Department of Computer Science Seminars
### A Mathematical Model for Quantum Communication

###
Speaker: R.D. Ogden

### Time: 12:30pm-1:30pm, September 30th 2005

### Location: Neuces Conference Room

## Abstract:

Quantum computation is conventionally modelled by quantum circuits acting on states modelled as qubits of length N in a 2N-dimensional state space, where N is the fixed number of bits involved in the computation. There are models
for quantum state entropy and the formulation and description of important
error-correcting codes necessary for a quantum computer to sustain an
N-qubit for a reasonable time period.
But communication of binary messages of arbitrary length requires an
infinite-dimensional space, quantum message space, which also allows for
serial message generation starting from an empty-string state.
Quantum message space helps Alice (the traditional sender) send a mesage to
Bob (traditional receiver) as a qubit of arbitrary length unknown to Bob
in advance. It enables us to formulate and answer questions such as :
>>>How does Alice compose a message of arbitrary length as a qubit of the same length?
>>>Alternatively, how does she sample a source for the message?
>>>How should she encode her message (assuming she knows the dyamics of the quantum transmission and the "noise" distribution) to get more faithful reception?
>>>What does Bob do to receive the message? How likely is the message he receives to be the one he was sent?
Finally, we speculate about the possible physical realization of quantum message space.