[Paper Analysis] - Quantum Shannon theory with superpositions of trajectories

[NicolaBernini]

Overview

Reading through the paper

Quantum Shannon theory with superpositions of trajectories

It looks like an important milestone in perspective

[NicolaBernini]

Overview

• Classical Shannon Theory models both channel and the information carrier in a classical way: at each point in time, the information carrier has well defined states and trajectories, however noise is also present and this requires to rely ultimately on a probabilistic framework to mix to introduce random variables and statistics

  • It means there are basically 2 types of systems with related State Space Degrees of Freedom (DoF)

  • the Information Carrier (IC) State Space

  • the Channel (Chan) State Space which defines the possible IC trajectories

• Quantum Shannon Theory starts to introduce QM properties for the information carrier, like the states superposition while the channel is still modeled in a classical way: it means this quantum information carrier evolves in space-time according to a (single) classical trajectory

  • It consisted of quantizing the IC State Space

• This paper introduces a theory relying on a second level of quantization, an improvement of the traditional Quantum Shannon Theory as not only the information carrier but also the channel (defining the trajectory in space-time) is modeled in QM Framework: it means the quantum information carriers can now evolve in space-time along multiple trajectories simultaneously

  • It consisted of quantizing the Chan State Space hence allowing the IC to evolve (simultaneously) along QM trajectories rather a classical one

  • This means a q-information carrier can now experience a superposition of alternative trajectories

• The underlying intuition behind this model is that Noise, which is a trajectory / channel specific phenomenon, can be better canceled because of this superposition of alternative trajectories QM phenomenon

• Elements

  • S = Signal
  • E = Environment, leads to Noise
  • A, B = Regions (location specific Hamiltonians)

• Interaction between Signal and Environment regulated by a location specific Hamiltonians, this leads to what is considered a noisy signal in a classical perspective

• The idea is noise results from using the classical framework: from a QM perspective, the superposition of states at the receiver side allows to recover exactly S and E so to discard to latter and have a perfectly clean former one