Transmission of coherent information at the onset of interactions

Abstract

In this work, we investigate the parameters governing the rate at which a quantum channel arises at the onset of an interaction between two systems, $A$ and $B$. In particular, when system $A$ is pre-entangled with an ancilla, $\tilde{A}$, we quantify the early-time transmission of pre-existing entanglement by calculating the leading order change in coherent information of the complementary channel ($A\to B^{\prime }$). We show that, when $A$ and $B$ are initially unentangled and $B$ is pure, there is no change in coherent information to first order, while the leading (second) order change is divergent. However, this divergence may be regulated by embedding the conventional notion of coherent information into what we call the family of $n$-coherent informations, defined using $n$-Rényi entropies. We find that the rate of change of the $n$-coherent information at the onset of the interaction is governed by a quantity, which we call the $n$-exposure, which captures the extent to which the initial coherent information of $A$ with $\tilde{A}$ is exposed to or `seen by' the interaction Hamiltonian between $A$ and $B$. We give examples in qubit systems and in the light-matter interaction.

Accepted for publication in Journal of Physics A: Mathematical and Theoretical

References in corpus (13)

• Quantum Computing
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum circuits with many photons on a programmable nanophotonic chip
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Entanglement spectrum in one-dimensional systems
• The quantum Rabi model: solution and dynamics
• Scaling advantage in quantum simulation of geometrically frustrated magnets
• Digital Quantum Rabi and Dicke Models in Superconducting Circuits
• Approximate quantum error correction, random codes, and quantum channel capacity
• Calculating Renyi Entropies with Neural Autoregressive Quantum States
• The Dynamics of Entropies at the Onset of Interactions
• Detection of genuine tripartite entanglement by two bipartite entangled states
• A universal neural network for learning phases and criticalities

Cited by in corpus (2)

• The Transfer of Entanglement Negativity at the Onset of Interactions
• Adiabatic Dynamics of Entanglement