The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography

Abstract

This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to derive a one-to-one relation between the spectra of a bipartite quantum state and its reduced states, and the Kronecker coefficients of the symmetric group. In the second part, the focus lies on the entanglement of bipartite quantum states. Drawing on an analogy between entanglement distillation and secret-key agreement in classical cryptography, a new entanglement measure, `squashed entanglement', is introduced.

arXiv commentPhD thesis, February 2006, University of Cambridge. Part I contains results from quant-ph/0409016 and quant-ph/0511029, and analyses Horn's problem in this context. Part II reviews entanglement measures, presents results from quant-ph/0308088 and quant-ph/0501090, and provides new material on entanglement measures, information-gain versus disturbance tradeoffs and cheat sensitive quantum string commitment

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• Computing finite-dimensional bipartite quantum separability
• Information vs. Disturbance in Dimension D

Cited by in corpus (56)

• Fundamental Limits of Repeaterless Quantum Communications
• General Benchmarks for Quantum Repeaters
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• Holographic Entanglement of Purification
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• Quantum conditional mutual information and approximate Markov chains
• Quantum Reverse Shannon Theorem
• Faithful Squashed Entanglement
• General paradigm for distilling classical key from quantum states
• Theory of channel simulation and bounds for private communication
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• Permutationally invariant state reconstruction
• The squashed entanglement of a quantum channel
• Correlation Detection and an Operational Interpretation of the Renyi Mutual Information
• Fundamental rate-loss tradeoff for the quantum internet
• Principles of Quantum Communication Theory: A Modern Approach
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• Fundamental limitation on quantum broadcast networks
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• Measuring Quantum Entropy
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• Squashed entanglement in infinite dimensions
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• Entanglement Theory and the Quantum Simulation of Many-Body Physics
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• Bell correlations at finite temperature
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• Optimality of the pretty good measurement for port-based teleportation
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• Converse bounds for quantum and private communication over Holevo-Werner channels
• Cryptography in a Quantum World
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• Complexity is not Enough for Randomness
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