Location
M3 4206
Candidate
Rabsan Galib Ahmed | Applied Mathematics, University of Waterloo
Title
Fractional Extendibility of Quantum States and Channels
Abstract
Quantum correlation is known to be monogamous, so if it is shared among more than two parties, the correlation between any pair cannot be very strong. In this spirit, the (integer) extendibility of a quantum channel quantifies the strength of quantum correlation between the sender and the receiver by measuring how many parties in the environment can simulate the output at the receiver’s end. Some convenient properties of extendibility include invariance under multiple uses and monotonicity under pre- and post-processing, which impose strong limits on information-processing tasks involving channels and states with certain extendibility. However, such a characterization appears too crude to distinguish between channels that are expected to have a clear ordering in their noise. In this talk, we introduce a notion of fractional extendibility and establish it as a refined quantification of how much quantum correlation leaks into the environment. Furthermore, we show that this finer notion of extendibility shares the desired properties as the integer extendibility. We demonstrate the application of fractional extendibility by solving two long-standing open problems in quantum information theory: (1) Hastings’ problem on channel simulation: Can many uses of an erasure channel with erasure probability q, with arbitrary encoding and decoding, simulate an erasure channel with erasure probability p, where q>p>=0.5?(2) Gaussian repeaters in forward quantum communication: Can a general Gaussian repeater protocol enhance the rate of forward quantum communication over a pure-loss attenuation channel? We expect this formalism to find more applications in the future