# Can momentum be transmitted by using quantum teleportation?

I have read that you can use quantum teleportation to transmit states from one place to another.

If you have two entangled systems A and B you can measure the A system in such a way that measuring the B system will give you correlated measurements. For example measuring spin up on one photon of an entangled pair implies you will measure spin down on the other one. Can this be made with momentum?

If I understand correctly entanglement happens because of conservation laws. When two systems become entangled some properties (like spin) become entangled or "undetermined" until the moment you interact with some part of the system at which point the measurement gives you a concrete but random answer for that subsystem alone which automatically fixes any measurement outcome for the other subsystem in order to maintain the conservation law.

Since momentum is a conserved quantity I though perhaps this could also be done with momentum.

Could this be used to transfer momentum from one place to another? If it can be done then you could make a rocket engine where the propellant and the engine itself are located on earth and the rest of the ship on space. Of course you would need a classical communication channel between the two parts.

Thanks.

• The answer is probably yes (to the teleportation of momentum, not the rocket thing). Teleporting states works with any state, you could have two system with defined momentum states that you could exchange. The real question is how feasible is that in practice. Commented Sep 14, 2020 at 17:10

Could this be used to transfer momentum from one place to another?

Quantum teleportation transfers information about spins, not the spins themselves.

Quantum teleportation is a process in which quantum information (e.g. the exact state of an atom or photon) can be transmitted (exactly, in principle) from one location to another, with the help of classical communication and previously shared quantum entanglement between the sending and receiving location.

italics mine

You are correct that the laws of conservation of momentum and energy can be used to transfer information, similar to conservation of angular momentum (for transfering information about spins). For example a pi0 particle has definite energy/momentum when it decays into two photons. If you measure the photon on the earth you know (information) the energy and momentum of the photon going to the moon and measured at the moon.

It is not transfer of momentum , quantum teleportation cannot be used the way you envisage.

• Please correct me if I'm wrong, If you entangle two particles and then separate them, their spin will be undetermined until you interact with any of the particles, at that point you are effectively creating a physical change on the other particle, since the conservation law forces a predictable and anticorrelated outcome on the measurement of the other particle. Momentum and energy would be conserved globally on any similar experiment. Could you interact in some way with particle A, so that the final outcome would make it move forward, while B moves on the opposite direction? Commented Sep 16, 2020 at 12:11
• That would allow you to use B as a reaction mass, even if it isn't located in your spaceship and locally it would look like a reactionless engine, but not globally of course. You wouldn't need teleportation I guess, because you don't care about the direction of the particles on side B of the experiment, you would just need entanglement. I'm sure this can't be done btw.. I just want to understand why it can't be done. Commented Sep 16, 2020 at 12:13
• You can create a situation of entanglement, but that is it. If you interact with any of the paraticles the entanglement ends. If you measure one then you have information about the other from conservations laws there is no transfere,it is all in your head,you lab notes. There is no forcing, just mathematics. If you know twins, alex and john, and are told one works in New York and the other in Calciuta, if you meet john in calcuta, you know alex is in new york. It is information that exists that is evaluated in your head. similar to entanglement. Commented Sep 16, 2020 at 12:54