Entanglementpartners

Entanglementpartners is a descriptive term used to refer to the subsystems of a quantum system that share quantum entanglement with one another. In a bipartite system described by a state in the Hilbert space H_A ⊗ H_B, the subsystems A and B are entanglement partners. In multipartite systems, an entanglement partner for a given subsystem is any other subsystem that exhibits nonclassical correlations with it, although the entanglement structure can be more complex than a single pair.

Identification and measurement: Determining whether two subsystems are entanglementpartners involves examining the joint state and its reductions. If the global state is not a product state, entanglement is present between the parties. Entanglement can be characterized and quantified using measures such as entanglement entropy obtained from Schmidt decomposition, concurrence, negativity, or more general multipartite criteria. The Peres–Horodecki criterion (PPT) and related tests may be used to detect entanglement in mixed states.

Examples: The Bell state |Φ+⟩ = (|00⟩ + |11⟩)/√2 has A and B as clear entanglement partners, with maximal entanglement. In a three-party GHZ state (|000⟩ + |111⟩)/√2, each pair of subsystems exhibits correlations that reflect entanglement with the rest of the system, illustrating more intricate partner relations in multipartite settings.

Applications: Entanglementpartners form the links in quantum networks and protocols such as quantum teleportation, superdense coding, and entanglement swapping, where entangled subsystems enable nonclassical communication and information processing between distant parties.

See also: quantum entanglement, bipartite entanglement, multipartite entanglement, Schmidt decomposition, entanglement measures.