# Title: Many shades of decoherence
# Presenter: Wojciech Krzemien
# Date: 14.04 2025
# Participants:
Wojciech Krzemień (WK)
Konrad Klimaszewski (KK)
Lech Raczynski (LR)
Roman Shopa (RS)
Wojciech Wislicki (WW)
Adam Szabelski (AS)
# Discussion:
RS: Does the decoherence correspond to the full or partial suppression of the interference term?
WK: The decoherence can lead to either full or partial suppression. I will show some examples that quantifies the level of suppression.
WW: For Phi->0, the interference term doesn't vanish. The expectation value should be added.
LR: It seems ok if we assume what WK has just explained, that we would average over many realisations with random phases. Only the
off-diagonal terms would be affected
WK: You are right, the slide is slightly misleading. What I meant is that we average over many "interactions", each of which changes the phases randomly, then, on average, the phase factor will go to zero.
The slide was updated in the newest version of the presentation.
AS: Do Kraus operators conserve the probability current?
WK: By definition, Kraus operators are trace-preserving and positivity-preserving operators called CPCT maps.
But they allow describing the system transformation from pure to mixed states.
KK: Did I understand correctly that by applying the Kraus representation, we encode the influence of the environment?
Exactly, the usage of Kraus operators allows for encoding the influence of the environment, e.g. decoherence process.
WW: Are Kraus operators only projection operators?
WK: No. They can be, but in general, they are not. e.g. they can represent the transformation from a pure state to the mixed one as I showed in the previous example. In the Compton scattering model, we have one Kraus operator which is projective, e.g. sets the polarisation after the measurement, but
the other one has no such interpretation.
RS: What is the meaning of the k index in the Kraus decomposition?
WK: The number of Kraus operators used in the decomposition. This is the problem that the decomposition is not unique. There are a priori many ways of defining
the Kraus operators and their number for a given quantum process. But there is a theorem that states that all systems of Kraus operators
for given quantum process are related by unitary operations.
LR: Do Kraus operators form a basis? From the enumerated properties, it doesn't seem so.
WK: No. The only conditions are shown in the slides. They are trace-preserving and positivity-preserving, and they fulfil this
"completeness" condition. They form a completely positive map between the quantum states characterised by the density matrices.
WW: Small remark, Kraus should be written with s, not with z
WK: Fixed in the updated version of the presentation