Algorithmic cooling
A qubit (or quantum bit) is a unit of information that can be in a superposition of two states, denoted as formula_1 and formula_2. The general superposition can be written as formula_3where formula_4 and formula_5. If one measures the state of the qubit in the orthonormal basis composed of formula_1 and formula_2, one gets the result formula_1 with probability formula_9 and the result formula_2 with probability formula_11.
Bell state
In this example, Alice is trying to communicate two bits of classical information, one of four two bit strings: formula_13or formula_14. If Alice chooses to send the two bit message formula_15, she would perform the phase flip formula_16to her qubit. Similarly, if Alice wants to send formula_17, she would apply a CNOT gate; if she wanted to send formula_14, she would apply the formula_19gate to her qubit; and finally, if Alice wanted to send the to bit message formula_20, she would do nothing to her qubit. Alice performs these quantum gate transformations locally, transforming the initial entangled state formula_21 into one of the four Bell states.