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- W4298154080 abstract "The general stable quantum memory unit is a hybrid consisting of a classical digit with a quantum digit (qudit) assigned to each classical state. The shape of the memory is the vector of sizes of these qudits, which may differ. We determine when N copies of a quantum memory A embed in N(1+o(1)) copies of another quantum memory B. This relationship captures the notion that B is as at least as useful as A for all purposes in the bulk limit. We show that the embeddings exist if and only if for all p >= 1, the p-norm of the shape of A does not exceed the p-norm of the shape of B. The log of the p-norm of the shape of A can be interpreted as the maximum of S(rho) + H(rho)/p (quantum entropy plus discounted classical entropy) taken over all mixed states rho on A. We also establish a noiseless coding theorem that justifies these entropies. The noiseless coding theorem and the bulk embedding theorem together say that either A blindly bulk-encodes into B with perfect fidelity, or A admits a state that does not visibly bulk-encode into B with high fidelity. In conclusion, the utility of a hybrid quantum memory is determined by its simultaneous capacity for classical and quantum entropy, which is not a finite list of numbers, but rather a convex region in the classical-quantum entropy plane." @default.
- W4298154080 created "2022-10-01" @default.
- W4298154080 creator A5031305513 @default.
- W4298154080 date "2002-03-20" @default.
- W4298154080 modified "2023-09-26" @default.
- W4298154080 title "The capacity of hybrid quantum memory" @default.
- W4298154080 doi "https://doi.org/10.48550/arxiv.quant-ph/0203105" @default.
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