[NCTS TG1.1 Seminar] Is quantum Shannon theory robust? An almost i.i.d. perspective
Title: [NCTS TG1.1 Seminar] Is quantum Shannon theory robust? An almost i.i.d. perspective
Speaker: Filippo Girardi (PhD Candidate, Scuola Normale Superiore)
Time: 2026/7/6 (Mon.) 10:30-11:30
Place: Rm. 307, 3F, Cosmology Hall, NTU
Abstract
The asymptotic rates of information-theoretic protocols – including error exponents, data-compression rates, and channel capacities – are traditionally derived under the idealised assumption that the underlying resources are independent and identically distributed (i.i.d.). Somewhat surprisingly, even slight departures from the exact i.i.d. structure can drastically alter the asymptotic behaviour predicted by the i.i.d. theory. If the precise nature of the perturbation is known, for instance in the case of a pointwise defect, one can design a bespoke protocol that compensates for it, e.g. by discarding the corrupted subsystem. In realistic physical settings, however, exact i.i.d. behaviour cannot be guaranteed, and deviations from the ideal regime cannot generally be identified precisely. This raises a fundamental question: which notions of almost i.i.d. structure are sufficiently robust to preserve the asymptotic predictions of quantum Shannon theory? We investigate this question for three central information-theoretic tasks: asymmetric hypothesis testing, classical and quantum data compression, and classical communication through quantum channels. Rather than designing protocols tailored to specific defects, we seek robust protocols that remain asymptotically optimal and that are universal within a broad class of almost i.i.d. resources whose precise deviations from the ideal regime are unknown. To this end, we study three inequivalent notions of almost i.i.d. structure, and determine which of them preserve the asymptotic rates and error exponents predicted by the i.i.d. theory.