Quantifying Superposition

By Johan Aberg. 2006

298 citations recorded by the source corpus.

Measures are introduced to quantify the degree of superposition in mixed states with respect to orthogonal decompositions of the Hilbert space of a quantum system. These superposition measures can be regarded as analogues to entanglement measures, but can also be put in a more direct relation to the latter. By a second quantization of the system it is possible to induce superposition measures from entanglement measures. We consider the measures induced from relative entropy of entanglement and entanglement of formation. We furthermore introduce a class of measures with an operational interpretation in terms of interferometry. We consider the superposition measures under the action of subspace preserving and local subspace preserving channels. The theory is illustrated with models of an atom undergoing a relaxation process in a Mach-Zehnder interferometer.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/6726121d3e758fe95f9b698cf51667de0a687a61

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Robustness of asymmetry and coherence of quantum states (2016, background): “In this case, asymmetry with respect to such a d-dimensional representation of U(1) can be regarded as coherence, that is, quantum superposition with respect to the reference basis {| j〉}d−1 j=0 in the Hilbert space H = Cd [4, 6, 9, 10, 13].”
Coherence effects in the performance of the quantum Otto heat engine (2018, methodology): “where ε (·) = ∑ n Πn (·) Πn is the full dephasing map and C (ρ) = S (ε (ρ)) − S (ρ) is the relative entropy of coherence (in the reference state basis) [12–16].”
Description of quantum coherence in thermodynamic processes requires constraints beyond free energy (2014, unknown): “For α→ 1, we have A1(ρ) ≡ A(ρ) which is the asymmetry measure introduced in [33, 36, 37].”
Colloquium: quantum coherence as a resource (2016, methodology): “A very general approach to quantify coherence was presented by (Åberg, 2006) within the framework of quantum superposition.”
Operational Resource Theory of Coherence. (2015, background): “For our purposes, a QRT has three ingredients: (1) free states (separable state in ET), (2) resource states (entangled state in ET), (3) the restricted or free operations (LOCC in ET).”