A quantum computer is a computation device that makes direct use
of quantum-mechanical phenomena, such as superposition and
entanglement, to perform operations on data.
Why Quantum Computation?
● No limitations on computation imposed by the extended Church-
● Random number
● No cloning
● Quantum teleportation
● Non-locality (entanglement)
What is Quantum Computation?
Qubits (or quantum bit)
The basic entity of quantum information (analogue of the bit for
Sfera di Bloch
Curiosity: how many information can be
stored by a qubit?
Exactly 2, like a classical bit
Can we say what the state of each of
the individual qubits is? NO: entanglement!
Bell's states (or EPR pairs)
maximally entangled states of two
EPR Paradox (1935)
Can quantum mechanics
Einstein Podolsky Rosen
1. Physics reality
There exist local hidden variables!
Bell's Inequality (1964)
(experimentally Aspect and co-workers, 1981)
“There does not exist any local
hidden variable theory consistent
with outcomes of quantum physics”
● Entanglement is not paradossal
● Quantum correlations in an EPR pair are
“stronger” than classical correlations
Example: more efficient information
processing by use of shared entanglement
Recall (superpositional principle and rotation matrix)
In general, rotation of a state
by an angle in the two-dimensional state space gives the rotaded state
Hence the probability of measuring a 0 for the rotated state is given by
With Quantum Computer you can win more often!
YOU WIN 85% OF THE TIMES
- Paradosso EPR
- Teoria delle variabili nascoste
- Teorema di Bell
- Entanglement quantistico
- Notazione bra-ket
- Informatica quantistica
- Ampiezza di probabilità
● Introduction, Axioms, Bell Inequalities (Lecture 1, Spring 2007,
● Qubit gates and EPR (Lecture 5, Fall 2007, C/CS/Phys C191)
● Entanglement can facilitate information processing (Lecture 5,
Fall 2005, C/CS/Phys C191)
About the course
Very interesting course, in many respects. These
activities improve people and institutions. I hope it will
be the first of many others.
About Quantum Computation
I think that the current paradoxes about quantum
mechanics are comparable to Zenone's paradoxes.
One day, perhaps, all things will be clearer.
“God does not throw dice”
But we really love doing it!