When is a system coherent or decoherent?

[zekise]

...

Hi Michael,

Is it fair to say that whether system A is coherent or decoherent, it is always with respect to another system B? Of course the environment is another system (E), and an observer yet another system (O). So when we specify coherence or decoherence of system A, it is in respect to another system B (or E or O). It is a relational concept. For example A can be coherent w.r.t. B but decoherent w.r.t. system C. A system is not coherent or decoherent by itself.

Now, is it correct to say that if A is fully (100%) decoherent w.r.t. C, then the two systems are entangled?

And if A is fully (100%) coherent w.r.t. B, then A appears as a superposition to B?

Finally, coherence (ǂ) and decoherence (≡) is commutative. A ǂ B ==> B ǂ A, A ≡ B ==> B ≡ A .
Decoherence is transitive, but coherence is not. A ≡ B & B ≡ C ==> A ≡ C .

Coherence (or disentanglement) results in a loss of quantum information between A & B. Thus energy is required.
Decoherence (or entanglement) results is a gain of information between A & B, and energy is released.

Your opinion is appreciated.
Zek

 

[Michael Price]

Is it fair to say that whether system A is coherent or decoherent, it is always with respect to another system B? O
[...]
Now, is it correct to say that if A is fully (100%) decoherent w.r.t. C, then the two systems are entangled?

And if A is fully (100%) coherent w.r.t. B, then A appears as a superposition to B?

Finally, coherence (ǂ) and decoherence (≡) is commutative. A ǂ B ==> B ǂ A, A ≡ B ==> B ≡ A .
Decoherence is transitive, but coherence is not. A ≡ B & B ≡ C ==> A ≡ C .

Coherence (or disentanglement) results in a loss of quantum information between A & B. Thus energy is required.
Decoherence (or entanglement) results is a gain of information between A & B, and energy is released.

Your opinion is appreciated.
Zek

I think of decoherence as the release of more than k of entropy, which randomises phases. Entropy requires energy, in the sense that entropy is the release of uncontrolled energy. When that energy is absorbed by another system the two systems will become entangled (their states become correlated), which would seem to be a commutative event. (The two systems become entangled with respect to each other.) Two systems could be entangled together without a third system being involved, but if it were, then they would all be entangled together.

Coherence is simply the state before decoherence, when phase relationships are known. Once coherence is lost it is pretty much lost forever.

Hopefully I have answered all your points?

 

[zekise]

... Two systems could be entangled together without a third system being involved, but if it were, then they would all be entangled together.

Coherence is simply the state before decoherence, when phase relationships are known. Once coherence is lost it is pretty much lost forever.

Thanks Michael. I am not sure what you mean by phases or how entropy figures into decoherence.

Is it correct to say that if system A is coherent to system B, then A appears as a superposition to B. And if system A decoheres wrt system B, then an entanglement has been established between the two systems. If so, if TAB is a measure of entanglement between A & B and SAB is a measure of superposition, then TAB.SAB = 1?

Notation: coherence (ǂ) and decoherence (≡). Are the following correct?:

If A ≡ B and A ≡ C then B ≡ C.
If A ≡ B and A ǂ C then B ǂ C.

Since ǂ is commutative, when a photon P is emitted from a laser diode towards a screen (call it environment E), and before it collides with the screen, then P ǂ E. Therefore, it must be the case that E is coherent to P. We can figure the wave function for P, which is typically in respect to the environment E. Can we also figure the wave function for E in respect to P? I hope I am making sense.