Glossary: Difference between revisions

===Bloch Sphere===

In quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit). The Bloch sphere is a unit 2-sphere, with antipodal points corresponding to a pair of mutually orthogonal state vectors. The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors <math>|0\rangle</math>, <math>|1\rangle</math> respectively, which in turn might correspond e.g. to the spin-up and spin-down states of an electron. This choice is arbitrary, however. The points on the surface of the sphere correspond to the pure states of the system, whereas the interior points correspond to the mixed states.

===Quantum One Way Function===

* '''Classical To Quantum QOWF'''

#Easy to compute: The mapping <math>f : k\rightarrow |f_k\rangle</math> is easy to compute by a quantum polynomial-time algorithm.

#Hard to invert: Given <math>|f_k\rangle</math>, it is impossible to invert k by virtue of fundamental quantum information theory.

===Gate Teleportation===  

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This shows that for a pair of <math>\mathrm{CZ}</math> entangled qubits, if the second qubit is in <math>|+\rangle</math> state (not an eigen value of <math>\mathrm{Z}</math>) then one can teleport (transfer) the first qubit state operated by any unitary gate <math>\mathrm{U}</math> to the second qubit by performing operations only on the first qubit and measuring it. Next, we would need to make certain Pauli corrections (in this case <math>{\mathrm{X}}^{\mathrm{m}}</math>) to obtain <math>\mathrm{U}|\psi\rangle</math>. In other words, we can say the operated state is teleported to the second qubit by a rotated basis measurement of the first qubit with additional Pauli corrections.

===Graph states===