formula_15 are now entangled at a distance twice that of the initial entangled pairs. It can be seen that a network of such repeaters can be used linearly or in a hierarchical fashion to establish entanglement over great distances.
   It is one thing to say that physical measurement of the first particle's momentum affects uncertainty in its "own" position, but to say that measuring the first particle's momentum affects the uncertainty in the position of the "other" is another thing altogether. Einstein, Podolsky and Rosen asked how can the second particle "know" to have precisely defined momentum but uncertain position? Since this implies that one particle is communicating with the other instantaneously across space, i.e., faster than light, this is the "paradox".
   Some have interpreted this result to mean that the delayed choice to observe or not observe the path of the idler photon changes the outcome of an event in the past. Note in particular that an interference pattern may only be pulled out for observation "after" the idlers have been detected (i.e., at "D" or "D").
   Identification and reconstruction of trajectories from the digitised output of a modern tracker can, in the simplest cases, in the absence of a magnetic field and absorbing/scattering material, be achieved via straight-line segment fits. A simple helical model, to determine momentum in the presence of a magnetic field, might be sufficient in less simple cases, through to a complete (e.g.) Kalman Filter process, to provide a detailed reconstructed local model throughout the complete track in the most complex cases.
  