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Interferometry versus projective measurement of anyons · Around

2015

Interferometry versus projective measurement of anyons

Freedman, Michael H., Levaillant, Claire I.

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The distinct methods for measuring topological charge in a non-abelian anyonic system have been discussed in the literature: projective measurement of a single point-like quasiparticle and interferometric measurement of the total topological charge of a group of quasiparticles.

Projective measurement by definition is only applied near a point and will project to a topological charge sector near that point.
Thus, if it is to be applied to a \emph{group} of anyons to project to a \emph{total} charge, then the anyons must first be fused one by one to obtain a single anyon carrying the collective charge.
We show that interferometric measurement is strictly stronger: Any protocol involving projective measurement can be simulated at low overhead by another protocol involving only interferometric measurement.

Built on

Quantum invariants of knots and 3 3 -manifolds
Turaev, V. G · 1994
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Fault-tolerant quantum computation
Preskill, J · 1998
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Inequivalent classes of interference experiements with non-abelian anyons
Overbosch, B., and Bais, F · 2001
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Fault-tolerant computation by anyons
Kitaev, A · 2003
Earlier work this paper cites.
Topologically-protected qubits from a possible non-abelian fractional quantum hall state
Das Sarma, S., Freedman, M., and Nayak, C · 2005
Earlier work this paper cites.

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