Explicit convergence rates for noncommutative SOS hierarchies on the Pauli algebra are bounded using smallest roots of Krawtchouk polynomials.
SDP bounds on quantum codes
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The 14-qubit state Φ_E8 is entangled, certified by an explicit entanglement witness obtained as a rational infeasibility certificate for a semidefinite program that combines moment matrices with symmetric extension.
An updated review plus new results: a general negativity formula for reduced AME states and a frequency-square decomposition of the golden AME(4,6) state.
A quantum anonymous secret sharing scheme is constructed using permutation-invariant codes, with leakage in ramp schemes quantified by quantum conditional min-entropy related to Knill-Laflamme conditions.
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Convergence rates of Sum-of-Hermitian-Squares Hierarchies for the Pauli algebra
Explicit convergence rates for noncommutative SOS hierarchies on the Pauli algebra are bounded using smallest roots of Krawtchouk polynomials.
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Combining moment matrices, symmetric extension, and Lov\'asz theta: $\Phi_{\text{E8}}$ is entangled
The 14-qubit state Φ_E8 is entangled, certified by an explicit entanglement witness obtained as a rational infeasibility certificate for a semidefinite program that combines moment matrices with symmetric extension.
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Absolutely maximally entangled pure states of multipartite quantum systems
An updated review plus new results: a general negativity formula for reduced AME states and a frequency-square decomposition of the golden AME(4,6) state.
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Quantum Anonymous Secret Sharing with Permutation Invariant Codes
A quantum anonymous secret sharing scheme is constructed using permutation-invariant codes, with leakage in ramp schemes quantified by quantum conditional min-entropy related to Knill-Laflamme conditions.