Schur-Weyl duality for the Clifford group with applications: property testing, a robust Hudson theorem, and de Finetti representations
DOI10.1007/s00220-021-04118-7zbMath1468.81021arXiv1712.08628OpenAlexW2780472999MaRDI QIDQ2041634
Sepehr Nezami, Michael Walter, David J. Gross
Publication date: 23 July 2021
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.08628
Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Quantum stochastic calculus (81S25) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Reliability, testing and fault tolerance of networks and computer systems (68M15) Tensor products in functional analysis (46M05) Quadratic spaces; Clifford algebras (11E88) General theory for finite permutation groups (20B05) Quantum information, communication, networks (quantum-theoretic aspects) (81P45) Matrix models and tensor models for quantum field theory (81T32) Computational stability and error-correcting codes for quantum computation and communication processing (81P73)
Related Items (6)
Cites Work
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- The spectra of quantum states and the Kronecker coefficients of the symmetric group
- Aspects of generic entanglement
- Nonzero Kronecker coefficients and what they tell us about spectra
- Averaging sets: A generalization of mean values and spherical designs
- A de Finetti-type theorem with m-dependent states
- Finite exchangeable sequences
- Holographic duality from random tensor networks
- Small representations of finite classical groups
- Quantum spectrum testing
- Self-dual codes and invariant theory
- Quantum de Finetti theorems under local measurements with applications
- One-and-a-half quantum de Finetti theorems
- Symmetric states of infinite tensor products of \(C^ *\)-algebras
- An ideal characterization of the Clifford operators
- Invariants of the local Clifford group
- Finite de Finetti Theorem for Infinite-Dimensional Systems
- Multiple-particle interference and quantum error correction
- The resource theory of stabilizer quantum computation
- Rank-deficient representations in the theta correspondence over finite fields arise from quantum codes
- Symmetric informationally complete–positive operator valued measures and the extended Clifford group
- A de Finetti representation for finite symmetric quantum states
- Hudson’s theorem for finite-dimensional quantum systems
- SECURITY OF QUANTUM KEY DISTRIBUTION
- Quantum Property Testing
- Quantum Margulis expanders
- The Finite Simple Groups
- A most compendious and facile quantum de Finetti theorem
- Witt's Extension Theorem for mod Four Valued Quadratic Forms
- Locally normal symmetric states and an analogue of de Finetti's theorem
- Quantum cryptography based on Bell’s theorem
- Error Correcting Codes in Quantum Theory
- Representations of the multi-qubit Clifford group
- Sample-optimal tomography of quantum states
- SU(p,q) coherent states and a Gaussian de Finetti theorem
- Unknown quantum states: The quantum de Finetti representation
- Efficient quantum tomography II
- Negative quasi-probability as a resource for quantum computation
- On the Power of the PPT Constraint in the Symmetric Extensions Test for Separability
- Efficient quantum tomography
- Stabilizer information inequalities from phase space distributions
- A quasipolynomial-time algorithm for the quantum separability problem
- Quantum de finetti theorems under local measurements with applications
- An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups
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