| entanglement (quantum) | |
|---|---|
| Name | Quantum entanglement |
| Field | Quantum mechanics |
| Introduced | 1935 |
| Introduced by | Albert Einstein, Boris Podolsky, Nathan Rosen, Erwin Schrödinger |
entanglement (quantum)
Entanglement in quantum mechanics is a nonclassical correlation between two or more quantum systems such that the state of each system cannot be described independently of the others, even when separated by large distances. This phenomenon underlies foundational tests of locality and enables technologies in quantum information science such as quantum computing, quantum cryptography, and quantum teleportation.
Quantum entanglement arises when a composite wavefunction or state vector of a multipartite system is not factorable into a product of states for each subsystem. For a bipartite system AB described on the tensor product Hilbert space H_A ⊗ H_B, an entangled state cannot be written as |ψ⟩_A ⊗ |φ⟩_B. Historically entanglement was emphasized in the EPR paradox paper by Albert Einstein, Boris Podolsky, and Nathan Rosen and named and analyzed by Erwin Schrödinger. Entanglement challenges classical intuitions about separability and prompted developments in the study of quantum nonlocality and information-theoretic resources. Practical generation uses physical carriers such as photons, electron spins, trapped ions, and superconducting qubits.
Formal criteria for entanglement use algebraic and operator tools. A mixed state ρ on H_A ⊗ H_B is separable if it can be expressed as a convex sum ρ = Σ_i p_i ρ_A^i ⊗ ρ_B^i; otherwise it is entangled. Important mathematical constructs include the Schmidt decomposition for pure bipartite states, which provides Schmidt coefficients and a rank indicating entanglement rank, and the partial trace and reduced density matrix for subsystem descriptions. Entanglement detection uses criteria such as the Peres–Horodecki criterion (positive partial transpose, PPT), entanglement witness operators, and computable measures like entanglement entropy, concurrence, and negativity. In multipartite systems, classes like Greenberger–Horne–Zeilinger (GHZ) states and W-state illustrate inequivalent entanglement structures under SLOCC.
Entangled states are routinely generated in laboratories. Common photonic methods use spontaneous parametric down-conversion in nonlinear crystals or four-wave mixing in optical fibers and cold atomic ensembles. Matter-based platforms include ion trap experiments at institutions such as University of Innsbruck and NIST, nitrogen-vacancy center spins in diamond, and superconducting qubit circuits developed by groups at Google and IBM. Measurement and tomography employ Bell state measurement devices, quantum state tomography, and coincidence counting with single-photon detectors like avalanche photodiode. Metrology exploits entanglement in quantum sensors and atomic clock ensembles to surpass classical limits.
Entanglement is a key resource in quantum information theory. It powers quantum teleportation protocols first demonstrated by groups at Caltech and University of Innsbruck, and underlies superdense coding. In quantum computing, algorithms such as those executed on Shor's algorithm-capable architectures and Grover's algorithm rely on multipartite entanglement for quantum parallelism. Entanglement-based quantum key distribution protocols include Ekert 1991 (E91) which uses Bell inequality violations for security. Entanglement distillation, entanglement swapping, and quantum repeaters are central to proposals for long-distance quantum communication networks like those pursued by China's Micius satellite and international quantum internet testbeds.
Entanglement has deep implications for the interpretation of quantum theory. Discussions involve interpretations such as Copenhagen interpretation, Many-worlds interpretation, and de Broglie–Bohm theory, each offering distinct accounts of nonlocal correlations. Foundational results include the Bell's theorem derivations by John Bell and subsequent experimental tests by teams including Alain Aspect that constrained local hidden variable models. Entanglement also features in modern approaches to quantum foundations like quantum Bayesianism (QBism) and operational reconstructions of quantum theory. Philosophical debates consider concepts like realism, causality, and counterfactual definiteness in light of entangled correlations.
Empirical tests of nonlocality use entangled states to violate Bell inequality constraints derived for local realistic theories. Early experiments by John Clauser and later loophole-closing tests by teams at Delft University of Technology, NIST, and Vienna addressed the locality, freedom-of-choice, and detection-efficiency loopholes. Variants such as CHSH inequality and multipartite inequalities probe stronger forms of nonlocality; GHZ experiments provide deterministic contradictions without inequalities. Statistical analysis and device-independent protocols exploit Bell violations to certify randomness and security in device-independent quantum cryptography.
Entanglement is fragile under interaction with environments; decoherence converts coherent quantum correlations into classical mixtures. Studies of entanglement dynamics analyze sudden death and revival effects in open quantum systems using master equations, quantum channels, and noise models like amplitude damping and dephasing. Quantification employs entanglement measures (entanglement of formation, relative entropy of entanglement) and operational benchmarks such as distillable entanglement and entanglement cost. Control techniques including dynamical decoupling, quantum error correction (developed from Peter Shor and Andrew Steane codes), and reservoir engineering aim to protect or generate entanglement in scalable platforms.
Category:Quantum mechanics Category:Quantum information theory