Agents, subsystems, and the conservation of information

04/05/2018
by   Giulio Chiribella, et al.
0

Dividing the world into subsystems is an important component of the scientific method. The choice of subsystems, however, is not defined a priori. Typically, it is dictated by our experimental capabilities, and, in general, different agents may have different capabilities. Here we propose a construction that associates every agent with a subsystem, equipped with its set of states and its set of transformations. In quantum theory, this construction accommodates the traditional notion of subsystems as factors of a tensor product, as well as the notion of classical subsystems of quantum systems. We then restrict our attention to systems where all physical transformations act invertibly. For such systems, the future states are a faithful encoding of the past states, in agreement with a requirement known as the Conservation of Information. For systems satisfying the Conservation of Information, we propose a dynamical definition of pure states, and show that all the states of all subsystems admit a canonical purification. This result extends the purification principle to a broader setting, in which coherent superpositions can be interpreted as purifications of incoherent mixtures. As an example, we illustrate the general construction for subsystems associated with group representations.

READ FULL TEXT
research
11/24/2018

Implementing Entangled States on a Quantum Computer

The study of tensor network theory is an important field and promises a ...
research
02/07/2021

On the Algorithmic Content of Quantum Measurements

We show that given a quantum measurement, for an overwhelming majority o...
research
08/09/2018

Algorithmic No-Cloning Theorem

We introduce the notions of algorithmic mutual information and rarity of...
research
08/24/2021

Quantum adaptive agents with efficient long-term memories

Central to the success of adaptive systems is their ability to interpret...
research
05/25/2018

Nilpotent Morse algebra and time evolution of certain associated coherent states

We provide the time evolutions of the linear and nonlinear coherent stat...
research
09/24/2021

Process tomography in general physical theories

Process tomography, the experimental characterization of physical proces...
research
05/22/2023

Constructions of k-uniform states in heterogeneous systems

A pure quantum state of n parties associated with the Hilbert space ^d_1...

Please sign up or login with your details

Forgot password? Click here to reset