entanglementin

Entanglementin is not a standard term in physics; the content below describes quantum entanglement, which is the phenomenon likely meant by the phrase.

Quantum entanglement is a property of composite systems in which the joint state cannot be factored into independent states of its parts. In an entangled state, measurements performed on one subsystem influence the outcomes on another, even when the systems are separated by large distances. The concept emerged in discussions of the Einstein-Podolsky-Rosen paradox (1935) and was formalized through Bell’s theorem (1964), which showed that entanglement leads to correlations that cannot be explained by local hidden variables. Experimental tests of Bell inequalities have repeatedly supported quantum predictions, though practical implementations must address loopholes.

Mathematically, entanglement is most clearly described using density matrices and the tensor product structure of Hilbert spaces. Pure bipartite states can be expressed via Schmidt decomposition; entanglement exists when the reduced state of a subsystem is mixed. For mixed states, several measures—such as entanglement entropy, concurrence, and negativity—quantify the degree of entanglement. Entanglement can be classified as bipartite or multipartite, with increasing complexity in multipartite cases.

Entanglement is a fundamental resource in quantum information science. It enables quantum teleportation, where a quantum state is transferred using entangled pairs and classical communication; superdense coding, which transmits two classical bits by sending one qubit; and various quantum cryptography protocols. It is also central to quantum computing and quantum metrology, where entangled states can provide computational advantages and enhanced measurement precision.

Challenges include maintaining entanglement in open systems, counteracting decoherence, and distributing entangled states over long distances.