# Researchers demonstrated violation of Bell's inequality on frequency-bin entangled photon pairs

Quantum entanglement, one of the most intriguing features of multi-particle quantum systems, has become a fundamental building block in both quantum information processing and quantum computation. If two particles are entangled, no matter how far away they are separated, quantum mechanics predicts that measurement of one particle leads to instantaneous wave-function collapse of the other particle.

Such "spooky action at a distance" is non-intuitive, and in 1935, Einstein attempted to use entanglement to criticize quantum mechanics to suggest that the quantum description of physical reality is incomplete. Einstein believed that no information could travel faster than light, and suggested that there might be some local hidden variable theories that could explain the world in a deterministic way, if and only if they obey realism and locality. In 1964, J. S. Bell showed that the debate can be experimentally resolved by testing an inequality; by measuring correlations between entangled parties, the result calculated from local hidden variable theories should be constrained by the Bell inequality, which, on the other hand, can be violated in the predictions of quantum mechanics.

By reducing the velocity of light dramatically, researchers at the Hong Kong University of Science and Technology implemented a Bell Test and were able to generate frequency-bin entangled narrowband biphotons from spontaneous four-wave mixing (SFWM) in cold atoms with a double-path configuration, where the phase difference between the two spatial paths can be controlled independently and nonlocally.

Their findings were published in the journal *Optica* on April 15, 2017.

"We tested the CHSH Bell inequality and registered |S|=2.52±0.48|S|=2.52±0.48, which violates the Bell inequality |S|≤2," said Shengwang Du, professor of Physics at HKUST and the leader of the research team. "We have unambiguously demonstrated the generation of frequency-bin entangled narrowband (about 1 MHz) biphotons, which can efficiently interact with stationary atomic quantum nodes in an atom-photon quantum network. Because of their narrow bandwidth, these biphotons can be stored and retrieved from a quantum memory with high efficiency."

"Our result, for the first time, tests the Bell inequality in a nonlocal temporal correlation of frequency-bin entangled narrowband biphotons with time-resolved detection," said Xianxin Guo, a co-author of the paper. "This will have applications in quantum information processing involving time-frequency entanglement."

The study revealed temporal details that agree well with theory calculations based on quantum mechanics, and implies the possibility of encoding and decoding qubit information in the time domain.

"Our narrowband frequency-bin entangled biphoton source in this work can be ideally implemented to produce pure heralded single photons in a two-color qubit state with a tunable phase, making use of entanglement, linear optics, and time-resolved detection," said Guo.

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**More information:**Xianxin Guo et al, Testing the Bell inequality on frequency-bin entangled photon pairs using time-resolved detection,

*Optica*(2017). DOI: 10.1364/OPTICA.4.000388

**Citation**: Researchers demonstrated violation of Bell's inequality on frequency-bin entangled photon pairs (2017, May 8) retrieved 24 July 2019 from https://phys.org/news/2017-05-violation-bell-inequality-frequency-bin-entangled.html

## User comments

AmritSorliAmritSorliDa SchneibRyan1981For me this is too complex a description to understand what is going on.

antialias_physorgI have the same problem. Looking around the nety I'll try to give what I found. Maybe DaSchneib can correct me on the points that I misrepresent:

1) Biphotons

A 'biphoton' are two photons that are entangled.

2) Frequency entanglement:

Entanglement can be had from many properties. The one most are 'familiar' with is probably polarization, but you can entangle spin, position, momentum....

A 'frequency entanglement' happens when you take a very narrowband source (e.g. a monochromatic pump laser) and create two entangled photons from one 'pump' photon. This gives you two photons where the SUM of the frequencies is well defined (ferquency is directly related to energy of a photon - and you know the energy of the initial photon), but the frequencies of EACH ONE is uncertain.

The frequencies of the two photons are entangled (measure one and you know the other).

antialias_physorgThis is a function of the detectors. The detectors can detect photons in a certain energy range - not exact energies. If two photons are within the energy range of a detector then they are said to lie in the same 'bin'. If they are in the same bin then they are not distinguishable. (If they come to lie in different bins then they are distinguishable)

4) Four wave mixing:

In some non-linear materials you can augment the frequency of n-1 wavelengths (photons) when you input n wavelengths (photons). In this case - since they are creating photon pairs - The input should be three photons and you get two up-converted, entangled photons (not tooooo sure if I interpret this correctly)

How exactly the rest tests for Bell inequality I haven't figured yout yet. Maybe tomorrow.

Seeker2Position only for bosons only, obviously? Would there be a restriction on the phase angles of the two entangled photons?

antialias_physorgI guess you could position-entangle fermions (like electrons), too. However the associated frequency would be very high because the wavelike properties are described by lambda = h / p

where lambda is the frequency, h is the planck number and p is the momentum. Since the momentum of an electron is far greater than that of your run-of-the-mill photon you get a very short effective wavelength.

https://en.wikipe...ter_wave

Reminds me of a question on a physics test in school: Teacher with mass 80kg walks into the room through a 80cm slit (door) at 6km/h: calculate his diffraction pattern.

If the only condition of these is 'monochromatic' then there is no restriction on phase. If they are monochromatic and phase correlated then there *might* be a restriction on phase - but that also depends on the material used for the up-conversion

Da SchneibjohnqsmithI appreciate the efforts by antialias and others to help, and I could understand their translations.

In the article it states: "In 1964, J. S. Bell showed that the debate can be experimentally resolved by testing an inequality; by measuring correlations between entangled parties, the result calculated from local hidden variable theories should be constrained by the Bell inequality, which, on the other hand, can be violated in the predictions of quantum mechanics."

What does this mean, please? to a non-professional.

Seeker2Da SchneibDa SchneibThe details are rather complex; I can gather them and comment if you're really interested. It's a good question, so I gave you a 5.

Da SchneibIncidentally, this paper is open access from the journal of record, and everyone should go read it. This is an important result, extending entanglement from the discrete to the continuous realm. Not unexpected; but this is another of those experiments that's important because we didn't discover anything new.

Seeker2Da SchneibSeeker2imagephysics.stackexchange.com/a/171607/75518

Seeker2Da SchneibGood question. Unfortunately without a theory of quantum gravity we can't tell.

Da SchneibSeeker2DingboneDa SchneibSeeker2Da SchneibjohnqsmithSeeker2Da Schneib"Locality" means that local effects have local causes. "Realism" means that even though we cannot measure some parameters due to Heisenberg uncertainty, they still have exact values.

Bell's Theorem is a provable theorem of mathematics that shows that if both locality and realism are true, then measurements of Heisenberg uncertain parameters should obey a certain rule that limits their correlation to a value of 2; but if one or the other fails, then their correlations should obey rules of quantum mechanics, which make the correlation greater than 2.

Experiments, called "Bell Test experiments," have all shown correlation values greater than 2. Experiment, as always, trumps theory; any hypothesis that doesn't predict a value greater than 2 for the correlation is therefore untenable.

[contd]

Da SchneibClassical physics predicts a value of 2. Therefore, classical physics does not correctly predict quantum physics. Note that this does not mean quantum physics does not correctly predict classical physics. This is because in the limits of size and time, the value approaches 2. For further details, you should examine the proof of the Fluctuation Theorem, and experimental results pertaining to it.

I will not restate Greene's discussion here; I recommend you read the book. Note carefully that Bell's Theorem is a provable (and proven) theorem of mathematics; this is not a physical theory subject to possible future disproof.

Da SchneibSeeker2johnqsmithDa SchneibSeeker2Seeker2Please sign in to add a comment. Registration is free, and takes less than a minute. Read more