GHZ experiment

The GHZ experiment , named after the physicists Greenberger , Horne and Zeilinger , is a (thought) experiment in quantum mechanics, with which an important class of theories with hidden variables can be excluded. In 1989, Greenberger, Horne and Zeilinger proposed a state of three entangled particles, in which, in contrast to Bell's inequalitiesfour measurements are sufficient to show the correctness of quantum mechanics and refute the existence of hidden variables. After the instrumental possibilities were given, Zeilinger and colleagues were able to carry out a corresponding experiment for the first time in 1999 and the predictions of quantum mechanics were confirmed.

background

Two particles are created together in an entangled state and fly apart. These particles have only two possible states, and . If the state of one particle is measured (e.g. ), you know that the other particle is in the other state (i.e. ). Albert Einstein claimed that these properties of the particles were already determined before the measurements were carried out, and that the respective state of the particle was stored as a so-called "hidden variable" until the measurement. Quantum mechanics describes these two particles as a single wave function that makes both states equally probable for both particles. Only through observation, through a measurement, does this wave function collapse, and depending on which state was measured for one particle, you now know exactly the state of the other particle. ${\displaystyle |0\rangle }$ ${\displaystyle |1\rangle }$ ${\displaystyle |1\rangle }$ ${\displaystyle |0\rangle }$

Neither of the two interpretations can be proven with only two entangled particles in one experiment. In 1964, however, John Bell found a system of inequalities (Bell's inequality) which, given an infinite number of measurements, provides a statistically exact solution to this dilemma. Since an infinite number of measurements cannot be carried out in practice, the GHZ experiment enables an experimentally based analysis or solution of this contradiction.

GHZ condition

The GHZ state is a maximally entangled state of at least three particles, which in the case of qubits has the form

${\displaystyle |\mathrm {GHZ} \rangle _{M}=\textstyle {\frac {1}{\sqrt {2}}}(|0\rangle ^{\otimes M}+|1\rangle ^{\otimes M})=\textstyle {\frac {1}{\sqrt {2}}}(|0\ldots 0\rangle +|1\ldots 1\rangle )}$

owns. In the simplest case for three particles this corresponds to

${\displaystyle |\mathrm {GHZ} \rangle _{3}=\textstyle {\frac {1}{\sqrt {2}}}(|000\rangle +|111\rangle ).}$

Due to its entanglement, a GHZ state shows correlations during measurements in the GHZ experiment, which cannot be explained with the help of local hidden variables.

literature

• Daniel M. Greenberger, Michael A. Horne, Abner Shimony, Anton Zeilinger: Bell's theorem without inequalities. In: Am. J. Phys. 58, No. 12, 1990, pp. 1131-1143 ( doi : 10.1119 / 1.16243 , and the references listed there).

Individual evidence

1. ↑ Jian-Wei Pan , Dirk Bouwmeester , M. Daniell, Harald Weinfurter , A. Zeilinger Experimental test of quantum nonlocality in three-photon GHZ entanglement , Nature, Volume 403, 2000, pp. 515-519