Comments on Hastings' additivity counterexamples

DOI10.1007/s00220-010-0996-9zbMath1194.81037arXiv0905.3697OpenAlexW1965633412WikidataQ124817760 ScholiaQ124817760MaRDI QIDQ982455

Motohisa Fukuda, David K. Moser, Christopher K. King

Publication date: 6 July 2010

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.3697

zbMATH Keywords

quantum information theorytensor productquantum channeladditivity conjectureminimal output entropy

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Spaces of operators; tensor products; approximation properties (46B28) Communication, information (94A99) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items

On the extreme points of quantum channels ⋮ Gaussian optimizers and the additivity problem in quantum information theory ⋮ Almost one bit violation for the additivity of the minimum output entropy ⋮ Additivity violation of the regularized minimum output entropy ⋮ The minimum Rényi entropy output of a quantum channel is locally additive ⋮ Random quantum channels. II: Entanglement of random subspaces, Rényi entropy estimates and additivity problems ⋮ Additivity violation of quantum channels via strong convergence to semi-circular and circular elements ⋮ Gelfand-Tsetlin polytopes and random contractions away from the limiting shape ⋮ Hastings's additivity counterexample via Dvoretzky's theorem ⋮ Revisiting additivity violation of quantum channels ⋮ Channel capacities via \( p\)-summing norms ⋮ Asymptotically well-behaved input states do not violate additivity for conjugate pairs of random quantum channels ⋮ LOW ENTROPY OUTPUT STATES FOR PRODUCTS OF RANDOM UNITARY CHANNELS ⋮ Gaussianization and eigenvalue statistics for random quantum channels. III ⋮ Random matrix techniques in quantum information theory ⋮ Estimates for compression norms and additivity violation in quantum information ⋮ Nonadditivity of Rényi entropy and Dvoretzky’s theorem ⋮ Entanglement of random subspaces via the Hastings bound ⋮ Towards a state minimizing the output entropy of a tensor product of random quantum channels ⋮ ENTANGLEMENT AND ITS MULTIPARTITE EXTENSIONS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Remark on the additivity conjecture for a quantum depolarizing channel
• Equivalence of additivity questions in quantum information theory
• Aspects of generic entanglement
• Additivity of the capacity of depolarizing channels
• Simplification of additivity conjecture in quantum information theory
• Multiplicativity properties of entrywise positive maps
• Counterexamples to the maximal \(p\)-norm multiplicativity conjecture for all \(p>1\)
• Counterexamples to additivity of minimum output \(p\)-Rényi entropy for \(p\) close to 0
• Induced measures in the space of mixed quantum states
• Simplifying additivity problems using direct sum constructions
• The capacity of the quantum channel with general signal states
• Average entropy of a subsystem
• Minimal entropy of states emerging from noisy quantum channels
• The capacity of the quantum depolarizing channel
• Counterexample to an additivity conjecture for output purity of quantum channels
• Additivity for unital qubit channels
• On the additivity conjecture in quantum information theory