Random isometries almost never approximate-mask into two subsystems, but almost always into many subsystems, with the number of physical qubits scaling linearly in the number of logical qubits.
Quantum coding theorem from privacy and distinguishability
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We prove direct quantum coding theorem for random quantum codes. The problem is separated into two parts: proof of distinguishability of codewords by receiver, and that of indistinguishability of codewords by environment (privacy). For a large class of codes, only privacy has to be checked.
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Random approximate quantum information masking
Random isometries almost never approximate-mask into two subsystems, but almost always into many subsystems, with the number of physical qubits scaling linearly in the number of logical qubits.