Editing Quantum information (section)

== Quantum information processing ==
The state of a qubit contains all of its information. This state is frequently expressed as a vector on the Bloch sphere. This state can be changed by applying [[linear transformation]]s or [[quantum gate]]s to them. These [[unitary transformation (quantum mechanics)|unitary transformations]] are described as rotations on the Bloch sphere. While classical gates correspond to the familiar operations of [[Boolean Logic|Boolean logic]], quantum gates are physical [[unitary operator]]s.

* Due to the volatility of quantum systems and the impossibility of copying states, the storing of quantum information is much more difficult than storing classical information. Nevertheless, with the use of [[quantum error correction]] quantum information can still be reliably stored in principle. The existence of quantum error correcting codes has also led to the possibility of [[fault tolerance|fault-tolerant]] [[quantum computation]].
* Classical bits can be encoded into and subsequently retrieved from configurations of qubits, through the use of quantum gates. By itself, a single qubit can convey no more than one bit of accessible classical information about its preparation. This is [[Holevo's theorem]]. However, in [[superdense coding]] a sender, by acting on one of two [[quantum entanglement|entangled]] qubits, can convey two bits of accessible information about their joint state to a receiver.
* Quantum information can be moved about, in a [[quantum channel]], analogous to the concept of a classical [[communications channel]]. Quantum messages have a finite size, measured in qubits; quantum channels have a finite [[channel capacity]], measured in qubits per second.
* Quantum information, and changes in quantum information, can be quantitatively measured by using an analogue of [[Claude Shannon|Shannon]] [[information entropy|entropy]], called the von Neumann entropy.
* In some cases, [[quantum algorithm]]s can be used to perform computations faster than in any known classical algorithm. The most famous example of this is [[Shor's algorithm]] that can factor numbers in polynomial time, compared to the best classical algorithms that take sub-exponential time. As factorization is an important part of the safety of [[RSA (cryptosystem)|RSA encryption]], Shor's algorithm sparked the new field of [[post-quantum cryptography]] that tries to find encryption schemes that remain safe even when quantum computers are in play. Other examples of algorithms that demonstrate [[quantum supremacy]] include [[Grover's algorithm|Grover's search algorithm]], where the quantum algorithm gives a quadratic speed-up over the best possible classical algorithm. The [[complexity class]] of problems efficiently solvable by a [[Quantum Computer|quantum computer]] is known as [[BQP]].
*[[Quantum key distribution]] (QKD) allows unconditionally secure transmission of classical information, unlike classical encryption, which can always be broken in principle, if not in practice. Note that certain subtle points regarding the safety of QKD are debated.

The study of the above topics and differences comprises quantum information theory.