# Non-locality and topology

This is a purely speculative question:

Has there been any work that describes non-locality/entanglement in QM by using exotic topologies in configuration space?

The 'conceptual' picture that I have in mind is of two particles that are distant in the usual topology, but when entangled, being somehow part of the same 'irreducible' open set - so they can't be 'disentangled'. For this to have any chance of working, topologies would have to change with time.

• Entanglement by itself concerns no spatial separation. People can talk about entanglement between two qubits without referring to where the two qubits are located. As long as you can a tensor product of two Hilbert spaces, you can define entanglement for pure states (at least). But it may be worth pointing out that people have thought about relating entanglement to the geometry or topology of the Hilbert space of few qubits. – Isidore Seville Feb 6 '14 at 2:10
• Point taken. I was thinking more along the lines of the usual EPR paradox where widely spatially separated but entangled systems have non-local correlations. – Mozibur Ullah Feb 6 '14 at 2:22
• The word "non-local correlations" should be avoided. Locality has to do with information or energy signal "sent" at some space-time point and "received" at an other space-time point, and this cannot be done instantaneously. Correlations, on the other way, are what they are. In any probabilistic system (classical or quantum), it is always possible that 2 subsystems of a systems locally get correlations,then, after, it is possible that these 2 subsystems may evolve into spatially distant locations, anyway, the correlations remain the same, because they concern internal state of the subsystems. – Trimok Feb 6 '14 at 11:35
• Fun question. Two comments: 1) Actually quantum theory is local in configuration space. It is only non-local in real space, so I guess you should phrase your question in that space. 2) Holographic duality is a recent development that suggests deep links between entanglement and geometry/topology. For example there is the idea by Maldacena and Susskind that if you have two entangled particles, that they are in fact connected by a wormhole, related to your intuition (if you want to google more: ER = EPR''). [cont] – Ruben Verresen Feb 14 '16 at 2:46
• [cont] More generally dualities like AdS/CFT suggest that geometry (i.e. the metric) is in fact an emergent description due to underlying entanglement structures. – Ruben Verresen Feb 14 '16 at 2:46