quantum error correcting codes has also led to the possibility of 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 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 Shannon entropy, called the von Neumann entropy. In some cases quantum algorithms 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 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 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 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. Do note that certain subtle points regarding the safety of QKD are still hotly debated. The study of all of the above topics and differences comprises quantum information theory. Relation to quantum mechanics Quantum mechanics is the study of how microscopic physical systems change dynamically in nature. In the field of quantum information theory, the quantum systems studied are abstracted away from any real world counterpart. A qubit might for instance physically be a photon in a linear optical quantum computer, an ion in a trapped ion quantum computer, or it might be a large collection of atoms as in a superconducting quantum computer. Regardless of