Pauli Diagonal Channels Constant on Axes

Abstract

We define and study the properties of channels which are analogous to unital qubit channels in several ways. A full treatment can be given only when the dimension d is a prime power, in which case each of the (d+1) mutually unbiased bases (MUB) defines an axis. Along each axis the channel looks like a depolarizing channel, but the degree of depolarization depends on the axis. When d is not a prime power, some of our results still hold, particularly in the case of channels with one symmetry axis. We describe the convex structure of this class of channels and the subclass of entanglement breaking channels. We find new bound entangled states for d = 3. For these channels, we show that the multiplicativity conjecture for maximal output p-norm holds for p=2. We also find channels with behavior not exhibited by unital qubit channels, including two pairs of orthogonal bases with equal output entropy in the absence of symmetry. This provides new numerical evidence for the additivity of minimal output entropy.

References in corpus (12)

• Mixed State Entanglement and Quantum Error Correction
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• General Entanglement Breaking Channels
• Bound entanglement can be activated
• Largest separable balls around the maximally mixed bipartite quantum state
• Additivity for a class of unital qubit channels
• Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels
• Counterexample to an additivity conjecture for output purity of quantum channels
• Qubit Entanglement Breaking Channels
• A separability criterion for density operators
• Maximal output purity and capacity for asymmetric unital qudit channels
• Extending additivity from symmetric to asymmetric channels

Cited by in corpus (30)

• The structure of degradable quantum channels
• The geometry of bipartite qutrits including bound entanglement
• Detecting non-Markovianity of quantum evolution via spectra of dynamical maps
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• Mutually Unbiased Bases for Continuous Variables
• Mutually unbiased bases: tomography of spin states and star-product scheme
• Variations on a theme of Heisenberg, Pauli and Weyl
• Quantum channels irreducibly covariant with respect to the finite group generated by the Weyl operators
• Memory kernel approach to generalized Pauli channels: Markovian, semi-Markov, and beyond
• Classical capacity of the generalized Pauli channels
• Time deformations of master equations
• Realigning random states
• Absolutely separating quantum maps and channels
• Qudits of composite dimension, mutually unbiased bases and projective ring geometry
• Markovian semigroup from mixing non-invertible dynamical maps
• Engineering fidelity of the generalized Pauli channels via legitimate memory kernels
• Noninvertibility as a requirement for creating a semigroup under convex combinations of channels
• Measure of invertible dynamical maps under convex combinations of noninvertible dynamical maps
• Generalization of Pauli channels through mutually unbiased measurements
• Geometry of generalized Pauli channels
• Generalizations of $2$-dimensional diagonal quantum channels with constant Frobenius norm
• Engineering classical capacity of generalized Pauli channels with admissible memory kernels
• Regularized maximal fidelity of the generalized Pauli channels
• Enhancing phase-covariant channel performance with non-unitality
• Weyl channels for multipartite systems
• Two definitions of the Gell-Mann channels - a comparative analysis
• Spin polarization-scaling quantum maps and channels
• Pauli component erasing quantum channels
• Non-Markovianity of geometrical qudit decoherence
• Geometry of symmetric and non-invertible Pauli channels