* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Hoseong Lee
Quantum dot wikipedia , lookup
Quantum field theory wikipedia , lookup
Coherent states wikipedia , lookup
Hydrogen atom wikipedia , lookup
Density matrix wikipedia , lookup
Measurement in quantum mechanics wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Quantum computing wikipedia , lookup
Probability amplitude wikipedia , lookup
Quantum fiction wikipedia , lookup
Wheeler's delayed choice experiment wikipedia , lookup
Path integral formulation wikipedia , lookup
Double-slit experiment wikipedia , lookup
Orchestrated objective reduction wikipedia , lookup
Quantum machine learning wikipedia , lookup
Quantum group wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Many-worlds interpretation wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Quantum entanglement wikipedia , lookup
Delayed choice quantum eraser wikipedia , lookup
History of quantum field theory wikipedia , lookup
Quantum teleportation wikipedia , lookup
Quantum state wikipedia , lookup
Canonical quantization wikipedia , lookup
Quantum key distribution wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
EPR paradox wikipedia , lookup
Hidden variable theory wikipedia , lookup
Bell’s Inequality Quantum Mechanics(14/2) Hoseong Lee Hidden variables • Hidden variable theory – Argument about uncertainty property of quantum mechanics – Hidden variable • Investing quantum mechanics with local realism • Underlying deterministic unknown variable in quantum mechanics – Bohm’s hidden variable theory “God does not play dice!” Quantum Mechanics(14/2) Hoseong Lee Hidden variables • Local hidden variable theory – Locality • Principle that an object is only directly influenced by its immediate surroundings – EPR paradox – showed non-locality of quantum mechanics • Two photon that separated so far apart • The measurement of one photon ⇒ determining the other one’s states – Local hidden variable • a quantity whose value is presently unknown with local property “Spooky action at a distance!” Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality • Bell’s theorem – Proposed by John Stewart Bell, in the paper that “On the Einstein-Podolsky-Rosen paradox”, 1964. – A way of distinguishing experimentally between local hidden variable theories and the predictions of quantum mechanics – Bell’s inequality → • Inequality that derived from local hidden variable theory • Any quantum correlations under local hidden variable theory do not satisfy bell’s inequalities. • Demonstration by bell test experiments Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality • Simple version of a bell’s inequality – Various possible polarization combinations of the two EPR photons Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality • Simple version of a bell’s inequality – 𝑅1 ⊂ 𝑅2 ∪ 𝑅3 ⇒ 𝑃 𝑅1 ≤ 𝑃 𝑅2 + 𝑃 𝑅3 – Specific example for a Bell’s inequality. Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality • Simple version of a bell’s inequality – Quantum mechanical calculation • Photon linearly polarized at an angle θ to the horizontal • Probability that such a photon will pass a horizontally-oriented beamsplitter • Two different photon modes: propagating to the left (L) and to the right (R) • EPR state with the two orthogonal polarization states (generalized form: θ and θ+π/2, instead of horizontal and vertical) Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality • Simple version of a bell’s inequality – Quantum mechanical calculation • Consider that examine this state with a horizontal polarizer on the left and a polarizer at angle φ to the horizontal on the right, then amplitude is • Note that we can write Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality • Simple version of a bell’s inequality – Quantum mechanical calculation • Amplitude is independent of the angle θ of the polarization axis of the EPR pair. • We can conclude that the probability of the “left” photon passing the left polarizer at angle 0 and the “right” photon passing the right polarizer at angle φ is Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality • Simple version of a bell’s inequality – Quantum mechanical calculation • If a photon on the right passes at an angle φ, then it fails to emerge from the the other arm of a polarization beamsplitter, an arm that passes a photon of polarization angle φ-π/2. • Probability of the “left” photon passing the left polarizer at angle 0 and the “right” photon failing to pass the right polarizer at angle φ is • The choice of the polarizer orientation on the left as “horizontal” is arbitrary. Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality • Simple version of a bell’s inequality – Quantum mechanical calculation • 0.2500 > 0.0732 + 0.1464 • A calculation that also appears to agree well with experiment. Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality experiments • Notable experiments – Freedman and Clauser, 1972 • First actual Bell test – Aspect, 1981-2 • First and last used the CH74 inequality, 1981 • First application of the CHSH inequality, 1982 – Tittel and the Geneva group, 1998 • Long distance of several kilometers – Salart et al., 2008 • Long distance of 18 km Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality experiments • CHSH experiment – Proposed by John Clauser, Michael Horne, Abner Shimony, and Richard Holt, in the paper that “Bell’s theorem; experimental tests and implications”, 1969. – CHSH inequality – Quantum mechanics calculation: 𝑆 ≤ 2 2 – CHSH violations predicted by the theory of quantum mechanics Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality experiments • CHSH experiment – Set of four correlations; { ‘++’, ‘+-’, ‘-+’, ‘--’ } – Polarization: vertical (V or +) and horizontal (H or -) – Coincidence counts: { N++, N--, N+-, N-+ } – { a, a’, b, b’ } ⇒ { 0˚, 45˚, 22.5˚, 67.5˚ } (‘Bell test angles”) Quantum Mechanics(14/2) Hoseong Lee Bell’s inequality experiments • CHSH experiment – The experimental estimate for E(a,b) is then calculated as: 𝑁++ − 𝑁+− − 𝑁−+ + 𝑁−− 𝐸= 𝑁++ + 𝑁+− + 𝑁−+ + 𝑁−− – 𝑆𝑒𝑥𝑝𝑡 = 2.697 ± 0.015 > 2 – 𝑆𝑄𝑀 = 2.70 ± 0.05 > 2 – Demonstration to non-locality of quantum mechanics Quantum Mechanics(14/2) Hoseong Lee