In physics, a linear operator acting on a vector space of linear operators
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In physics, a superoperator is a linear operator acting on a vector space of linear operators.[1]
Sometimes the term refers more specially to a completely positive map which also preserves or does not increase the trace of its argument. This specialized meaning is used extensively in the field of quantum computing, especially quantum programming, as they characterise mappings between density matrices.
The use of the super- prefix here is in no way related to its other use in mathematical physics. That is to say superoperators have no connection to supersymmetry and superalgebra which are extensions of the usual mathematical concepts defined by extending the ring of numbers to include Grassmann numbers. Since superoperators are themselves operators the use of the super- prefix is used to distinguish them from the operators upon which they act.
^John Preskill, Lecture notes for Quantum Computation course at Caltech, Ch. 3, [1]
In physics, a superoperator is a linear operator acting on a vector space of linear operators. Sometimes the term refers more specially to a completely...
the Lindblad superoperator L is achieved. For one jump operator F {\displaystyle F} and no unitary evolution, the Lindblad superoperator, acting on the...
completely-positive maps should be considered as well. Quantum dynamical semigroup Superoperator Sudarshan, E. C. G.; Mathews, P. M.; Rau, Jayaseetha (1961-02-01). "Stochastic...
solve for χ {\displaystyle \displaystyle \chi } , which is a positive superoperator and completely characterizes E {\displaystyle {\mathcal {E}}} with respect...
irreversible thermodynamics and quantum operator theory, especially the time superoperator theory; he is awarded the Nobel Prize in Chemistry in 1977 "for his...
gives a denotational semantics for these languages in a category of superoperators. QML is a Haskell-like quantum programming language by Altenkirch and...
semigroup. In some fields, such as quantum optics, the term Lindblad superoperator is often used to express the quantum master equation for a dissipative...
to operator L ϱ ( A ) {\displaystyle L_{\varrho }(A)} is a (linear) superoperator. The symmetric logarithmic derivative is linear in A {\displaystyle...
c]\right)\,,} where the equation has been simplified using the Lindblad superoperator:: 105 D [ A ] a ≡ A a A † − 1 2 ( A † A a + a A † A ) . {\displaystyle...
_{\text{s}}={L}\rho _{\text{s}}~,} where L {\displaystyle {L}} is the Liouville superoperator described in terms of the system's Hilbert space, where the reservoirs...
commutator follows by a symmetry argument. Introduce also the commutation superoperator F ^ {\displaystyle {\hat {F}}} of an operator F {\displaystyle F} (in...
{L}}(\rho ),} where γ {\displaystyle \gamma } is the loss rate and superoperator L {\displaystyle {\mathcal {L}}} is called the Liouvillian. One can...
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