The decoupling approach to quantum information theory

Abstract

Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and have as corollaries entanglement-assisted and unassisted asymptotic coding theorems. The entanglement-assisted asymptotic versions can, in both cases, be considered as quantum versions of the best coding theorems known for the classical versions of these problems. The last chapter deals with a purely quantum phenomenon called locking. We demonstrate that it is possible to encode a classical message into a quantum state such that, by removing a subsystem of logarithmic size with respect to its total size, no measurement can have significant correlations with the message. The message is therefore "locked" by a logarithmic-size key. This thesis presents the first locking protocol for which the success criterion is that the trace distance between the joint distribution of the message and the measurement result and the product of their marginals be sufficiently small.

PhD Thesis, Université de Montréal, defended December 2009. 133 pages.

References in corpus (27)

• Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
• The capacity of the noisy quantum channel
• The operational meaning of min- and max-entropy
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• On the quantum, classical and total amount of correlations in a quantum state
• Superadditivity of communication capacity using entangled inputs
• "Squashed Entanglement" - An Additive Entanglement Measure
• Randomizing quantum states: Constructions and applications
• Quantum Communication With Zero-Capacity Channels
• The mother of all protocols: Restructuring quantum information's family tree
• Duality Between Smooth Min- and Max-Entropies
• Locking classical correlation in quantum states
• A Resource Framework for Quantum Shannon Theory
• The quantum capacity of channels with arbitrarily correlated noise
• A decoupling approach to the quantum capacity
• Entanglement of assistance and multipartite state distillation
• The exact cost of redistributing multipartite quantum states
• Quantum network communication -- the butterfly and beyond
• Quantum Network Coding
• A family of quantum protocols
• Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions
• Quantum broadcast channels
• A father protocol for quantum broadcast channels
• Quantum entropic security and approximate quantum encryption
• Coding for quantum channels with side information at the transmitter
• Multiple-Input Multiple-Output Gaussian Broadcast Channels with Confidential Messages
• Classical Information Capacity of the Bosonic Broadcast Channel

Cited by in corpus (44)

• The thermodynamic meaning of negative entropy
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• One-shot decoupling
• Chain Rules for Smooth Min- and Max-Entropies
• Decoupling with random quantum circuits
• Entanglement sampling and applications
• One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach
• Quantum message compression with applications
• Principles of Quantum Communication Theory: A Modern Approach
• Quantum Coding with Finite Resources
• An equality between entanglement and uncertainty
• Decoupling with unitary approximate two-designs
• The apex of the family tree of protocols: Optimal rates and resource inequalities
• One-shot entanglement-assisted quantum and classical communication
• Black Holes: Eliminating Information or Illuminating New Physics?
• Generalized Entropies
• Scrambling speed of random quantum circuits
• The Smooth Entropy Formalism for von Neumann Algebras
• From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking
• Entanglement Wedge Reconstruction and the Information Paradox
• Relative Thermalization
• Chain rules for quantum Rényi entropies
• One-shot holography
• Quantum Broadcast Channels with Cooperating Decoders: An Information-Theoretic Perspective on Quantum Repeaters
• A toy model for decoherence in the black hole information problem
• On the near-optimality of one-shot classical communication over quantum channels
• One-shot decoupling and Page curves from a dynamical model for black hole evaporation
• Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations
• One-shot quantum error correction of classical and quantum information
• Decoupling with random diagonal unitaries
• The black hole information puzzle and the quantum de Finetti theorem
• Quantum Causal Structure and Quantum Thermodynamics
• Information transmission with continuous variable quantum erasure channels
• Quantum Polarization of Qudit Channels
• "Pretty strong" converse for the private capacity of degraded quantum wiretap channels
• Novel one-shot inner bounds for unassisted fully quantum channels via rate splitting
• Strong converse for the quantum capacity of the erasure channel for almost all codes
• Asymptotic Compressibility of Entanglement and Classical Communication in Distributed Quantum Computation
• Converse bounds for classical communication over quantum networks
• High probability decoupling via approximate unitary designs and efficient relative thermalisation
• Random coding exponents galore via decoupling
• One-shot multi-sender decoupling and simultaneous decoding for the quantum MAC
• Hacking Quantum Networks: Extraction and Installation of Quantum Data
• Rényi divergence inequalities via interpolation, with applications to generalised entropic uncertainty relations