# Quantum information

**Quantum information** is information that is held in the "state" of a quantum system. The most popular unit of quantum information is the

qubit, a two-state quantum system. However, unlike classical digital states (which are discrete), a two-state quantum system can actually be in a superposition of the two states at any given time. So in reality, the quantum system has an infinite number of possible states.

Quantum information differs from classical information in several respects, among which we note the following:

- it cannot generally be read or duplicated without disturbance (no cloning theorem)
- it can exist in superpositions of different values; quantum information is exponentially more efficient than classical one, as one state can exist in superposition of all possible states at once.
- quantum information is probabilistic in nature.

The ability to manipulate quantum information enables us to perform tasks that would be unachievable in a classical context, such as unconditionally secure transmission of information.

Quantum information processing is the most general field that is concerned with quantum information. There are certain

algorithms and tasks which classical

computers cannot perform "efficiently" (ie. they cannot do it in less than O(a^N) time, which is more than any polynomial, including the quantum). However, a quantum computer can perform some of these algorithms in polynomial time. Examples of these include Shor's factoring algorithm and Grover's search algorithm. However, this has nothing to do with the quantum information

*per se*.

## Shannon entropy

The Shannon entropy of a

quantum ensemble with the

density matrix ρ is given by -Tr[ρln(ρ)].

D-Wave Systems - D-Wave is "the" quantum computing company. Based out of Vancouver, British Columbia, they are currently the only company in the world pursuing the development of quantum computing hardware and software.