# Mathematics Colloquia and Seminars

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### Capacity of Noisy Channels

**Mathematical Physics & Probability**

Speaker: | Prof. Mary Beth Ruskai, University of Massachusetts, Lowell & MSRI |

Location: | 493 Kerr |

Start time: | Tue, Dec 3 2002, 3:10PM |

Quantum particles can be used to transmit classical information typically encoding messages as strings of 0 and 1 represented by a pair of input states from a two-level quantum system or "qubit". as with classical communications, channels may have noise, a nd the capacity is a measure of the maximum information per bit that can be transmitted. The Holevo capacity measures the information per bit that can be transmitted through a memoryless channel when product inputs are used, but entangled measurements are permitted to determine the output. It is known that this can be strictly greater than the capacity restricted to product measurements and that in such cases, the optimal input states are generally not orthogonal. It is somewhat suprising that there are situations for which the optimal inputs are not a pair of states, but a triplet of non-orthogonal states. This does NOT mean that a single photon or spin 1/2 particle can be used to send information distinguishing between 3 possible inputs, but that more information can be transmitted using long strings when th eproduct inputs are chosen from among three states.