Quantum entanglement

This episode I will explore quantum entanglement. Quantum entanglement is itself not unknown – many experiments have proven it a pillar of the quantum world – but it does herald interesting practical applications and theories in other aspects of physics. First I’ll give an introduction to quantum principles, then explain the basics of entanglement. I will talk about the Einstein-Podolsky-Rosen experiment and Bell’s inequality. There are many concepts to investigate: faster-than-light communication, applications in quantum computing, the stitching of space-time, and finally, entanglement through time. 

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Transcript

Hello everyone, welcome to the fourth episode of ‘What We Don’t Know’, a podcast series that explores the boundaries of human knowledge, investigating the unanswered questions and theories that unravel them at the frontiers of science. During this podcast I hope to get you interested in new areas of science, maths and technology, teaching you about existing concepts and igniting a curiosity for the things we have yet to know.

This episode I will explore quantum entanglement. Quantum entanglement is itself not unknown – many experiments have proven it a pillar of the quantum world – but it does herald interesting practical applications and theories in other aspects of physics. First I’ll give an introduction to quantum principles, then explain the basics of entanglement. I will talk about the Einstein-Podolsky-Rosen experiment and Bell’s inequality. There are many concepts to investigate: faster-than-light communication, applications in quantum computing, the stitching of space-time, and finally, entanglement through time. 

The word ‘quantum’ gets thrown around a lot, particularly in science-fiction movies, but what does it actually mean? ‘Quantum’ comes from the word ‘quanta’ for discrete (individually distinct) quantities of energy, which exists in packets rather than on a continuum. From this ‘quantisation’ of energy, by Max Planck in 1900, came the rich field of quantum physics. The ‘quantum world’ describes the behaviour of anything smaller than an atom. It is very different to the classical world with which we many-atom organisms are familiar with.

Aside from the discretisation of energy, quantum weirdness involves wave-particle duality (which I touched on in the previous episode), the uncertainty principle (which states that the position and velocity of an object cannot both be measured exactly), and quantum entanglement. If two objects are ‘entangled’, then their physical properties are related in such a way that any measurement done on one will instantly improve knowledge about the other. 

For example, imagine two electrons in a system. Each electron has an inherent property called spin, which can be up or down. In this system there are four possible combinations of spin measurements: up, up; up, down; down, up; and down, down. Quantum physics tells us that when these electrons are not being measured, they are in a superposition of all possible states, and when we do a measurement, they collapse into one of these four. There is a mathematical expression describing the superposition of the states and the probabilities of finding each one during measurement. If this expression can be separated into two parts, the electrons are not entangled; if you cannot separate it, the electrons are entangled. In an entangled system, the probability distribution of finding electron B in a certain state (e.g. up) changes after we interact with electron A (e.g. by individually measuring A’s spin).

Unentangled states in quantum systems are rare, because whenever systems interact, correlations between states are produced. Despite the general application of this definition of entanglement, it is often illustrated using special cases such as Bell States, where the probability of both particles having spin up or both having spin down is zero. Before measurement, each particle has a 0.5 chance of having either spin. After measuring particle A to have spin up, you know particle B will have spin down: the probability of B being up becomes 0 and down becomes 1. 

The Einstein-Podolsky-Rosen (EPR) experiment seeks to demonstrate entanglement. Because it is quite complicated, I’ll instead outline the simplified version, later proposed by Bohr, which is reminiscent of the aforementioned Bell States.

Suppose you have a particle with total spin 0. The particle decays into two other particles and conserves the spin. One particle goes left, the other right. Neither particle can have spin 0, they must each have an absolute value with a spin of 1; since the spins must add to 0, the spins, if thought of as arrows, must be in opposite directions. These particles are entangled, because information from one instantly conveys information on the other. This experiment has been done many times and the spins proven to correlate in the proposed way. 

At first, this does not seem particularly impressive, since such correlation can be obtained in non-quantum experiments, for example a pair of shoes separated over a long distance. If one person opens a box to reveal the left shoe, then they instantly know that their friend’s box contains the right shoe. But this analogy is not actually applicable because the left-right quality of the shoe is determined before anyone opens any boxes. In contrast, quantum physics dictates that a particle does not have a distinct property until a measurement is made. In other words, the two particles of the EPR experiment cannot have their spins determined locally before a measurement is made; instead, measuring one particle’s state instantly determines the other, entangled particle’s state.

Einstein himself disliked this idea, calling it ‘spooky action at a distance’ for its implication that entanglement could violate locality, which states that an object is only influenced by its immediate surroundings. In 1964, John Bell devised a test that could prove whether information about entangled particles was encoded within a particle, then maintained when separated (as Einstein preferred), or if correlations were non-local. His inequalities give the degree of non-locality that requires a quantum explanation. They were first violated by Aspect et al in 1982, and the predictions reconfirmed many times since. The observed correlations between particles’ spins are stronger than they could possibly be if their spins were determined before measurement – quantum entanglement is, indeed, non-local.

Experiments show that if the entangled particles communicate to produce their correlations, such communication would be at least 10,000 times faster than the speed of light. This violates Einstein’s theory of relativity. So does that mean there is no communication? How, then, can particles be entangled? Do we just have to accept this paradox as a part of the quantum world?

Can we exploit entanglement for faster-than-light communication? The first three questions are unresolved, but the last is an unfortunate ‘No’. Although quantum mechanics seems nonlocal, there is no observable nonlocal communication, and we cannot use the correlations to transmit information of any kind from one particle to the other. This is because you cannot force an entangled particle into a particular state without disturbing the entanglement, nor can you force a measurement to produce a particular state, because measurement outcome is always random. The hypothetical physicists ‘sending’ information through quantum correlations can only see these correlations when they return together and compare measurements, a process done at or below the speed of light.

Luckily, entanglement is more successful in quantum computing. Computers use electrical pulses, representing zeroes or ones, called bits to store data and process information. Quantum computers use subatomic particles called qubits which exploit quantum phenomena to provide a much greater processing power. Entangling qubits exponentially increases computational power, partly because processing one qubit reveals information about other, entangled qubits.

Another interesting idea about entanglement comes from Brian Swingle, who argues that space-time and gravity may emerge from entanglement. Tensors are algebraic objects that describe a multilinear relationship between sets of algebraic objects related to a vector space. Tensor networks such as the multiscale entanglement renormalisation ansatz (MERA) combine information from complicated interactions between many quantum objects into a single geometric structure. Swingle, among others, hopes to further this emergent geometry into an explanation of how a smooth, continuous space-time can emerge from discrete quantum bits. The entanglement of quantum bits is critical to sewing this continuous space-time fabric. 

Entanglement holds promise in explaining how space-time may emerge from an even more fundamental layer of physics.

So far, I have only talked about spatial entanglement – entanglement of particles across space. What about temporal entanglement? Imagine a single polarised photon. Person A measures it, then person B measures it. Instead of two photons being separated by space, there is one separated by an interval of time, and the correlations familiar to spatial entanglement are replicated in this temporal case. At first, this seems obvious – of course actions on a particle affect its later properties!

But we know by now that quantum physics will surprise us. Stephen Brierley, at the University of Cambridge, lead a team in showing that the correlations are too strong to be explained classically, especially when one increases the number of possible polariser orientations and measurements made. The reason for this ‘supermemory’ is still undecided. 

Deepening our understanding of temporal entanglement may lead to advances in quantum cryptography. For example, Jay Olsen and Timothy Ralph, both at the University of Queensland, proposed quantum time capsules that encode information into photons in such a way that they can only be decrypted in the future, by exploiting temporal correlations. Furthermore, some cases of temporal entanglement suggest blurring of the causal order of events. Časlav Brukner, a physicist at the University of Vienna, performed experiments on particles that did just this. The loss of a ‘well-defined causal order’ may remove fundamental space-time, thus galvanising new theories on how quantum physics builds our classical universe.

This episode I introduced you to some fundamental ideas about quantum entanglement, delving into what it means for particles to be entangled across space, and the experiments that proved that quantum correlations are too strong to be locally determined. I crushed all our hopes for using entanglement to communicate faster-than-light, but raised them with possibilities in quantum computing and cryptography. I examined entanglement across time.

Quantum entanglement is a fundamental idea in quantum physics. It may be practically useful, and theoretically promising, particularly as a potential producer of space-time and breaker of cause-and-effect chains. Ultimately, its weirdness is an inescapable part of our reality. Steps to decoding why entanglement works as it does, are, therefore, steps to uncovering yet another of the universe’s secrets. 

Thank you for listening.