# What is the difference between entanglement and coherence

It is said that a coherent light beam is described by a single wave because all the individual waves add up in phase to produce a single big wave.

It is also said that entangled light is described by a single wavefunction.
https://qph.is.quoracdn.net/main-qimg-74a1e026576eb278294f9e2ac41996d2?convert_to_webp=true [Broken]

These two descriptions are similar and have been a source of confusion for years for me, even for the teachers at my university. They asked me to find out what the difference between light "described by a single wave" and light "described by a single wavefunction" is.

From the pictures above, I see no difference between coherence and entanglement, so the Internet won't do for explaining the difference to me. Please do so yourself.

Last edited by a moderator:

Related Quantum Physics News on Phys.org
f95toli
Gold Member
First of all, light does not have a wavefunction (there are some ways to formulate the math that will give a you something a bit similar, but it is not a QM wavefunction)
Hence. "Light described by a single wavefunction" has no physical meaning.

Secondly, I am not even sure how the two terms could be confused since they are used in different contexts. "Coherence" is a term that is used for many different systems, not only light, the most obvious example would be a single two-level system which can be coherent or incoherent depending on its dynamics .
Entanglement would be a property of (at least) two connected systems (or perhaps two parameters of a single system).

First of all, light does not have a wavefunction (there are some ways to formulate the math that will give a you something a bit similar, but it is not a QM wavefunction)
Hence. "Light described by a single wavefunction" has no physical meaning.

Secondly, I am not even sure how the two terms could be confused since they are used in different contexts. "Coherence" is a term that is used for many different systems, not only light, the most obvious example would be a single two-level system which can be coherent or incoherent depending on its dynamics .
Entanglement would be a property of (at least) two connected systems (or perhaps two parameters of a single system).
But coherence means constant phase difference. Adding waves with constant phase difference gives a single resultant wave, with higher or lower amplitude.

Therefore, coherent light is described by a single wave. A wave which is a displacement measured in micrometers from the equilibrium position of the electric force.

And entangled photons have the linked quantum state, which means their probabilities of having a state are connected. Wavefunction refers to probability, not to displacement from the equilibrium position of a force.

So entangled photons have linked probabilities and coherent photons have linked displacement vectors.

My question is, why can't coherent photons also considered to have linked quantum states? Doesn't linking displacement vectors also link probability amplitudies?

kith