Decades since the famous paper of Einstein, Podolsky and Rosen (EPR) and of John Bell’s quantitative reformulation of their critique of the completeness of quantum mechanics, this problem has re-emerged in the scientific limelight with unexpected intensity. Its implications range from epistemological questions in quantum physics to information theory. This dramatic development, however, has concentrated on the entanglement of angular momentum components and their related physical quantities only. In this case the two complementary systems of non-commutative variables are on equal footing and both allow correlation analysis in form of coincidence measurements between the corresponding entangled partners in a continuous way. This situation is different for the position and momentum variables, originally used by EPR in their argument critiquing the completeness of quantum mechanics. The scenario for these entangled variables has, however, never been experimentally realized and analyzed theoretically in full depth.
In this talk we present the first evidence for this kind of entanglement and show that entanglement of singular positions in ordinary space is not possible. Instead, ordinary space entanglement requires “double- positions” as basis states in the form of gerade and ungerade eigenstates of the parity operator. As eigenstates of the symmetry operator P, these states are entangled in the same way as the CP-eigenstates of the system of the neutral kaons. The corresponding entanglement cannot be projected onto correlation measurements between the entangled partners in ordinary space, because their phase correlation is fixed. However, the entanglement can be projected onto the complementary set of variables, which are the eigenstates of the non-symmetry operators, strangeness and momentum. This projection always appears in the time domain as an oscillation between the two components of the complementary entangled system. In contrast to the strangeness components of the neutral kaon system, the momentum components f/b of a system of entangled electrons ejected from a homonuclear diatomic molecule may also be projected onto the corresponding intensity variations in ordinary space. In a way this makes this system unique for the study of entanglement and reveals for the first time the entanglement of space-time, the “Dirac-qbit”, the counterpart of the “Schrödinger-Pauli qbit” describing the correlation properties of the angular momentum components in Poincaré space.