Twirled perfect tensor networks are introduced as a class satisfying computational covariance, bounding complexity by the Python's Lunch Conjecture exponent, and combining holographic features of perfect and random tensor networks including a lattice RT formula.
Absolutely max- imally entangled pure states of multipartite quantum systems
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abstract
Absolutely maximally entangled (AME) pure states of a system composed of $N$ parties are distinguished by the property that for any splitting at least one partial trace is maximally mixed. Due to maximal possible correlations between any two selected subsystems these states have numerous applications in various fields of quantum information processing including multi-user teleportation, quantum error correction and secret sharing. We present an updated survey of various techniques to generate such strongly entangled states, including those going beyond the standard construction of graph and stabilizer states. Our contribution includes, in particular, analysis of the degree of entanglement of reduced states obtained by partial trace of AME projectors, states obtained by a symmetric superposition of GHZ states, an orthogonal frequency square representation of the "golden" AME state and an updated summary of the number of local unitary equivalence classes.
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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.
LC-inequivalent graph-state blocks in random Clifford circuits yield distinct entanglement velocities v_E and butterfly velocities v_B, correlated with internal entanglement distribution and graph connectivity.
Quantum chaotic dynamics with positive entropy production universally links to von Neumann entropy and noise modeling in quantum information processing.
citing papers explorer
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Twirled Perfect Tensor Networks: Computationally covariant holographic tensor networks
Twirled perfect tensor networks are introduced as a class satisfying computational covariance, bounding complexity by the Python's Lunch Conjecture exponent, and combining holographic features of perfect and random tensor networks including a lattice RT formula.
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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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Graph-State Circuit Blocks control Entanglement and Scrambling Velocities
LC-inequivalent graph-state blocks in random Clifford circuits yield distinct entanglement velocities v_E and butterfly velocities v_B, correlated with internal entanglement distribution and graph connectivity.
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Quantum Chaos and Quantum Information: Interactions and Implications
Quantum chaotic dynamics with positive entropy production universally links to von Neumann entropy and noise modeling in quantum information processing.