quantum information theory Quantum information is the information of the quantum state, 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 re ...

, a quantum catalyst is an entanglement-assisted local quantum operations and classical communication, a special ancillary

quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...

whose presence enables certain local transformations that would otherwise be impossible. Quantum catalytic behaviour has been shown to arise from the phenomenon of catalytic

majorization In mathematics, majorization is a preorder on vectors of real numbers. Let ^_,\ i=1,\,\ldots,\,n denote the i-th largest element of the vector \mathbf\in\mathbb^n. Given \mathbf,\ \mathbf \in \mathbb^n, we say that \mathbf weakly majorizes (or ...

. The catalytic majorization relation can be used to find which transformations of jointly held pure quantum states are possible via local operations and classical communication (LOCC); particularly when an additional jointly held state is optionally specified to facilitate the transformation without being consumed. In the process sometimes referred to as entanglement catalysis, the catalyst can be understood as that temporarily involved entangled state. For bipartite pure entangled states that can be transformed in this way with unit probability, the respective Schmidt coefficients are said to satisfy the trumping relation, a mathematical relation which is an extension of the majorization relation. If correlations between the system and the catalyst are allowed, catalytic transformations between bipartite pure states are characterized via the

entanglement entropy The entropy of entanglement (or entanglement entropy) is a measure of the degree of quantum entanglement between two subsystems constituting a two-part composite quantum system. Given a pure bipartite quantum state of the composite system, it is pos ...

. Others have shown how quantum catalytic behaviour arises under a probabilistic approach via

stochastic dominance Stochastic dominance is a partial order between random variables. It is a form of stochastic ordering. The concept arises in decision theory and decision analysis in situations where one gamble (a probability distribution over possible outcomes, ...

with respect to the convolution of measures.

References

Quantum information science {{Quantum-stub