By Dominik Janzing
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Extra resources for Computer Science Approach to Quantum Control
The detailed version of the intuition above can be found in . We have proven that every state in the image of D ⊗n satisfies [ρ, a] 1 ≤ 2( 1 1 +√ ) 2 ǫn(1 − α ) nǫα for every 1 √ > α > 0. In the asymptotics for large n we obtain a commutator with a in the √ order of 1/ ǫn. For separable states one obtains O(1/ n). Furthermore we have shown that each observable B with B ≤ 1 defines an entanglement witness: Given a partition of the n qubits into subsets (“clusters”) of size l1 , . . , lk (with j lj = n).
Consider n + n two level systems as above with large n. How complex is the implementation of an optimal process π? e. the energy yield compared to the maximal yield) of the heat engine and the complexity of the quantum circuit? We will discuss these questions partly in Chapter 4. 6 Classifying Thermodynamic Resources The essential feature of the transformations considered above was that they are not energy conserving. The cooling mechanism requires energy for the implementation and the heat engine releases energy.
To achieve different temperatures would already be a non-trivial control problem. It is less clear which measurements and unitary control operations are basic. From the pragmatic point of view this is just an issue of experimental physics. Nevertheless, it would be interesting to understand in which way the mathematical structure of the fundamental interactions in physics support some operations and not others. First of all, the fact that these forces are pair-interactions is closely related to the special role of one- and two-qubit or two-qudit gates.
Computer Science Approach to Quantum Control by Dominik Janzing