Erlangen 2018 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 46: Quantum Information (Concepts and Methods) IV

Q 46.6: Vortrag

Mittwoch, 7. März 2018, 15:15–15:30, K 1.019

Optimal catalytic quantum randomness — •Paul Boes, Henrik Wilming, Rodrigo Gallego, and Jens Eisert — Freie Universität Berlin

We investigate how much randomness is necessary to bring a system from one state to another state that is majorized by the initial one. We solve the problem completely by providing an optimal protocol showing that a maximally mixed state with dimension square-root of the system dimension is in general necessary and sufficient to implement such a state transition. The process we construct has the additional feature that the source of randomness is catalytic, i.e., remains in the maximally mixed state and can hence be re-used for different systems. We turn to considering several applications of this result, ranging from problems in decoherence and minimal measurement systems over scrambling of information to notions of cryptography. In particular, we introduce a novel cryptographic protocol, somewhat similar to superdense coding, with which two parties can communicate two classical bits securely over a public quantum channel of two qubits and a single private shared ebit. The protocol has the advantage that the ebit, after the two classical bits have been securely transmitted, returns exactly to its initial state and can be re-used to transmit further classical information securely. We also sketch how similar techniques can be used to establish a novel secret sharing scheme, where a given classical message can only be decoded if all parties of a given group consent. We complement the exact analysis of pinching maps with a discussion of approximate protocols based on quantum expanders.