Contractivity of positive and trace preserving maps under $L_p$ norms

Abstract

We provide a complete picture of contractivity of trace preserving positive maps with respect to $p$-norms. We show that for $p>1$ contractivity holds in general if and only if the map is unital. When the domain is restricted to the traceless subspace of Hermitian matrices, then contractivity is shown to hold in the case of qubits for arbitrary $p\ge 1$ and in the case of qutrits if and only if $p=1,\infty$. In all non-contractive cases best possible bounds on the $p$-norms are derived.

References in corpus (1)

• Entropy production rates of bistochastic strictly contractive quantum channels on a matrix algebra

Cited by in corpus (102)

• Quantifying Coherence
• Trace-distance measure of coherence
• Dividing Quantum Channels
• Sandwiched Rényi Divergence Satisfies Data Processing Inequality
• Maximal Coherence and the Resource Theory of Purity
• Randomized Benchmarking with Confidence
• Genuine quantum coherence
• The ${\chi }^2$-divergence and Mixing times of quantum Markov processes
• Collision model for non-Markovian quantum dynamics
• Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem
• Information preserving structures: A general framework for quantum zero-error information
• Temporal Information Processing on Noisy Quantum Computers
• Tight, robust, and feasible quantum speed limits for open dynamics
• Randomized benchmarking with gate-dependent noise
• Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
• Spectral conditions for positive maps
• On Hastings' counterexamples to the minimum output entropy additivity conjecture
• Geometric measures of quantum correlations: characterization, quantification, and comparison by distances and operations
• Necessity of Eigenstate Thermalization
• Quantum process reconstruction based on mutually unbiased basis
• Measures of coherence generating power for quantum unital operations
• A physical approach to Tsirelson's problem
• Quantum Zeno Dynamics from General Quantum Operations
• Bounding the average gate fidelity of composite channels using the unitarity
• Coherence measures with respect to general quantum measurements
• Learning Nonlinear Input-Output Maps with Dissipative Quantum Systems
• On the Contractivity of Hilbert-Schmidt distance under open system dynamics
• Practical Quantum Metrology in Noisy Environments
• Spectral convergence bounds for classical and quantum Markov processes
• Approximate Randomized Benchmarking for Finite Groups
• Scrambling of Algebras in Open Quantum Systems
• Multivariate trace estimation in constant quantum depth
• Quantum reservoir computing in finite dimensions
• A Holevo-type bound for a Hilbert Schmidt distance measure
• Continuity of the quantum Fisher information
• Random repeated quantum interactions and random invariant states
• Discord of response
• Efficient Unitarity Randomized Benchmarking of Few-qubit Clifford Gates
• Asymptotic evolution of quantum walks on the $N$-cycle subject to decoherence on both the coin and position degrees of freedom
• Progress towards a unified approach to entanglement distribution
• On limiting distributions of quantum Markov chains
• Eternal Adiabaticity
• Correlations enable lossless ergotropy transport
• Quantum causal correlations and non-Markovianity of quantum evolution
• Exponential Decay of Matrix $\Phi$-Entropies on Markov Semigroups with Applications to Dynamical Evolutions of Quantum Ensembles
• A polar decomposition for quantum channels (with applications to bounding error propagation in quantum circuits)
• Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and limit sets
• Uniqueness and Optimality of Dynamical Extensions of Divergences
• Hypercontractivity and the logarithmic Sobolev inequality for the completely bounded norm
• Hilbert-Schmidt quantum coherence in multi-qudit systems
• Fitting quantum noise models to tomography data
• There are many more positive maps than completely positive maps
• Limits of noisy quantum metrology with restricted quantum controls
• Generalized formalism for information backflow in assessing Markovianity and its equivalence to divisibility
• Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources
• Which Bath-Hamiltonians Matter for Thermal Operations?
• Discrete dynamics and non-Markovianity
• Characterizing coherence with quantum observables
• Construction of genuinely multipartite entangled subspaces and the associated bounds on entanglement measures for mixed states
• Robustness of Noether's principle: Maximal disconnects between conservation laws and symmetries in quantum theory
• Towards a general framework of Randomized Benchmarking incorporating non-Markovian Noise
• Group-covariant extreme and quasi-extreme channels
• Comparing randomized benchmarking figure with average infidelity of quantum gate-set
• Strict Positivity and $D$-Majorization
• Quantum data hiding in the presence of noise
• Matrix Product Density Operators: when do they have a local parent Hamiltonian?
• Noise-robust exploration of many-body quantum states on near-term quantum devices
• Optimization free measures of quantum resources
• In-situ Adaptive Encoding for Asymmetric Quantum Error Correcting Codes
• Non-monotonicity of trace distance under tensor products
• Reachable Sets from Toy Models to Controlled Markovian Quantum Systems
• Extremal elements of a sublattice of the majorization lattice and approximate majorization
• Efficient quantum algorithms for testing symmetries of open quantum systems
• Quantum-Dynamical Semigroups and the Church of the Larger Hilbert Space
• Finite-Dimensional Stinespring Curves Can Approximate Any Dynamics
• Geometric monotones of violations of quantum realism
• Non-classicalities via perturbing local unitary operations
• Tightening continuity bounds for entropies and bounds on quantum capacities
• GKSL Generators and Digraphs: Computing Invariant States
• Reachability in Controlled Markovian Quantum Systems: An Operator-Theoretic Approach
• Sequential Strong Measurements and Heat Vision
• Quantum Logspace Algorithm for Powering Matrices with Bounded Norm
• Limits on the Observable Dynamics of Mixed States
• Quantum distinguishability measures: projectors vs. states maximization
• Unitary-Scaling Decomposition and Dissipative Behaviour in Finite-Dimensional Linblad Dynamics
• Quantum Approximation of Normalized Schatten Norms and Applications to Learning
• SU(2)-equivariant quantum channels: semiclassical analysis
• Estimates of loss function concentration in noisy parametrized quantum circuits
• Adaptive random compiler for Hamiltonian simulation
• Potential output purity of completely positive maps
• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
• Quantum Finite Automata and Probabilistic Reversible Automata: R-trivial Idempotent Languages
• Super fidelity and related metric
• Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps
• A Spectral Lower Bound on Chromatic Numbers using $p$-Energy
• Characterization of preorders induced by positive maps in the set of Hermitian matrices
• A Shrinking Factor for Unitarily Invariant Norms under a Completely Positive Map
• Computing partial transposes and related entanglement functions
• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group
• On Ruelle transfer operators and completely positive maps
• A Small-Gain Theorem for Discrete-Time Convergent Systems and Its Applications
• Symmetry and Topology of Successive Quantum Feedback Control