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

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arxiv quant-ph/0604183 v1 pith:FGBURGSU submitted 2006-04-25 quant-ph

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keywords quantumstatesbipartiteentanglementcryptographygrouppartspectra
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Scaling Quantum Algorithms via Dissipation: Avoiding Barren Plateaus

    quant-ph 2025-07 conditional novelty 6.0 of 10

    Dissipative quantum circuits with periodic qubit resets provably avoid both unitary and noise-induced barren plateaus for gates near the final measurement.

  2. Bounds on quantum conference key agreement in pair-entangled networks

    quant-ph 2026-05 unverdicted novelty 5.0 of 10

    Upper bounds on distillable conference key in pair-entangled networks are derived depending on topology and entanglement, with tightness proven and optimality of pairwise distillation plus merging shown for specific cases.

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