| entanglement | |
|---|---|
| Name | Quantum entanglement |
| Field | Quantum mechanics |
| Discovered | 1935 |
| Discoverers | Albert Einstein (criticism), Boris Podolsky (criticism), Nathan Rosen (criticism); formal development by Erwin Schrödinger |
| Notable experiments | Aspect experiments, Bell test experiments |
entanglement
Entanglement is a quantum mechanical phenomenon in which the quantum states of two or more particles become correlated such that the state of each particle cannot be described independently of the state of the others, even when separated by large distances. It is central to Quantum information science and underpins technologies like quantum computing, quantum cryptography, and quantum teleportation. Entanglement challenges classical intuitions about locality and causality and plays a foundational role in debates about the interpretation of Quantum mechanics.
In quantum theory, a composite system is entangled when its state is not expressible as a tensor product of subsystem states but rather as a superposition of such products. For two subsystems A and B with Hilbert spaces H_A and H_B, a pure state |ψ⟩∈H_A⊗H_B is entangled if there exist no |φ⟩_A and |χ⟩_B with |ψ⟩=|φ⟩_A⊗|χ⟩_B. Entanglement leads to nonclassical correlations measurable by joint observables and statistical dependencies that violate classical bounds like those expressed by Bell's theorem and Bell test experiments. Mixed-state entanglement is detected via criteria such as the Peres–Horodecki criterion (positive partial transpose). Key concepts include quantum superposition, quantum correlation, and subsystem reduced density matrix.
The phenomenon was discussed explicitly by Erwin Schrödinger in response to the EPR paper by Albert Einstein, Boris Podolsky, and Nathan Rosen (1935). Schrödinger coined the term "Verschränkung" (entanglement) and emphasized its puzzling nonlocal features. Foundational theoretical advances included John Bell's 1964 inequalities showing experimentally testable distinctions between local hidden-variable theories and quantum mechanics. Landmark experimental tests were performed by Alain Aspect in the 1980s; later loophole-free Bell test experiments were conducted by groups such as those led by Anton Zeilinger, John Clauser, and Hideo Mabuchi's collaborators, culminating in definitive tests by teams including Saul Perlmutter? (note: experimental teams at NIST and Delft University). The growth of quantum information theory in the 1990s and 2000s, driven by figures like Charles H. Bennett and Peter Shor, broadened interest in entanglement as a resource.
Entanglement is formalized using the language of Hilbert space and operator theory. Pure-state entanglement is characterized by Schmidt decomposition: any bipartite |ψ⟩ can be written |ψ⟩=∑_i λ_i |u_i⟩_A⊗|v_i⟩_B with Schmidt coefficients λ_i; entanglement exists when more than one λ_i is nonzero. For mixed states ρ, separability means ρ=∑_k p_k ρ_A^k⊗ρ_B^k. Mathematical tools include the density matrix, partial trace, and entanglement witnesses (Hermitian operators detecting nonseparability). Algebraic structures from tensor product spaces and concepts from quantum channels and completely positive maps describe entanglement dynamics. Connections to group theory and representation theory arise in multipartite classification.
Entanglement comes in many forms: bipartite pure-state entanglement, bipartite mixed entanglement, and multipartite entanglement such as GHZ states and W states. Distinctions include free versus bound entanglement (non-distillable). Quantitative measures include entropy of entanglement (von Neumann entropy of reduced states), entanglement of formation, concurrence, negativity, and relative entropy of entanglement. Operational notions like distillable entanglement and entanglement cost connect to protocols in LOCC (local operations and classical communication). Classification theorems for multipartite systems use SLOCC equivalence.
Entanglement has been demonstrated in many physical platforms: photons via spontaneous parametric down-conversion (SPDC) in nonlinear crystals (work at institutions such as MIT and University of Innsbruck), trapped ions (e.g., experiments at NIST and by Rainer Blatt), superconducting qubits in devices from IBM and Google Quantum AI, and ultracold atoms in optical lattices (groups at Max Planck Institute for Quantum Optics). Detection methods include state tomography, Bell inequality violation measurements, entanglement witnesses, and measurement of concurrence or negativity. Scalable generation techniques underlie efforts in quantum computing platforms like ion trap quantum computers and superconducting quantum processors.
Entanglement is a resource in quantum information science enabling protocols such as quantum teleportation (first demonstrated by Bennett et al. experiments), superdense coding, and entanglement-based quantum key distribution (e.g., Ekert protocol). In quantum metrology, entangled states improve precision beyond classical limits (Heisenberg scaling). Entanglement is central to proposals for quantum networks and a quantum internet (research programs at DARPA and the European Commission). In condensed matter physics, entanglement measures characterize phases and criticality; tools include entanglement entropy in studies by John Cardy and others. Entanglement also influences emerging technologies in quantum sensing.
Entanglement raises questions about locality, realism, and causality explored in interpretations of quantum mechanics such as Copenhagen interpretation, Many-worlds interpretation, and de Broglie–Bohm theory. Bell's theorem and subsequent experiments constrain local hidden-variable models. Debates persist about whether entanglement implies "spooky action at a distance" (a phrase attributed to Einstein), or whether correlations are non-signaling and compatible with relativistic causality. Research in quantum foundations connects entanglement to topics like quantum decoherence, the measurement problem, and efforts to reconcile Quantum mechanics with General relativity in approaches such as quantum gravity and the holographic principle, where entanglement entropy has appeared in proposals like the Ryu–Takayanagi formula.
Category:Quantum mechanics Category:Quantum information theory