Can a photon be quantum entangled on more than one property/factor?

[San K]

can a particle/photon be quantum entangled on more than one property/factor?
(at the same time-- redundant phrase(?))

for example can two photons be entangled along say -

a) spin AND momentum

b) position and momentum

c) spin and position

d) polarization and spin

 

[StevieTNZ]

position and momentum: yes. That's all I know.

 

[DrChinese]

can a particle/photon be quantum entangled on more than one property/factor?
(at the same time-- redundant phrase(?))

for example can two photons be entangled along say -

a) spin AND momentum

b) position and momentum

c) spin and position

d) polarization and spin

Good question!

Absolutely, and usually they are as a matter of fact. Their observables which are "canonical conjugates" will be entangled, for example, photons created by Type II PDC crystals. Keep in mind that there are all kinds of setups so this is just a statement regarding the general case.

However, spin and position are not conjugates. Spin and polarization are essentially the same thing for photons. Usually spin has several degrees of freedom which are conjugates.

 

[lugita15]

Yes, particles can be entangled with respect to any two (or more) observables. Being entangled with respect to one observable does not prevent being entangled with respect to another. However, NOT being entangled with respect to one observable might prevent being entangled with respect to another observable, as in the case of position and momentum.

 

[San K]

thanks DrChinese, Lugita, Stevie. great information.

However, NOT being entangled with respect to one observable might prevent being entangled with respect to another observable, as in the case of position and momentum.

interesting...how conjugates work

this is stretching it a bit far however --- position is more like space, momentum/velocity like time
wonder if space and time are conjugates?

another quick question:

can quantum entanglement happen, or be-created, between particles that travel much slower than the speed of light?

one keeps reading that entanglement has been demonstrated for in various scenarios beyond our basic particles like photon/electron...

for example ...read somewhere that you could make frequency between two forks entangled...not sure how authentic that information is

 

[lugita15]

this is stretching it a bit far however --- position is more like space, momentum/velocity like time
wonder if space and time are conjugates?

No, position and momentum are conjugates, while time and energy are conjugate. (It should be noted that in nonrelativistic QM we don't usually treat time as an observable, but in relativistic QM the position 4-vector which consists of time and spatial position is conjugate to the energy-momentum 4-vector).

can quantum entanglement happen, or be-created, between particles that travel much slower than the speed of light?

Yes, there's no restriction on how fast or slow they have to be. Quantum entanglement is perfectly well described by non-relativistic QM.

for example ...read somewhere that you could make frequency between two forks entangled...not sure how authentic that information is

That's resonance.