The five-cycle graph state |C5> is the unique (up to local Clifford) 1-resistant five-qubit stabilizer state; no seven-qubit stabilizer state is m-resistant for nonzero admissible m.
Absolutely Maximally Entangled Qudit Graph States
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Absolutely maximally entangled (AME) states are multipartite entangled states that are maximally entangled for any possible bipartition. In this paper, we study the description of AME states within the graph state formalism. The graphical representation provides an intuitive framework to visualize the entanglement in graph states, which makes them a natural candidate to describe AME states. We show two different methods of determining bipartite entanglement in graph states and use them to define various AME graph states. We further show that AME graph states exist for all number of parties, and that any AME graph states shared between an even number of parties can be used to describe quantum secret sharing schemes with a threshold or ramp access structure directly within the graph states formalism.
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Stabilizer AME states do not exist for N=4n qudits of even local dimension d; optimal mixed AME states of purity 1/2 exist for d=6.
Graph-restricted tensors generalize 1-uniform states, dual-unitary operators and AME states, with exact analytic solutions for new examples motivated by holographic lattice models.
Entanglement purity in quadratic-phase states over finite fields is exactly determined by the rank of the phase matrix, with AME states existing precisely when all bipartition submatrices have full rank.
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.
The thesis compiles applications of maximal entanglement in quantum information and claims it constrains the QED vertex to predict a weak mixing angle near the measured value.
Review summarizing how dual-unitary circuits provide exact solvability for quantum many-body dynamics through space-time duality.
citing papers explorer
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A five-qubit 1-resistant graph state and stabilizer marginal certificates
The five-cycle graph state |C5> is the unique (up to local Clifford) 1-resistant five-qubit stabilizer state; no seven-qubit stabilizer state is m-resistant for nonzero admissible m.
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On Non-Existence of Stabilizer Absolutely Maximally Entangled States in Even Local Dimensions
Stabilizer AME states do not exist for N=4n qudits of even local dimension d; optimal mixed AME states of purity 1/2 exist for d=6.
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Graph restricted tensors: building blocks for holographic networks
Graph-restricted tensors generalize 1-uniform states, dual-unitary operators and AME states, with exact analytic solutions for new examples motivated by holographic lattice models.
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Entanglement-Rank Duality in Quadratic Phase Quantum States
Entanglement purity in quadratic-phase states over finite fields is exactly determined by the rank of the phase matrix, with AME states existing precisely when all bipartition submatrices have full rank.
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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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Maximal Entanglement: Applications in Quantum Information and Particle Physics
The thesis compiles applications of maximal entanglement in quantum information and claims it constrains the QED vertex to predict a weak mixing angle near the measured value.
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Exactly solvable many-body dynamics from space-time duality
Review summarizing how dual-unitary circuits provide exact solvability for quantum many-body dynamics through space-time duality.