Does entanglement always conserve something?

[Swamp Thing]

IIUC, entanglement sometimes plays a role in conserving come quantity like momentum or spin: the quantities measured for two particles must be correlated in order to get a certain total value.

But is this always the case? For example, what, if anything, is conserved in the Hong-Ou-Mandel experiment? Or, what conservation would be violated if one photon was detected at each output (or two electrons at the same output) ?

 

[anuttarasammyak]

Or, what conservation would be violated if one photon was detected at each output (or

Energy and momentum are conserved in the system of photon and detector.

 

[Swamp Thing]

Energy and momentum are conserved in the system of photon and detector.

Specifically in the HOM setup, if two photons enter and end up in different detectors (instead of the same detector), how would energy be violated?

Also, electrons and photons behave in opposite ways in the HOM situation (bunching / antibunching) , so they can't both be conserving momentum / energy ...?

 

[anuttarasammyak]

Specifically in the HOM setup, if two photons enter and end up in different detectors (instead of the same detector), how would energy be violated?

Now you proceed to two photons case. In the system of photons and detectors there are no violations of energy and momentum. Do you have any motivation on pursuiting the violations ?

 

[Vanadium 50]

I think you have it backwards. Momentum (for example) is always conserved, including in entangled systems.

 

[Swamp Thing]

I think you have it backwards.

I guess what I'm getting at is, sometimes conservation laws put constraints on the system that make certain correlations (entanglement) necessary. But sometimes such correlations can arise / exist without the need to comply with any such requirements?

 

[Vanadium 50]

Right, but conservation doesn't cause entanglement. As for detecting entanglement, how would you do this without looking at a conserved quantity?

 

[Demystifier]

Possibly relevant: https://arxiv.org/abs/quant-ph/0607181

 

[pines-demon]

I guess what I'm getting at is, sometimes conservation laws put constraints on the system that make certain correlations (entanglement) necessary. But sometimes such correlations can arise / exist without the need to comply with any such requirements?

Just curious. Would you say that there is a conservation law between the two entangled photons that are produced from entanglement swapping?

 

[DrChinese]

Just curious. Would you say that there is a conservation law between the two entangled photons that are produced from entanglement swapping?

Not an answer to your question, but an interesting fact: those entangled photons need not be of identical wavelength. In fact, you can even use photons to entangle (via swapping) spins of 2 distant electrons. In principle, there is no requirement that the particle types even be the same.

Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km