Simulating a single qubit channel using a mixed state environment

Abstract

We analyze the class of single qubit channels with the environment modeled by a one-qubit mixed state. The set of affine transformations for this class of channels is computed analytically, employing the canonical form for the two-qubit unitary operator. We demonstrate that, 3/8 of the generalized depolarizing channels can be simulated by the one-qubit mixed state environment by explicitly obtaining the shape of the volume occupied by this class of channels within the tetrahedron representing the generalized depolarizing channels. Further, as a special case, we show that the two-Pauli Channel cannot be simulated by a one-qubit mixed state environment.

Published version with minor changes

References in corpus (8)

• Quantum Cryptography
• Decoherence, einselection, and the quantum origins of the classical
• Teleportation as a Depolarizing Quantum Channel, Relative Entropy and Classical Capacity
• Atemporal diagrams for quantum circuits
• Unital quantum operators on the Bloch ball and Bloch region
• Affine maps of density matrices
• Quantum operations that cannot be implemented using a small mixed environment
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Cited by in corpus (15)

• The resource theory of informational nonequilibrium in thermodynamics
• Characterizing quantum dynamics with initial system-environment correlations
• Generating random quantum channels
• Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry
• Simulation of non-Pauli Channels
• Quantum and classical resources for unitary design of open-system evolutions
• Geometry of the Pauli maps and Pauli channels
• On thermalization of two-level quantum systems
• Measure of positive and not completely positive single-qubit Pauli maps
• Log-Convex set of Lindblad semigroups acting on $N$-level system
• Geometry of generalized Pauli channels
• Amplitude Damping for single-qubit System with single-qubit mixed-state Environment
• How two spins can thermalize a third spin
• Geometry of symmetric and non-invertible Pauli channels
• Superclassical non-Markovian open quantum dynamics