| quantum entanglement | |
|---|---|
| Name | Quantum entanglement |
| Field | Quantum mechanics |
| Introduced | 1935 |
| Notable people | Albert Einstein, Boris Podolsky, Nathan Rosen, Erwin Schrödinger, John Bell, John Stewart Bell |
| Related | Quantum information science, Quantum computing |
quantum entanglement
Quantum entanglement is a physical phenomenon in which the quantum states of two or more particles become correlated so that the state of each particle cannot be described independently of the others, even when the particles are separated by large distances. It is a central feature of Quantum mechanics and underlies many protocols in Quantum information science and Quantum computing. Entanglement challenges classical intuitions about locality and has practical implications for secure communication, metrology, and computation.
Quantum entanglement occurs when the joint wavefunction of a composite system is not factorable into a product of states for its subsystems, producing inseparable correlations in observables such as spin, polarization, or position and momentum. Formally, for a bipartite system with Hilbert spaces H_A and H_B, a pure state |ψ⟩ ∈ H_A ⊗ H_B is entangled if it cannot be written as |ψ_A⟩⊗|ψ_B⟩. Mixed-state entanglement is characterized by inseparability of the density operator ρ_AB. Entanglement is quantified by measures like Von Neumann entropy (for pure states), entanglement entropy, concurrence, and entanglement of formation. Its nonclassical correlations are resources in frameworks such as the resource theory of entanglement.
Entanglement was highlighted by Erwin Schrödinger in 1935 and critiqued in the famous EPR paradox paper by Albert Einstein, Boris Podolsky, and Nathan Rosen the same year. The conceptual tension between quantum predictions and classical locality led to formulations of testable inequalities by John Bell (see Bell's theorem). Pivotal experiments include those by John Clauser and Stuart Freedman (1972) and later decisive tests by Alain Aspect (1981–1982) that closed some loopholes in optical Bell tests. Recent experiments closed locality and detection loopholes simultaneously, notably at institutions like Delft University of Technology and laboratories such as NIST and University of Vienna's Institute for Quantum Optics and Quantum Information. Long-distance entanglement distribution has been demonstrated using optical fiber and satellite links, for example by the Micius (satellite) project led by Chinese institutions.
The formal description of entanglement uses the mathematics of Hilbert spaces, tensor products, and density matrix formalism. For pure bipartite states, the Schmidt decomposition provides a canonical form and a direct route to entanglement entropy S(ρ_A) = −Tr(ρ_A log ρ_A). For mixed states, separability criteria such as the Peres–Horodecki criterion (positive partial transpose) and entanglement witnesses are used. Quantitative measures include concurrence (Wootters), entanglement of formation, negativity, and logarithmic negativity. Multipartite entanglement introduces classes like GHZ state and W state with inequivalent entanglement structure. Theoretical resources link to quantum channel capacities, quantum error correction, and tasks in quantum cryptography.
Entanglement has been realized across many physical platforms. Photonic entanglement is routinely produced using spontaneous parametric down-conversion in nonlinear crystals and manipulated with integrated photonic circuits. Trapped ions in systems developed by groups at Institute for Quantum Optics and Quantum Information, Max Planck Institute, and commercial ventures like IonQ realize high-fidelity entangling gates. Superconducting qubits, advanced at IBM, Google Quantum AI, and Rigetti Computing, enable entanglement in microwave circuits. Solid-state platforms include nitrogen-vacancy centers in diamond, quantum dots, and atomic ensembles used in quantum memory experiments at institutions like Harvard University and Yale University. Hybrid systems and optomechanical devices explore macroscopic entanglement and transduction between degrees of freedom.
Entanglement is a foundational resource in protocols such as quantum teleportation, superdense coding, and entanglement-based quantum key distribution (e.g., the Ekert protocol). It enables quantum-enhanced sensing and metrology, exemplified by applications of NOON states and squeezed states for phase estimation approaching the Heisenberg limit. In Quantum computing, entanglement is central to algorithms like Shor's algorithm and Grover's algorithm and to model architectures including measurement-based quantum computation (cluster-state model). Quantum networks and repeaters rely on entanglement swapping and purification to extend entanglement across long distances, forming the basis for envisioned quantum internet projects and efforts by consortia such as the Quantum Internet Alliance.
Entanglement has deep implications for the interpretation of quantum theory and debates over realism and locality. Violations of Bell inequalitys demonstrate that no local hidden-variable theory can reproduce quantum predictions, challenging classical intuitions embodied in Einstein locality. Interpretations affected include the Copenhagen interpretation, Many-worlds interpretation, de Broglie–Bohm theory, and objective-collapse models where entanglement and measurement play divergent roles. Philosophers and physicists continue to analyze the nature of quantum correlations, the role of decoherence studied by researchers like Wojciech Zurek, and operational reconstructions of quantum theory from information-theoretic axioms developed in schools including Perimeter Institute and Institut d'Optique Graduate School. Experimental and theoretical progress continues to shape views on nonlocality, causality, and the resource character of entanglement in emergent quantum technologies.
Category:Quantum mechanics Category:Quantum information theory