Abstract
Motivated by the gate set tomography we study quantum channels from the perspective of information which is invariant with respect to the gauge realized through similarity of matrices representing channel superoperators. We thus use the complex spectrum of the superoperator to provide necessary conditions relevant for complete positivity of qubit channels and to express various metrics such as average gate fidelity.
Highlights
Gauge symmetries are among the most influential concepts of modern physics
It is important to stress that this conceptual association is right only if we cannot get Łukasz Rudnicki: rudnicki@cft.edu.pl the full information concerning X, so that both Φ and M are truly equivalent. Such a situation is inherent to gate set tomography (GST) [1, 2], a modern view [3] on quantum process tomography [4], in which gauge-related terminology is common in use
After we derived the gauge invariant necessary criteria for complete positivity of unital quantum channels, an obvious way of continuation shall concern the general case of an arbitrary translation vector k = 0
Summary
Gauge symmetries are among the most influential concepts of modern physics. They provide suitable underlying structures for all known field theories such as Electrodynamics, General Relativity or Yang-Mills theory. An unknown square matrix Φ is provided to us through a similar matrix M Such a situation is inherent to gate set tomography (GST) [1, 2], a modern view [3] on quantum process tomography [4], in which gauge-related terminology is common in use. In this scheme, the matrix Φ is a superoperator which represents a true quantum channel, while M is its reconstruction based on experimental data. We would like to point out that unexpectedly (at least for the authors) there are still interesting and non-trivial problems associated with the sole description of single qubit channels
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