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Physik-Institut

Entanglement

Quantum mechanical entanglement describes the phenomenon whereby two or more particles (e.g., electrons, photons, or atoms) exist in a state in which their properties are linked, regardless of the distance between them. This connection means that the state of one particle can only be described in relation to the state of the others. This concept has no equivalent in classical physics and has caused much confusion since its discovery. Entangled quantum bits make quantum computers possible. The fact that objects can be entangled over arbitrarily long distances is the basis for quantum communication.

Application: Encrypted Communication

A satellite transmits entangled photons (light quanta) to two widely separated ground stations. Millions of entangled photon pairs are generated every second and linked via their polarization state. These quantum networks can enable encrypted communication.

In 2016, a satellite succeeded in transmitting entangled photons over a distance of more than 1,200 kilometers, and in 2017, a tap-proof quantum telephone call was made between Vienna and Beijing.

Photon Entanglement
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Illustration of communication with 2 entangled photons between Vienna and Beijing. Picture: Ruth Bründler, UZH

 

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Next: Superposition

More on: Quantum mechanical entanglement

Entanglement can be most simply represented if we consider objects characterised by a few quantum mechanical states. For example, an electron's magnetic moment, or spin, can point up (|↑⟩) or down (|↓⟩), using the notation introduced by Paul Dirac. Two spatially separated electrons (i.e. distinguishable electrons) then have four possible states, which we can write as follows:  |↑↑⟩, |↑↓⟩, |↓↑⟩, |↓↓⟩, where the first arrow indicates the state of the first electron and the second indicates the state of the second electron. To explain entanglement, we need to describe two more things:

Superposition of states (superposition principle):
Like superposition of multiple waves, quantum mechanics allows a system of two electrons to be in a superposition of multiple states. For example, we can write |↑↓⟩+|↓↑⟩ to indicate that the two electrons are in a superposition of the states |↑↓⟩ and |↓↑⟩. This can be illustrated by the polarisation of a light wave, for example, where the superposition of up-down and left-right oscillations results in a diagonally upwards oscillation. However, electron spins do not allow any intermediate movements, so we can only speak of the superposition of |↑⟩ and |↓⟩.

2) Measurement in quantum mechanics:
According to a principle of quantum mechanics, the measurement of a system can only ever provide one classical result. For example, if you measure the spin of an electron, you will get the result of either 'up' or 'down'. This is unambiguous if the electron's state is either |↑⟩ or |↓⟩. But what if the electron to be measured is a superposition, such as |↑⟩+|↓⟩? In this case, you will still only get one of the two results in a measurement, but each result can occur with the same probability. Therefore, if you repeat the same experiment 100 times, you will measure the spin as being in the up state approximately 50 times and in the down state 50 times. The measurement thus becomes a question of probabilities. This can be imagined more vividly with the polarisation of light waves. A diagonally polarised wave that falls on a vertical polariser is only partially transmitted. This reduced intensity corresponds to the reduced probability of finding a particle in one of the two superimposed states, so the incident polarisation can be determined from this intensity.  After the measurement, the system is also in the state that corresponds to the result of the measurement. For example, if an electron is measured in the state|↑⟩+|↓⟩ and the result is found to be ↑, then the electron is definitely in the state  |↑⟩. The same applies to the (light) wave in a polarisation measurement: a diagonally polarised wave is measured with a vertical polariser and the transmitted wave is then vertically polarized.

 
Now, let's return to the two electrons in the state |↑↓⟩+|↓↑⟩. They are entangled in this state. This can be seen in measurements if you first measure electron 1 and then electron 2.  If you measure  ↑  for electron 1, for example, then the system of the two electrons will certainly be in the state |↑↓⟩ after the measurement. If electron 2 is then measured, the result will certainly be ↓. However, if electron 2 is measured without electron 1 having been measured beforehand, the result ↑ or ↓ for electron 2 is 50% likely. Thus, the measurement on electron 1 influences the possible result for electron 2 — a consequence of their quantum mechanical entanglement. In principle, this also works if electrons 1 and 2 are infinitely far apart. In practice, it has already been possible to entangle objects over 1000 km apart.

 

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