What quantum teleportation actually is the steps to teleport quantum information and actually show you how to write this using open chasm, which is quantum assembly language, so make sure to hit the like button and subscribe if youre new here for more content on quantum tech and coding, Quantum teleportation is a critical concept that takes advantage of the powers of quantum mechanics, its the key behind quantum key distribution and long distance quantum communication and its also used in quantum computing. It allows you to teleport, which means actually move a quantum state from one qubit to another. So why do we need something special to copy quantum information for classical computing? Its pretty easy? We read the bit the zero, the one and we copy it to another place, but we actually cant do that in a quantum system. If we read out a quantum state, the superposition and the entanglement is destroyed and the no cloning theorem says we cant actually copy an unknown quantum state exactly so we have to do something a little bit different quantum teleportation is not actually teleporting or copying information. It means we move the quantum state from one qubit to another, and this actually requires destroying the state of the first qubit, so were not violating the no cloning theorem. Quantum teleportation has actually been successful in the real world, where we can actually teleport over four miles over fiber optics and weve done this experiment in multiple locations. Weve also done this in space over 870 miles in the quantum experiments at space scale, project and, of course, theres always a relevant xkcd for everything, including quantum teleportation.

So first lets go through the steps of quantum teleportation. Quantum teleportation requires three qubits and two classical bits to complete the protocol. Lets say: alice wants a quantum teleport, a qubit to bob who is some distance away. So the first step is to prepare the quantum message in the first qubit q message. So we prepare the quantum state of this qubit and it can be any unknown state, which means we can apply any sequence of x, y and z gates to get any arbitrary state in our circuit. That were writing here. Im going to use the u3 gate, which is a rotation gate, so some quantum frameworks call this the rotation gates? U gates, it really depends but its a gate that rotates the qubit along any of the three axes in whatever angle that you want. While this is not officially part of the quantum teleportation protocol, we do want to have some interesting state here that we can get out at the end. So lets call this qubit the message qubit, the one with the data that we want to send, and this will be the first qubit in our quantum register. Qmessage has some unknown quantum state and thats a state that we actually want to teleport that we created now step two is we want to entangle the two other qubits, the qubit that alice has and the qubit that bob has alice will actually do this. Shell entangle, the two qubits and shell keep one.

This is going to be q alice and the other one shes going to send to bob when we say particles are entangled. What we really mean is that the states of the two are linked or theyre, not separable. That means the state of one qubit cant be described without the state of the other, and this is really a purely quantum phenomena and it doesnt really exist in the classical world, so its almost like information is spread across these particles. So then we write that alice entangles, these cubes by applying first a hadamard gate to queue alice and then a cena gate on queue, alice and cubob, with the queue alice being the control and the kubob being the target, the hadamard gate and the cnod is the Protocol to entangle a pair of qubits, the hadamard gate is a single cubic gate, so it only operates on the one qubit and what it does is it puts a qubit in a superposition, so it has a half probability of collapsing into the zero state and half Probability of collapsing into the one state, the cena gate or the controlled knot gate is a two cubic gate, which means theres a control qubit and a target qubit. This gate performs a not gate on the target qubit. If and only if, the control qubit is in one state and a not gate is a bit flip, which means that the target qubit was in the zero state and it will then become in the one state and vice versa.

So you see here how the states of the cubits depend on each other, and this is how the circuit is going to look like. So now we can send this entangled qubit to bob and by send we mean actually physically transport and remember. This is important. A lot of people have the misconception that quantum communication is faster than speed of light. But when you think of us actually sending the qubit, even if its a photon, its still going to be limited by the classical channels or the fiber optics or the speed of light step, four is to do a bell measurement. Now alice still has q message, which is the original message, and she has q alice, which is one half of the pair of entangled qubits. Then we perform the bell measurement on these two qubits that we have, which is a quantum mechanical measurement that actually determines which of the four bell states these two qubits are in then we apply a c naught gate and thats applied to the qubits q message in Q alice and then a hadamard gate on q message. This c naught unentangles these two qubits. This takes our quantum information and translates it back to classical information thats. What a bell measurement is so, when alice measures, our cubits theres, going to be four possible combinations. Shes going to get 0 0, 0, 1, 1, 0 or 1 1.. Those are the bell states alice sends this information to bob as well and thats transferred over those two classical qubits that i talked about.

The result from the q message is the first bit and the result from q alice is the second bit and again. This is why its not faster than the speed of light. Of course, when you measure two entangled states, we always say that they collapse right, but we dont know how to interpret the measurement and their correlations until we get this classical information from alice and it doesnt matter. If she actually sends that data or calls bob or anything its still limited, because we need that classical information in the next steps, so the next step is to recreate the quantum state after the measurement, depending on what bob receives, he does some operations to his qubit. If the first qubit that bob receives is a 1, then he applies a z gate. If the second cubit here receives is a 1, he applies an x gate, which means, if alice, transmits, 0 0 bob does nothing to his cubit. If she transmits 0 1. He only applies the x gate if she transmits one zero. He only applies the z gate and applies both gates if she sends one one and now bob has a cubit with the original state that alices qubit had congratulations. Youve now teleported an unknown quantum state, but why does this actually work? This works because the state of alices, qubit and bobs cubit actually depend on each other. Lets. Look at the full circuit here. Q0 is the queue message with the unknown quantum state q1.

Is q, alice and q2 is cubob? The classical information we receive from alice tells bob how the state of his qubit actually differs from alices, and that tells us what gates we need to apply to to get back to the original state. Really, the key to understanding the circuit is epr pairs. The epr pair is a key concept in quantum computing and it tells us how measurements are correlated. The correlation between these pairs means that the results will always be equal if one is a zero. The other is zero if one is a one. The other is also a one. However, the key here is and why its confusing and why we have to apply gates, is that they have to be in the same basis. A base of state is just the components of how we can measure any state in the system using these two components, so you can create any combination of these two to get to any point in the vector space. So if we have these two vectors thats one basis set, these are just different vectors that are transformed by the hadamard gate, but we can still actually use them to describe where a state is in the vector space, just in slightly different terms. Thats. What alices classical information send actually tells us? It tells us how we need to change our basis state to get back to the one where theyre perfectly correlated. We need to make sure that this cube bob gets back into the right basis, state and then theyre perfectly correlated, which means that q message and q bob are going to be the same.

The first two qubits, the q message and q alice are now discarded. So this does not violate no cloning theorem, because the q message state has now collapsed and weve transferred that unknown quantum state into cuba now go ahead and do it yourself try using open chasm? You can do this in q sharp. You can do this in circ.