1. Basic Q.C. One moose, two moose Red moose, blue moose Live moose, dead moose

2. A ‘qubit’ can be in an infinite number of states |Ψ> = a|0> + b|1> Probability of 0: |a|² Probability of 1: |b|² |a|² + |b|² = 1 Superposition States

3. “A full system of m qubits has a basis of 2 m states.”* A classical system of m bits can be set to any of these states. A quantum system can be set to all of those states at once. More on superposition states *Introduction to Quantum Computation and Information (Lo, Popescu, Spiller 2000)

4. Entanglement The states of qubits in a closed system are ‘entangled’. Consider a system of two qubits, A and B. |Ψ> AB = 2 -1/2 (|0> A |0> B + |1> A |1> B ) Cannot be written in factored form. The two qubits don’t have states of their own - they are ‘entangled.’

5. Reversible Unitary Evolution A.K.A. Reversibility For any truly closed quantum system, you can reverse the system and get back to the original state Works on paper, but not usually in theory.

6. Irreversibility, Measurement, Decoherence “[Irreversibility] has to be stopped from biting before some desired unitary quantum evolution of the system has been completed.”* In short, it has to work right or it won’t work right. *Introduction to Quantum Computation and Information (Lo, Popescu, Spiller 2000)

7. No Cloning No matter how hard you try, you can’t copy the state of a superpositioned quantum system. If you observe it to copy it, it collapses into a base state. This makes absolutely secure communication possible using a quantum media and the One- Time Pad, or Vernam’s Cipher