Quantum entanglement by interference of different sources

We superpose multiple beams of light on a beamsplitter represented by a haf-silvered mirrror with a large surface area in order to entangle them by bringing them to interference. We know that a beamsplitter can entangle photons from different sources by the means of interference because of the experimental work of N. J. Cerf, Gerd Leuchs, E. S. Polzik mentioned in the book „Quantum Information with Continuous Variables of Atoms and Light”. Also we know this from the article on http://www.livescience.com/19975-spooky-quantum-entanglement.html, where Zeilinger told LiveScience that "The way you entangle them is to send them onto a half-silvered mirror. It reflects half of the photons, and transmits half. If you send two photons, one to the right and one to the left, then each of the two photons have forgotten where they come from. They lose their identities and become entangled and from the article on http://www.mpq.mpg.de/4859974/12_07_13 where the setup description says: „ Travelling through separate glass fibres the two photons reach a beam splitter where they are brought to interference. The simultaneous detection of two photons at different output ports of the beam splitter gives notice of successful entanglement”.

We use white light in the experiment instead of monochromatic light because various material particles can be entangled with each other from the distance only by absorbing light at one of their resonant frequencies. White light contains a broad band of  frequencies, from which these particles can „choose” the frequency to absorb.

Various particles at many  sizes have been entangled by various scientists, from rubidium atoms (Julian Hofmann, Michael Krug, Norbert Ortegel, Lea Gérard, Markus Weber, Wenjamin Rosenfeld and Harald Weinfurter, Heralded Entanglement between Widely Separated Atoms, Science, July 6, 2012;  Quantum interference of photon pairs from two remote trapped atomic ions, Letters, June 10, 2007)  to macroscopic objects such as diamonds (Lee, K. C. et al. Entangling Macroscopic Diamonds at Room Temperature. Science 334, 1253- 1256, doi:10.1126/science.1211914 (2011)) or large ensembles of particles such as gaseous clouds of atoms (Deterministic quantum teleportation between dist ant atomic objects, H. Krauter, D. Salart, C. A. Muschik, J. M. Petersen, Heng Shen, T. Fernholz & E. S. Polzik, Nature Physics 9, 400–404, doi:10.1038/nphys2631 (2013); Quantum teleportation between remote atomic-ensemble quantum memories, Xiao-Hui Bao, Xiao-Fan XuChe-Ming Li, Zhen-Sheng Yuan, Chao-Yang Lu and Jian-Wei Pan, arXiv:1211.2892v1 [quant-ph] 13 Nov 2012).

A conclusion to the above mentioned experiments is that both light from many sources which has been interfered on a beamsplitter and light first passed through a beamsplitter and then absorbed by the surrounding material particles are examples of entangled light.

Both light absorbed by particles and light emitted by particles can help entangle these particles from distance as long as the light is superposed at a beamsplitter after its emission or before its absorbtion, respectively.

Thus matter particles can be entangled indirectly by entangling the photons that are emitted or absorbed by them.

Beamsplitters can entangle incident light beams even if they have different frequencies and polarizations as long as the detectors that herald their entangled state are insensitive to these properties, according to the work that the author Alessandro Fedrizzi mentioned in his article, „Entangling Photons with Mismatched Colors” published in the online journal APS Physics.

Before  we let them cross the beamsplitter, we subjected the light beams to spectral separation using a glass prism in order to form coherent monochromatic rays.

The detector we used forms a separate entanglement with each of the incident photons and indirectly, with the material particles that absorb or emit these photons.

These quantum correlations imply entropy transfer from the particles to the detector, so that the particles can negative mutual entropy and the entropy of the entire ensemble of quantum systems is zero.

Absorbtion of entropy from photons also results in the absorbtion of entropy from the material particles that absorb or emit them because these particles are entangled themselves with the photons they absorb or emit.

We reached the conclusion that a detector can absorb entropy from an ensemble of particles by forming a separate entanglement with each one of them from the work of Ken Funo, Yu Watanabe, Masahito Ueda mentioned in the article  „Thermodynamic work from entanglement” published in the online journal APS Physics.

The matter particles to be entangled play the role of detectors because they absorb the light waves and collapse their wavefunction, but in the case of particles emitting the light, artificial detectors must be provided in order to absorb photons emitted by the particles that must be entangled.

We can still entangle light from many sources by using something else than a beamsplitter with large surface area. We use a diffraction grating with large surface area. Light incident on a diffraction grating becomes entangled by interference because it uses the phenomenon of diffraction, of light waves spreading in space when they meet an obstacle or an opening of comparable size to their wavelength.

When the light waves incident on the diffraction grating spread in space, they superpose with each other and undergo constructive and destructive interference, by the means of which they get entangled.

Diffraction gratings can entangle multiple beams of light (https://www.itp.uni-hannover.de/~zawischa/ITP/multibeam.html) and they also spectrally separate them by transmitting or reflecting different wavelengths of light at different angles (http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/grating.html).

Light absorbed   by material particles after it hits the diffraction grating or light hitting the diffraction grating after being emitted by the material particles entangles the material particles from the distance just as in the case of the beamsplitter.