A dynamical point of view of Quantum Information: entropy and pressure

Details A dynamical point of view of Quantum Information: entropy and pressure A dynamical point of view of Quantum Information: entropy and pressure

2011-04-14

arxiv.org/abs/1104.2868v1

Physics

Quantum Physics

Scientific paper

10.1007/978-3-642-11456-4

Quantum Information is a new area of research which has been growing rapidly since last decade. This topic is very close to potential applications to the so called Quantum Computer. In our point of view it makes sense to develop a more "dynamical point of view" of this theory. We want to consider the concepts of entropy and pressure for "stationary systems" acting on density matrices which generalize the usual ones in Ergodic Theory (in the sense of the Thermodynamic Formalism of R. Bowen, Y. Sinai and D. Ruelle). We consider the operator $\mathcal{L}$ acting on density matrices $\rho\in \mathcal{M}_N$ over a finite $N$-dimensional complex Hilbert space $\mathcal{L}(\rho):=\sum_{i=1}^k tr(W_i\rho W_i^*)V_i\rho V_i^*,$ where $W_i$ and $V_i$, $i=1,2,...k$ are operators in this Hilbert space. $\mathcal{L}$ is not a linear operator. In some sense this operator is a version of an Iterated Function System (IFS). Namely, the $V_i\,(.)\,V_i^*=:F_i(.)$, $i=1,2,...,k$, play the role of the inverse branches (acting on the configuration space of density matrices $\rho$) and the $W_i$ play the role of the weights one can consider on the IFS. We suppose that for all $\rho$ we have that $\sum_{i=1}^k tr(W_i\rho W_i^*)=1$. A family $W:=\{W_i\}_{i=1,..., k}$ determines a Quantum Iterated Function System (QIFS) $\mathcal{F}_{W}$, $\mathcal{F}_W=\{\mathcal{M}_N,F_i,W_i\}_{i=1,..., k}.$

Affiliated with

Also associated with

No associations

Rating

A dynamical point of view of Quantum Information: entropy and pressure does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A dynamical point of view of Quantum Information: entropy and pressure, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A dynamical point of view of Quantum Information: entropy and pressure will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-167613