Applications of coherent classical communication and the Schur transform to quantum information theory

Abstract

Quantum mechanics has led not only to new physical theories, but also a new understanding of information and computation. Quantum information began by yielding new methods for achieving classical tasks such as factoring and key distribution but also suggests a completely new set of quantum problems, such as sending quantum information over quantum channels or efficiently performing particular basis changes on a quantum computer. This thesis contributes two new, purely quantum, tools to quantum information theory--coherent classical communication in the first half and an efficient quantum circuit for the Schur transform in the second half.

176 pages. Chapters 1 and 4 are a slightly older version of quant-ph/0512015. Chapter 2 is quant-ph/0205057 plus unpublished extensions (slightly outdated by quant-ph/0511219) and chapter 3 is quant-ph/0307091, quant-ph/0412126 and change. Chapters 5-8 are based on quant-ph/0407082, but go much further

References in corpus (21)

• Coding Theorem and Strong Converse for Quantum Channels
• A Resource Framework for Quantum Shannon Theory
• Superdense coding of quantum states
• Classical and quantum communication without a shared reference frame
• Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
• Generalized remote state preparation: Trading cbits, qubits and ebits in quantum communication
• Relating quantum privacy and quantum coherence: an operational approach
• Quantum marginal problem and representations of the symmetric group
• Fault-Tolerant Postselected Quantum Computation: Schemes
• Decoherence-full subsystems and the cryptographic power of a private shared reference frame
• A geometric approach to quantum circuit lower bounds
• Decoherence, Control, and Symmetry in Quantum Computers
• Another subexponential-time quantum algorithm for the dihedral hidden subgroup problem
• Simultaneous classical-quantum capacities of quantum multiple access channels
• The Quantum Schur Transform: I. Efficient Qudit Circuits
• Relation between classical communication capacity and entanglement capability for two-qubit unitary operations
• Quantum searching a classical database (or how we learned to stop worrying and love the bomb)
• Relations for classical communication capacity and entanglement capability of two-qubit operations
• Inequalities and separations among assisted capacities of quantum channels
• Implementing high dimensional unitary representations of SU(2) on a Quantum Computer
• Universal distortion-free entanglement concentration

Cited by in corpus (40)

• Quantum conditional mutual information and approximate Markov chains
• Quantum Reverse Shannon Theorem
• Sample-optimal tomography of quantum states
• Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
• The Church of the Symmetric Subspace
• No-Signalling Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number
• Thermodynamic Capacity of Quantum Processes
• A Survey of Quantum Property Testing
• An efficient high dimensional quantum Schur transform
• Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
• Quantum Computation Beyond the Circuit Model
• Measuring Quantum Entropy
• On Composite Quantum Hypothesis Testing
• Defining quantum divergences via convex optimization
• Universal super-replication of unitary gates
• Matrix integrals over unitary groups: An application of Schur-Weyl duality
• Hypothesis Testing on Invariant Subspaces of the Symmetric Group, Part I - Quantum Sanov's Theorem and Arbitrarily Varying Sources
• Quantum simulation of partially distinguishable boson sampling
• Discriminating distinguishability
• On zero-error communication via quantum channels in the presence of noiseless feedback
• Bell correlations at finite temperature
• Testing symmetry on quantum computers
• The Classical-Quantum Channel with Random State Parameters Known to the Sender
• Optimality of the pretty good measurement for port-based teleportation
• Towards efficient decoding of classical-quantum polar codes
• Streaming quantum state purification
• Mixing indistinguishable systems leads to a quantum Gibbs paradox
• SnCQA: A hardware-efficient equivariant quantum convolutional circuit architecture
• A Classical Algorithm for Quantum $\text{SU}(2)$ Schur Sampling
• Approximate exchange-only entangling gates for the three-spin-$1/2$ decoherence-free subsystem
• A solution to two party typicality using representation theory of the symmetric group
• Quantum superreplication of states and gates
• Symmetric functions of qubits in an unknown basis
• How a Clebsch-Gordan Transform Helps to Solve the Heisenberg Hidden Subgroup Problem
• Universality of swap for qudits: a representation theory approach
• Quantum Spectrum Testing
• On some new hook-content identities
• Quantum Entanglement & Purity Testing: A Graph Zeta Function Perspective
• Compression for Qubit Clocks
• Testing identity of collections of quantum states: sample complexity analysis