Dense network coding computes group operations over multiaccess networks with half the classical communication cost using shared entanglement plus quantum channels, and yields measurement-device-independent quantum key growing.
Group Representations, Error Bases and Quantum Codes
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abstract
This report continues the discussion of unitary error bases and quantum codes begun in "Non-binary Unitary Error Bases and Quantum Codes". Nice error bases are characterized in terms of the existence of certain characters in a group. A general construction for error bases which are non-abelian over the center is given. The method for obtaining codes due to Calderbank et al. is generalized and expressed purely in representation theoretic terms. The significance of the inertia subgroup both for constructing codes and obtaining the set of transversally implementable operations is demonstrated.
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Introduces hybrid Clifford codes by extending representation-theoretic quantum error correction to hybrid classical-quantum information and projective representations using the operator algebra framework.
This review compiles fourteen equivalent formulations of the open existence problem for maximal mutually unbiased bases in composite dimensions and summarizes known analytic, computer-aided and numerical results along with potential solution strategies.
citing papers explorer
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Communication Advantages from Quantum Dense Network Coding
Dense network coding computes group operations over multiaccess networks with half the classical communication cost using shared entanglement plus quantum channels, and yields measurement-device-independent quantum key growing.
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Hybrid Clifford Codes via Operator Algebra Quantum Error Correction and Projective Representation Theory
Introduces hybrid Clifford codes by extending representation-theoretic quantum error correction to hybrid classical-quantum information and projective representations using the operator algebra framework.
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Mutually Unbiased Bases in Composite Dimensions -- A Review
This review compiles fourteen equivalent formulations of the open existence problem for maximal mutually unbiased bases in composite dimensions and summarizes known analytic, computer-aided and numerical results along with potential solution strategies.