# Micius and the Journey of Spaceborne Entangled Photons

November 1, 2017

Recently, scientists measured entangled photon pairs that were created on a satellite and traveled two separate paths to different ground stations on Earth—1200 km apart—where they were measured. This is the longest journey and the largest separation of entangled photons ever measured! But what does entanglement mean, in a physical sense, and what does this exciting result mean for us?

## Quantum States

Quantum systems are defined by a mathematical function called a wave function, which describes the state of a particle and is related to the probability of measuring something like that particle’s position. It is statistical in nature: the wave function’s value is related to the probability of finding the particle in a given state at a given time.

Schrödinger’s cat is often used as a common example of a wave function that has a superposition of states. Imagine Schrödinger’s cat placed in a closed box, with a toxic substance in a breakable container within the box. A radioactive material, also in the box, acts as a "switch"; If the radioactive substance decays, it will trigger the release of a hammer that will fall and break open the container of poison, killing the cat.

Figure 1: The wave function (equation of state) of Schrödinger’s cat would be described as a superposition of states between dead and alive, but once the box is opened, the measurement causes the cat to be forced into one state or the other. Image Credit: wiki user Dhatfield, via Wikimedia Commons

The state of the cat, before opening the box, must be described by the probability of the cat being alive, and the probability of the cat being dead. In other words the cat’s equation of state would be alive and dead simultaneously. This is known as a superposition of states.

The most common and accepted interpretation of measurement in quantum mechanics is the Copenhagen Interpretation–that the act of measurement collapses the wave function to a single, real state. Hopefully, in the case of the cat, it is still alive—but there is no way to know the state before the measurement.

The Copenhagen interpretation has not failed yet in terms of its description of the universe, but it is disconcerting to many. It means that the cat must be described as both alive and dead simultaneously, which goes against most people’s intuitions—Schrödinger himself designed the thought experiment to demonstrate the intuitive “unfriendliness” of the Copenhagen interpretation.

## Quantum Communication

The recent experiment by scientists using the Micius satellite, a spacecraft designed for quantum communications experiments, is a big step forward toward quantum communications and has placed a feather in the cap of quantum mechanics.

The experiment achieved three milestones: It showed that satellite-based quantum communication is possible, it measured entangled photons separated over the longest distance ever, and it provided more evidence that quantum entanglement is governed by “spooky action at a distance” (more on this below).

One of the important features of using quantum mechanics for communications is privacy. If you want to send a private message, the most common way to do it is to write the message in code, and send the person receiving the message the key to the code. One problem with this method is that if the message or key were intercepted and read before being sent to the intended recipient, no one would ever know. With quantum communications, keys are still needed and interception of keys or messages can still occur, but if a key is looked at, everyone knows. Quantum communication utilizes entangled states, and the mere act of trying to measure an entangled quantum state alters it, making any covert attempt to read the message or key impossible.

There’s also a rule in quantum mechanics that a state cannot be “cloned”. One might be able to duplicate a single state, but not a superposition of states, so the message, if read, cannot be reproduced—providing no covert way to read a message or key.

## Micius' Entangled States

On the Micius satellite, a satellite dedicated to studying space-based quantum communications, entangled photons (packets of electromagnetic radiation) are created by taking laser light and sending it two different ways through a special crystal that converts a single laser photon to two photons, each with twice the wavelength (half the energy), but one with vertical polarization and one with horizontal polarization. Polarization is the direction of the electric field. This entangled pair has a wave function that the scientists write as:1

The wave function shows the superposition of the possibilities that the first photon has horizontal polarization and the second has vertical polarization, and the possibility that the first photon has vertical polarization and the second has horizontal polarization. The photons are indistinguishable, so there is no way to know which is which. Further, the two photons were created together by a common causal event, so they are correlated due to this common cause—they are entangled. The wave function is in a superposition of states that is not separable; it is an entangled state.>/p>

This pair of photons was created obeying all the laws of physics, such as conservation of energy and conservation of momentum. These physical laws are the reason why there must be a vertical and horizontal polarization state between the two photons, but without measurement there is no way to know which photon is in which state, and so before a measurement is made we must consider each photon to have the possibility of both states, as is shown by the wave function that was described above.

## Spooky Action at a Distance and Local Hidden Variables

Recall the Copenhagen interpretation of quantum mechanics—that the particle is not in a specific state until a measurement is made. This implies that when you measure an entangled pair of photons, if you measure one photon with vertical polarization, you immediately know that the other photon, if measured, would be in the horizontal state, because they were created together so they have a common cause, and together they obey the conservation rules of physics.

But what if the entangled particles traveled two light years apart, without ever interacting with anything else, and then a measurement was made? If the state is unknown before measurement, then both photons are in a superposition state of up and down, and entangled. If a measurement is made on one photon and it is found to be in the vertical polarization state, then the other photon is measured in the horizontal polarization state satisfying the conservation rules. Does this mean the information from the first measurement would have to travel faster than the speed of light? According to Einstein’s theories of relativity, nothing can travel faster than the speed of light.

Three scientists, Einstein, Podolsky, and Rosen (EPR) were so discomfited by this, but understood that quantum mechanics was a good theory, that they proposed “local hidden variables.” These hidden variables represented something we did not know yet, and, if we could figure them out, they would explain this “spooky action at a distance,” and resolve the apparent paradox.

Shortly thereafter, the physicist J. S. Bell presented a beautiful calculation showing that if there are local hidden variables, an inequality relating the average measured values of the product of the two measured states must hold true. He showed this by presenting an argument with an entangled pair similar to the entangled pair of photons created on Micius. Bell's thought experiment considered detectors that would measure the entangled property, such as the polarization, and utilize the fact that it was 100% sure that if detector 1 was measuring only horizontal polarization, and detector 2 was measuring only vertical polarization, then with certainty the probability of measuring a horizontal polarization in detector 1 would result with a vertical measurement in detector 2, as expected. But what if the detectors were not set this way? What if detector 1 remained in the horizontal position, but detector 2 was selected at random orientations just before the photons reached either detector? If it were true that there were some local variable involved that we weren’t sure about, then it would still have to obey the same mathematical restrictions based on probability measurements. Bell’s calculations provided an upper bound relating to the probability measurements if local hidden variables existed, even if we did not know exactly what these variables might be. Bell’s result is known as Bell’s inequality. Every time Bell’s inequality is violated, it provides proof that there are no local hidden variables and support for the idea of spooky action at a distance.

Time and again, experiments have shown Bell’s inequality to be violated. With this Micius experiment, it has been violated by an entangled pair of photons separated by 1200 km!

## Does This Mean Something Travels Faster Than the Speed of Light?

Measuring the wave function causes it to “collapse” out of the superposition of states and into one state or the other. If the collapse occurs at a finite speed, then you could imagine measuring the second photon’s polarization before the collapse information made its way to it. In this case the second photon would still have a 50% chance of vertical or horizontal polarization. This would violate conservation of angular momentum—and it never happens.

When one entangled photon is measured, the other is always measured in the appropriate state to obey conservation rules. And this makes sense since the pair was created obeying conservation rules. All experiments lead to an instantaneous collapse of the correlated wave functions upon measurement of one. (And sometimes this instantaneous collapse seems to defy time, which is even weirder, as demonstrated in the "Delayed Choice Quantum Eraser" experiment.)5

Common causality is extremely important in the creation of entangled pairs and in the utilization of entangled pairs to carry an encoded message. The encoded message is meaningless without measurements of the states of both photons, and it is meaningless without comparing the photons. Recall that the laws of physics must be upheld when the pair is created, so without a doubt the system has certain properties between both particles (for example polarization). The measurement of one particle collapses the entire wave function of the pair of particles. Entangled states have a common causality and cannot be expressed individually. They are correlated by a common cause, and what you measure in one determines what may be known about the other.

If you measure a horizontal polarization for one of the photons in the entangled pair created on Micius, then without a doubt the paired photon will be measured in the vertical state provided the entangled pair has not been compromised by an interaction along the way.

However, if the polarizations are measured at an angle, not directly on the horizontal or vertical, then you cannot be sure which state the photon measured is in, and you cannot be sure what the measurement of the second photon will be; all you can know is the probability of the possible measurements you could get, and that the two measurements will be correlated if they truly are entangled. To know if the measurements are correlated requires comparison of the measurements.

The goal of this Micius satellite experiment was two-fold. To measure the number of entangled photons that made it to the ground base stations, and to verify Bell’s inequality. This was done by measuring the polarization of the photons at various angles with the horizontal (and hence vertical) directions.

## Micius Leads the Way Toward Quantum Communications

Quantum communication is desirable because it cannot be intercepted without a trace, which is why scientists believe this technique would be wonderful for encryption key distribution. However, entangled pairs going along conventional fibers or cables are degraded quickly by the interaction with neighboring atoms. Without some difficult, and yet-to-be-perfected technology, the entangled pair can’t go very far at all. The researchers in reference 1 note that if 10 million entangled photon pairs are sent down two fiber optic cables, then using typical loss rates, after 600 km of fiber optic cables, the signal would degrade to about 1 correlated pair every trillion seconds, or one correlated pair every 31,700 years. The technology to overcome these issues and reduce loss rate is getting better, but a different method than fiber optic cables would likely be better.

With Micius, the main interference region entangled photons travel through is Earth’s lower atmosphere. Earth’s atmosphere extends out to roughly 100 km, but only about 13 km is of concern. Even our densest atmosphere is sparse compared to the density in a fiber optic cable, so entangled photons have much less of a chance of interacting with something during their journey to a land-based receiver. Micius lives in an orbit about 500 km above Earth’s surface, so much of the journey for the entangled photons is through empty space.

The land-based receivers, all in China, are located in Delingha, Lijiang, and Nanshan, with distances between Delingha and Lijiang is 1203 km, and between Delingha and Nanshan is 1120 km.1

On the Micius satellite, about 5.9 million entangled photon pairs are produced each second, and about 1.1 entangled pairs per second are detected at two stations. The scientists had a measuring window of 295 seconds, which meant around 324 entangled pairs detected each night. This may not seem like a lot, but it is significant enough to provide proof of concept, and many, many orders of magnitude better than the use of fiber optics. The signal they detected was also about eight times above the noise level.

## Future Research and Development

The scientists note in their article1 that this Micius experiment proved that entangled photons may be used for quantum encryption key distribution right away. They also noted that the entangled photons between the two stations can be used to prepare and control quantum states in distributed quantum networks. Scientists will continue to develop their satellite-to-ground-based system to further quantum communications and conduct experiments on fundamental quantum theories.

## References and Resources

1. J. Yin, et al., Satellite-based entanglement distribution over 1200 km, Science, 356, 6343 (2017) http://science.sciencemag.org/content/356/6343/1140

2. G. Popkin, "Spooky action achieved at record distance," Science, 356, 6343 (2017) http://science.sciencemag.org/content/356/6343/1110

3. L. Billings, China Shatters "Spooky Action at a Distance" Record, Preps for Quantum Internet, Sci. Amer. June 2017 https://www.scientificamerican.com/article/china-shatters-ldquo-spooky-action-at-a-distance-rdquo-record-preps-for-quantum-internet/#

4.Entangled Diamonds, APS PhysicsCentral: Physics in Action, February 2012: http://www.physicscentral.com/explore/action/entangled-diamonds.cfm