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We consider distance functions on a quotient module $M/K$ induced by distance functions on a module $M$. We define error-correction for codes in $M/K$ with respect to induced distance functions. For the case that the metric is induced by a homogeneous weight, we derive analogues of the Plotkin and Elias-Bassalygo bounds and give their asymptot
We study the performance of quantum error correction codes(QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the most promi
Let m and n be any integers with n>m>=2. Using just the entropy function it is possible to define a partial order on S_mn (the symmetric group on mn letters) modulo a subgroup isomorphic to S_m x S_n. We explore this partial order in the case m=2, n=
We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault tolerant quantum error correcting circuit for a $d=3$ Steane and surface code. We find
Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of
A sort of planar tensor networks with tensor constraints is investigated as a model for holography. We study the greedy algorithm generated by tensor constraints and propose the notion of critical protection (CP) against the action of greedy algorith