Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry

Abstract

Single-qubit channels are studied under two broad classes: amplitude damping channels and generalized depolarizing channels. A canonical derivation of the Kraus representation of the former, via the Choi isomorphism is presented for the general case of a system's interaction with a squeezed thermal bath. This isomorphism is also used to characterize the difference in the geometry and rank of these channel classes. Under the isomorphism, the degree of decoherence is quantified according to the mixedness or separability of the Choi matrix. Whereas the latter channels form a 3-simplex, the former channels do not form a convex set as seen from an ab initio perspective. Further, where the rank of generalized depolarizing channels can be any positive integer upto 4, that of amplitude damping ones is either 2 or 4. Various channel performance parameters are used to bring out the different influences of temperature and squeezing in dissipative channels. In particular, a noise range is identified where the distinguishability of states improves inspite of increasing decoherence due to environmental squeezing.

12 pages, 4 figures

References in corpus (5)

• Entanglement generated by dissipation and steady state entanglement of two macroscopic objects
• Completely Positive Maps and Classical Correlations
• The squeezed generalized amplitude damping channel
• Open system quantum dynamics with correlated initial states, not completely positive maps and non-Markovianity
• Geometric Phase of a qubit interacting with a squeezed-thermal bath

Cited by in corpus (34)

• Non-Markovian evolution: a quantum walk perspective
• Non-Markovian dephasing and depolarizing channels
• Temporal self-similarity of quantum dynamical maps as a concept of memorylessness
• Resource-efficient and fault-tolerant topological quantum computation with hybrid entanglement of light
• Facets of quantum information under non-Markovian evolution
• A comparative study of protocols for secure quantum communication under noisy environment: single-qubit-based protocols versus entangled-state-based protocols
• Quantum cryptography over non-Markovian channels
• Study of temporal quantum correlations in decohering B and K meson systems
• All-photonic architectural roadmap for scalable quantum computing using Greenberger-Horne-Zeilinger states
• Analysis of atmospheric effects on satellite based quantum communication: A comparative study
• Characterization of Unruh Channel in the context of Open Quantum Systems
• Characterization of quantum dynamics using quantum error correction
• Thermodynamics of one and two-qubit nonequilibrium heat engines running between squeezed thermal reservoirs
• Quantum Communication using Code Division Multiple Access Network
• Hierarchy of quantum correlations under non-Markovian dynamics
• Decoherence can help quantum cryptographic security
• Characterizing qubit channels in the context of quantum teleportation
• Quantum Fisher and Skew information for Unruh accelerated Dirac qubit
• Probing inequivalent forms of Legget-Garg inequality in subatomic systems
• Singularities, mixing and non-Markovianity of Pauli dynamical maps
• Virtual distillation with noise dilution
• Volume of the space of qubit-qubit channels and state transformations under random quantum channels
• Violation of Leggett-Garg type inequalities in a driven two level atom interacting with a squeezed thermal reservoir
• Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps
• A study of coherence based measure of quantumness in (non) Markovian channels
• The operator sum-difference representation for quantum maps: application to the two-qubit amplitude damping channel
• Quantum key distribution based on orthogonal state encoding
• Quantumness of channels
• Exploring the Non-Markovian Dynamics in Depolarizing Maps
• Quantum key distribution over noisy channels by the testing state method
• Husimi phase distribution in non-Gaussian operations
• Distinguishing environment-induced non-Markovianity from subsystem dynamics
• A study of the quasi-probability distributions of the Tavis-Cummings model under different quantum channels
• Projective measurements under qubit quantum channels