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There is a dispute on PhysicsForums related to what are the conditions necessary for two photons to be entangled by a beam splitter. Lots of references given by the forum users but they never arrive at the same conclusions. https://www.physicsforums.com/threads/quantum-entanglement-by-the-means-of-beam-splitters.852464/

Must they already be part of entangled pairs and does the beam splitter just swap the entanglement between the members of the different pairs? Can the beam splitter be used alone to entangle photons or can it entangle them only in the presence of many other elements like polarizers, wave plates, prisms, dichroic mirrors? Can the input photons be distinguishable or must they always be indistinguishable?

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The articles by Chris Monroe describe the following situations: (1) use of an already entangled pair of photons to transfer the entanglement, resulting in ion-ion entanglement; (2) interference of photons from independent sources, A, B, not previously entangled, such that no experiment can determine from which source a particular photon originated.

Method (2) typically relies on a beam splitter; Quantum interference of photon pairs from two remote trapped atomic ions shows this clearly, with the photons from the two independent sources being mixed together at the first beamsplitter, labeled BS.

The entanglement depends on lack of which-way information. The degree of entanglement acquired in this fashion may be less than that of down-converted photon pairs. Coincidence detection is required to keep members of a given pair temporally together.

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  • $\begingroup$ Finally someone that I agree with. $\endgroup$ – Quantum Journalist Apr 30 '16 at 4:50
  • $\begingroup$ @QuantumJournalist: The goal is to provide a clear and correct answer to the question; if this one is satisfactory, then you should return to the answers provided in the original forum, and test them against this one; then test this one against several of the papers. Report back with any discrepancies, and I'll attempt to clarify. I assume your goal is to understand this well enough to write your article. If desired, I can add some of the mathematical structure, etc. $\endgroup$ – Peter Diehr Apr 30 '16 at 20:02
  • $\begingroup$ It is not only the interference that makes two objects entangled, the detectors project the interfered photons into an entangled state. The whole Bell state measurement setup is needed, also for projecting into symmetric entangled states you need to use a polarizing beam splitter too. $\endgroup$ – Quantum Journalist May 1 '16 at 5:39
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The process of ensuring that two photons arrive at a beamsplitter at the same time, with frequency and polarization similar enough that they emerge from the beamsplitter with their origins impossible to determine, ensures that the photons are already entangled. An example: phase-lock two lasers, and it's possible to make a hologram using the beam from one laser as a reference beam and the beam from the other laser as an object beam. Of course, it's possible to detect the photons upstream from the beamsplitter and know their origins, but that destroys the entanglement just as detecting photons at the slits in a double-slit interferometer destroys the interference.

I don't know if the single-photon version of the experiment has been done, but it should be possible to attenuate the beams enough to ensure single-photon detection events, and obtain the same result. In this case, the fact that the two lasers are phase-locked establishes a very strong correlation between the states of the photons emitted by the two lasers. Perhaps it's not entanglement in the usual sense, but it is surely a form of entanglement.

Edit April 20, 2019: Anything that is done to ensure simultaneous arrival of photons at a beamsplitter, whether at the source (e.g., simultaneous production of the photons via a pulsed laser as in the referenced paper ) or at the detector (e.g., only paying attention to simultaneous detections), is a source of entanglement.

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