quantum information theory Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both ...

, quantum state merging is the transfer of a quantum state when the receiver already has part of the state. The process optimally transfers partial information using entanglement and classical communication. It allows for sending information using an amount of entanglement given by the

conditional quantum entropy The conditional quantum entropy is an entropy measure used in quantum information theory. It is a generalization of the conditional entropy of classical information theory. For a bipartite state \rho^, the conditional entropy is written S(A, B)_ ...

H(A, B)\,=\,H(AB)-H(B) \, .

with

H(A)

the

Von Neumann entropy In physics, the von Neumann entropy, named after John von Neumann, is an extension of the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics. For a quantum-mechanical system described by a density mat ...

H(A):=-Tr\rho_A\log\rho_A

. It thus provides an operational meaning to this quantity. Unlike its classical counterpart, the quantum conditional entropy can be negative. In this case, the sender can transfer the state to the receiver using no entanglement, and as an added bonus, this amount of entanglement can be gained, rather than used. Thus quantum information can be negative. The amount of classical information needed is the

mutual information In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the " amount of information" (in units such as ...

I(A:R):=H(A)+H(R)-H(AR)

. The case where the classical communication is replaced by quantum communication was considered in. This is known as the Fully Quantum Slepian-Wolf Theorem, since everything is sent down the

quantum channel In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit. An example of classical information i ...

. A single-shot version of state merging was found by Berta, and a multiparty single shot version was found in. The

quantum discord In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entangle ...

has been interpreted using state merging.

References

{{reflist Quantum information science