Quantum Weirdness: Superposition and entanglement

It was the closing years of the nineteenth century when scientists started to notice something wasn’t right. Physics worked rather well when describing the motion of planets or how electricity traverses a cable to make bulbs work. Experiments revealed that the microscopic world was made up of atoms. And that atoms themselves had structure, being composed of a positively charged nucleus with negatively charged electrons moving around it [1]. The problem was that when physicists used what they knew to try and describe these objects, it didn’t work: classical physics was no good at describing the atomic world [2].

Quantum physics rose from the ashes left behind by this failure of classical physics. Decades of work led to one of the most solid physical theories ever formulated, and today it is a common fixture of the everyday life: it is behind the laser, mobile phones, computers or solar panels, just to name a few examples [3,4]. Surprisingly though, scientists do not really understand quantum mechanics, they just accept and are exceptionally good at using it.


What makes the quantum world so different?


To see why quantum physics is hard to grasp, it is useful to think about coins [5]. A coin has two sides, heads and tails. If you place one on a table, there are two possibilities: heads is facing up, or tails is facing up. In physical lingo, these two possibilities are known as states [6]. The coin can only be in one state at the same time. Or at least this is how the classical world of people, cars and planets works.

In the quantum world things are different. A hypothetical quantum coin would also have the two states of heads and tails. But due to a property called superposition, it can also be in states in between these two. The coin could be in a half heads and half tails state. This is the similar to Schrödinger’s cat, which is dead and alive at the same time [7,8]. However, you can never observe this. Once you try to determine the state of the quantum coin, it will take on either a definite heads or tails state(physicists call this collapse of the wave function [9]).

This is an obvious difference with the “classical” coin, which was obviously in a well determined state whether you took a look at it or not. Superposition is part of the mystique of quantum mechanics. It is also one of the aspects of the quantum world that physicists know is there, know how to use, but lack in fundamental understanding of its origin. Matters only escalate with what comes next: entanglement.


Quantum entanglement


Suppose now that instead of one quantum coin, there are now two and we want to treat them as a single system. Classically, the two-coin system could be found in a one of four states: heads and heads, heads and tails, tails and heads or tails and tails. Once again, in the quantum world, there are these four special states, plus everything in between. Lets say, for arguments state, that the coins are in a state made up of equal amounts of four special states described above. Then take a look at the first coin. What will happen? Well, as in the previously discussed case, because it is equally shared between heads and tails, we will see one or the other with 50% chance. What about the second coin? Well, it is still in a superposition, because it has been left alone. Once someone checks it out, it will choose which face to show (in this case, the states of both coins are separated).

In the previous case looking at one coin didn’t tell us anything about the other: we needed to perform two measurements to be sure about the state of the full two-coin system. So now instead consider a different setup: a 50% heads-tails and 50% tails-heads state. Suppose you measure the first coin and get heads. Then the second coin is necessarily tails! And vice-versa. This time one measurement sufficed to get all the information about the system. In fact, checking out the first coin actually forced the second to stop existing in a superposition and take on either heads or tails. And whichever it chose depended on what was found for the first coin.

This is an example of quantum entanglement, another property of the microscopic world which is not evident in the realm of people and planets. When a system is said to be entangled, it means that the state of its different parts are intimately related, or more technically, correlated. Knowledge of one part necessarily carries knowledge of the other. How much you can know about one part from what you know about the other depends on how correlated the system is, or on how much entanglement is present. The case discussed above is known as maximally entangled, as measuring ,one part reveals all there is to know about the other! [10,11]


Can we see entanglement in the classical world?


The closest classical analogue one could come up with is to have two coins, one heads up and one tails up, and covering each of them up with your hands. If someone asked you to reveal a coin with heads facing up, then you would automatically know that the other will show tails. It would do so though because it was always tails, never anything else. In the quantum case, neither coin is heads nor tails until they are observed. Classical physics has no notion of entanglement. Like superposition, this property is unique to quantum mechanics, and contributes to its weirdness.

Of course, there are many new features of the quantum world which are not present in the realm of classical physics. But most will boil down to superposition and entanglement. And as was mentioned above, as weird as these properties are, scientists are very good at using them to are advantage. In particular, they are at the very foundation of quantum information science and quantum computing, which promises incredibly fast computing power for some applications, and the obsolescence and undermining of others, such as some aspects of cryptography and cybersecurity. Quantum mechanics could even make cryptocurrency unfeasible. But how so? And more importantly, how can we use quantum mechanics to solve the problems which this science itself may deliver?


[1] https://history.aip.org/exhibits/rutherford/sections/alpha-particles-atom.html

[2] https://physics.weber.edu/carroll/honors/failures.htm

[3] https://www.forbes.com/sites/chadorzel/2015/08/13/what-has-quantum-mechanics-ever-done-for-us/#1357d7334046

[4] https://www.smithsonianmag.com/science-nature/five-practical-uses-spooky-quantum-mechanics-180953494/

[5] The first place were I found the coin analogy to explain quantum superposition, and in particular qubits, was in Leonard Susskind’s Theoretical Minimum series of lectures at Stanford University, available at http://theoreticalminimum.com/

[6] https://en.wikipedia.org/wiki/Quantum_state

[7] http://www.physics.org/article-questions.asp?id=124

[8] https://en.wikipedia.org/wiki/Quantum_superposition

[9] https://en.wikipedia.org/wiki/Wave_function_collapse

[10] https://www.quantamagazine.org/entanglement-made-simple-20160428/

[11] https://en.wikipedia.org/wiki/Quantum_entanglement

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