Short answer: Hyperentanglement means a photon pair is entangled in more than one property at once, such as polarization, spatial mode and time-energy. Three experiments cover the first demonstration in 2005, entanglement of two photons differing by 600 quanta of orbital angular momentum in 2012, and a narrow-band polarization and OAM source made from cold atoms in 2019. All are laboratory demonstrations.
What is hyperentanglement?
The 2005 Physical Review Letters abstract reports what the authors call the first quantum system entangled in every degree of freedom. They use pairs of photons from spontaneous parametric down-conversion and verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode and time-energy. They also produce and characterise maximally hyperentangled states, and novel states that show both quantum and classical correlations at once. They report tomography of a 2 x 2 x 3 x 3 system, which has a 36-dimensional Hilbert space, and say they believe it is the first photonic entangled system of this size to be characterised in this way.
What did the 2012 OAM experiment show?
The Science abstract explains that single photons with helical phase structures can carry a quantized amount of orbital angular momentum (OAM). Because there is no theoretical upper limit on the number of OAM quanta a photon can carry, the authors say entanglement between two particles with an arbitrarily large difference in quantum number is possible in principle. By transferring polarization entanglement to OAM with an interferometric scheme, they generate and verify entanglement between two photons differing by 600 in quantum number, and say the only restrictions on higher numbers are current technical limitations. They also demonstrate experimentally that entanglement of very high OAM can improve the sensitivity of angular resolution in remote sensing. That last claim is theirs, from a laboratory demonstration.
What did the 2019 cold-atom source show?
The 2019 Physical Review Letters abstract notes that quantum repeaters and quantum memory often impose a strict bandwidth requirement on entangled photons, while there is increasing demand for entangling more degrees of freedom. The authors report direct generation of narrow-band OAM and polarization hyperentangled photons from cold atoms. The narrow-band pair is naturally entangled in polarization and OAM, in addition to time-frequency, because of spin and orbital angular momentum conservation in spontaneous four-wave mixing in a cold atom ensemble. They say the source is expected to play important roles in quantum-memory-based long-distance quantum communication, which is their expectation.
Why does the number of degrees of freedom matter?
Each extra degree of freedom multiplies the size of the shared state space. The 2005 paper's 36-dimensional example comes from combining 2, 2, 3 and 3 levels across its characterised degrees of freedom. The 2012 abstract points to a different use, higher OAM quantum numbers, which the authors link to finer angular resolution. The 2019 abstract points to a third: sources narrow enough in bandwidth to match quantum memory. None of the abstracts claims a communication or sensing system built from these sources, so those remain stated motivations.
How to read this
The three papers use different sources, down-conversion crystals in 2005 and 2012 and cold atoms in 2019, so they illustrate a progression of techniques and not one measured trend. A 36-dimensional system is the authors' count of the combined Hilbert space. The post is based on abstracts and visible page text, and full texts were not checked. It makes no claim about products or networks in use.
FAQ
What degrees of freedom were entangled in 2005?
Polarization, spatial mode and time-energy.
How large an OAM difference was entangled?
600 quanta, in the 2012 Science paper.
Why use cold atoms?
The 2019 authors say narrow-band photons suit quantum repeaters and memory.
Can OAM entanglement help sensing?
The 2012 authors report it improved angular-resolution sensitivity in a demonstration of remote sensing.
All field notes