# Particle/antiparticle annihilation and entanglement

This is a basic question. Suppose that A and B are completely entangled particles and so are C and D. If B and C are antiparticles that annihilate each other will A and D be entangled as a result. It seems they should be in order to satisfy conservation laws. Also if the initial pairs were the results of pair creation events then the Feynman diagram of the entire can also be interpreted as a single particle starting as A emitting and absorbing photons and emerging as D.

More generally if the state of the 4 particle system just before annihilation was represented as $$\alpha_{ij}\, |A_i\rangle\, |B_j\rangle\; \beta_{kl}\, |C_k\rangle\, |D_l\rangle$$ would the state of A and D just the after the B-C annihilation be $$\sum_j\alpha_{ij}\beta_{jk}\,|A_i\rangle\, |D_k\rangle$$ in a product state with the state of the emitted photons.

Is this correct?

• What conservation law are you thinking about when you say A and D will now be entangled?
– BMS
Mar 9 '14 at 21:02
• If A and B are entangled in a way that the sum of say their momenta has a definite value and so are C and D, then afterwards A and D (and the emitted photon?) should be entangled such that the total sum of momenta has a definite value equal to the sum of the definite momenta of the initial pairs. Mar 9 '14 at 21:18