# One More Note on Quantum Teleportation

Yesterday, I posted a detailed explanation of the technique of quantum teleportation and hopefully demonstrated that the process is not as complicated as one might expect! And also that it is not going to lead to Star Trek transporters anytime soon. No, unfortunately, we will have to settle for a mere quantum Internet instead.

But even that technology has its hurdles to overcome, one being the problem of transporting an entangled qubit to the destination you would like to send your message. As those who have been following along all know, entanglement is a quantum state. Quantum states, it turns out, can be quite fickle; they are very easy to disrupt! In previous posts, I have loosely (and carelessly) thrown around the concept of collapsing a wave function. (I am fairly confident that I linked to the Wikipedia article on wave function collapse somewhere, but alas I cannot find it!) What that expression means is that if you have a quantum object whose wave function is a superposition (read: combination) of different states, whenever that object is "observed," its wave function collapses down to one of the possible states. From that point on, any other time the object is measured, the probability of finding it in that one state is $$100\%$$—in other words, it's the only state possible until the object's wave function changes again.

As an example, think back to our quantum playing cards, which are described by the wave function$$\lvert \psi \rangle = \frac{1}{\sqrt{2}} \left( \lvert \spadesuit \rangle + \lvert \diamondsuit \rangle \right) \label{040817:qpc}$$as long as they are face down. At the instant the card is turned face up, its wave function collapses to either\begin{equation*} \lvert \psi \rangle = \lvert \spadesuit \rangle, \label{270717:qpcs} \end{equation*}or\begin{equation*} \lvert \psi \rangle = \lvert \diamondsuit \rangle. \label{270717:qpcd} \end{equation*}So long as the card remains face-up, its wave function continues to be one of those two options, and the card's value does not change. Only when the card is turned face down is its wave function reset to the original state. (Note: there is nothing in quantum mechanics which says the card's wave function must reset when it is turned face down; that's simply the way I programmed it for the sake of demonstration.)

Now, this fact seems to imply that there is something special about "observers" in quantum mechanics, and much ink is spilled by nonexperts who take that expression and run with it off into the realm of nonsense. However, in physics, an "observer" is anything that interacts with that quantum object, including other objects. Say our object is a sub-atomic particle, and it collides with another particle. That interaction can change our particle's wave function. If our particle is in an entangled state and it collides with another particle, the collapse of our particle's wave function destroys its entanglement. If our particle is no longer entangled, then we cannot use it to teleport a qubit! Needless to say, we do not want this to happen, and the best way to prevent it is by isolating our particle from all others.

However, we then run into the problem that everything in the Universe is made out of particles! The wires or optical fibers that we might use to relocate our entangled qubits? Those are made out of particles, and when our qubits collide with these particles, their wave functions collapse and we lose entanglement. What if we shoot our entangled particles through the air? Well, that too is made out of particles, and colliding with any of them destroys our entanglement! In fact, to minimize the risk of collisions, we must send our entangled particles through a vacuum, and no turbomolecular pump in the world can pull a stronger vacuum than that which exists naturally in outer space! Therefore, space is a natural setting in which to place the infrastructure of a quantum Internet, but even that will do us no good if we cannot access it from the surface of Earth.

Therein lies the true significance of the Chinese team's experiment. They are not testing whether or not quantum teleportation is possible, as it has been done many times before. They are setting a new distance record, but so far that has only been limited by how far one can separate one's particles before losing entanglement—in a pure vacuum, this distance is infinite. Instead, the significant result here is the uplink between an entangled particle on the ground and one in orbit, which allows a qubit to be sent to an environment in which it can easily be transferred around the world. One of the more technically challenging aspects of this procedure is that it requires incredibly precise aim. Teleporting qubits between entangled particles in different locations? That's easy! Getting one of those particles to its desired location on board a satellite traveling thousands of miles per hour hundreds of miles overhead? Now, that is hard! Here is how they pulled it off with lasers, telescopes, and fast steerable mirrors:

Figure $$(1)$$: A schematic of the experimental apparatus taken from the team's paper. (Click to enlarge.)

The ground station for this experiment is an astronomical observatory located in Ngari, Tibet at an altitude of $$5100 \, \mathrm{m}$$, already well above much of Earth's atmosphere. The satellite receiver is called Micius, and its orbit is about $$500 \, \mathrm{km}$$ above Earth's surface. Micius' orbit is also what is called "sun-synchronous," meaning that the satellite passes over a given point on the Earth at the same time every day; in this case, midnight. Both the observatory and the satellite are equipped with reflecting telescopes with gimbaled mirrors, thus allowing the two telescopes to aim at each other as the satellite flies over Tibet. Additionally, the light passing through each telescope reflects off of one or more "faster-steering mirrors" (FSM), which allows for even more precise aiming. The aim is so precise, in fact, that the system can overcome the atmospheric turbulence that alters the path of light near Earth's surface! This turbulence is what causes stars to twinkle, and the twinkling of starlight was therefore observed and coupled into the system to help it correct for these atmospheric conditions. To lock on to each other, the observatory and the satellite exchanged laser pulses through their telescopes. Thus, the accuracy and precision needed to send and receive entangled photons was established.

Over the course of thirty-two midnights, for the three hundred and fifty seconds throughout which Micius was visible from Ngari, the apparatus diagramed in figure $$(1)$$ generated entangled photon pairs and shined one of them, photon $$3$$, at the satellite. The other photon, $$2$$, was then entangled with yet another photon, $$1$$, whose state was to be teleported. In each event, one of six different quantum states was teleported, combinations of the perpendicular linear photon polarization states; horizontal, $$\lvert H \rangle$$, and vertical, $$\lvert V \rangle$$ (basically, $$\vert 0 \rangle$$ and $$\vert 1 \rangle$$ for photons.):
\lvert \psi \rangle_1 = \begin{cases}
\lvert H \rangle_1 & \text{Horizontal Linear Polarization}, \\[2ex]
\lvert V \rangle_1 & \text{Vertical Linear Polarization}, \\[2ex]
\lvert + \rangle_1 = \frac{1}{\sqrt{2}} \left( \lvert H \rangle_1 + \lvert V \rangle_1 \right) & \text{Symmetric Superposition}, \\[2ex]
\lvert - \rangle_1 = \frac{1}{\sqrt{2}} \left( \lvert H \rangle_1 - \lvert V \rangle_1 \right) & \text{Antisymmetric Superposition}, \\[2ex]
\lvert R \rangle_1 = \frac{1}{\sqrt{2}} \left( \lvert H \rangle_1 + i \lvert V \rangle_1 \right) & \text{Right-Handed Circular Polarization}, \\[2ex]
\lvert L \rangle_1 = \frac{1}{\sqrt{2}} \left( \lvert H \rangle_1 - i \lvert V \rangle_1 \right) & \text{Left-Handed Circular Polarization}. \\[2ex]
\end{cases} \label{080417psi1}
Data collection was triggered by the detection of a fourth photon that was split off from photon $$1$$ prior to its entanglement with photon $$2$$. The entangled Bell state of photons $$1$$ and $$2$$ was then measured on the ground to commence teleportation while Micius caught photon $$3$$ and measured its state to see whether or not it matched the original state of photon $$1$$. The closeness of the match was quantified with a "fidelity" value that ranges between $$0$$ and $$1$$. It can be shown that in a world without quantum entanglement and teleportation, this value cannot be greater than $$2/3$$. Therefore, if a greater fidelity is achieved, then entanglement and teleportation must be in play. In all, data was captured for $$911$$ four-photon events, and the observered fidelities for each quantum state are shown in figure $$(2)$$:

Figure $$(2)$$: Experimental results from the team's paper. The dashed line represents the maximum fidelity without quantum entanglement and teleportation. The error bars represent one standard deviation calculated from the raw detection events. Fidelities are well above the $$2/3$$ limit for all quantum states.

Overall, an average fidelity of $$0.80 \pm 0.01$$ was obtained, which again is well above what one would expect in the absence of entanglement and teleportation. To quote the last line of the team's abstract,

Therefore, even though we are not going to have Star Trek style transporters anytime soon, and sensationalist headlines completely missed the point, we still have much about which to get excited!

So there you have it—live long and prosper, my friends.

🖖 Aaron

P.S. Click the "source" link below to read the original paper. It's interesting stuff, I promise!