# What is the invariant associated with constant (quantum) information?

(PhysOrg.com) -- In the classical world, information can be copied and deleted at will. In the quantum world, however, the conservation of quantum information means that information cannot be created nor destroyed. This concept stems from two fundamental theorems of quantum mechanics: the no-cloning theorem and the no-deleting theorem.

From here.

If I remember correctly, Noether's theorem states that under broad assumptions, there is an invariant iff there is a constant. My understanding from the statement above is that there is a constant (quantum information).

1. does the theorem applies in this context?
2. if yes, what is the associated invariant?
• to talk of "constant X" you need to precisely define which quantity you are talking about. "Quantum information" isn't associated to a specific quantity in the general case. Unless you are thinking of an invariant associated with constant von Neumann entropy of a quantum state?
– glS
Commented Mar 2, 2021 at 9:34
• Thanks @glS . I do not know enough to precisely define the quantity. I understood from the article that it was a well defined, measurable quantity, though. My first reaction was: in classical physics, constant information = invariance over flipping the arrow of time. The question here is whether that is also the conclusion from this experiment (I though that this had been already measured on the lab before, though, thus this question). Commented Mar 2, 2021 at 12:05
• well, in classical physics information/entropy also does not come from some conserved quantity. Rather, its invariance reflects whether the physical evolution is described as deterministic or not. The same things applies in QM (QM is also deterministic as long as one considers unitary evolution without measurements). This is not a "conclusion of an experiment"; I'd say it's rather just another way of stating the deterministic nature of the physical laws describing the dynamics
– glS
Commented Mar 2, 2021 at 17:57