About me Academic degrees: 1999 M.Sc. Royal Institute of Technology (KTH). 2004 PhD. (Quantumentanglement: theory and an experiment) Royal Institute of Technology Postdoctoral Fellowships: Wenner-Gren Foundations 2005-01-01-2005-11-27. Japan Society of the Promotion of Science (JSPS), 2005-11-28-present, nominated by The Royal Swedish Academy of Science.
About me Research interests: Quantum entanglement and non-locality Other interests: Experimental projects: Single photon non-locality Quantum soliton squeezing Theory projects: Quantifying and classifying multipartite quantum entangled states. Exploring the geometry and topology of multipartite entangled states Mathematics, Mathematical physics, Quantum field theory and String theory
Sweden
Sweden Area: 450,000 km² third largest country in Western Europe Forests: 53% Mountains: 11% Cultivated land: 8% Lakes and rivers: 9% Area: 499 km 1,574 km MoreInformation: http://www.sweden.se
Sweden Capital: Stockholm Population: 9 million Languages: Swedish; minority languages: Sami, Finnish
Sweden Form of government: Constitutional monarchy, parliamentary democracy. Parliament: The Riksdag, with 349 members in one chamber. Average life expectancy: men years, women 82 years. men 78
Sweden Most important export goods: Electrical and Electrical and telecom equipment, machinery, passenger cars, paper, iron and steel. Most important imported goods: Electrical and Electrical and telecom equipment, machinery, foodstuffs, crude oil, textile products, passenger cars.
Sweden Welfare : The The world's most generous general social welfare system,, with such elements as virtually free, schools, child care, health care, pensions, elder care, social services and various economic security systems. Education: The principle of access to free education for the whole populations Education: Tax: The world's highest tax
Stockholm one of theworld's most beautiful capitals.
Stockholm Sightseeing Stadshuset Globen Skansen Kulturhuset Vasamuseet. Nordiska museet
Djurgården The Riksdag The Riksdag Globen
Quantum Theory? Quantum Classical small roughly size large
Classical Mechanics 1. An object in motion tends to stay in motion. 2. Force = mass times acceleration 3. For every action there is an equal and opposite reaction. Sir Isaac Newton Classical mechanics is everyday mechanics.
Quantum Mechanics Classical mechanics explains most of what we usually observe in nature. But it could not explain the results of certain experiments such as the Hydrogen spectrum:
Quantum Theory? Weak Force Quantum Electromagnetic Force Gravitational Force Theory Strong Force
The Fundamental Postulates of Quantum Mechanics 1. The wavefunction postulate 2. The Schrödinger Equation 3. The measurement postulate 4. The composite systems
Physical Systems - Quantum Mechanics Postulate 1 Isolated physical system Hilbert Space Postulate 2 Evolution of a physical system Unitary transformati on Postulate 3 Measurements of a physical system Measuremen t operators Postulate 4 Composite physical system Tensor product of components
Postulate 1: The Wavefunction Postulate 1: All information about a system is given by the system s wavefunction. Ψ( x) x Interesting facts about the wavefunction: The squared amplitude of the wavefunction at position x is equal to the probability of observing the particle at position x. 2 Pr( x) =Ψ ( x) x
The strangeness of The Wavefunction postulate The Heisenberg Uncertainty Principle: It is impossible to know all properties of a particle simultaneously. Classical elephant: Quantum elephant: The elephant is definitely big and gray. The elephant is definitely big. or The elephant is definitely gray.
Quantum bit (Qubit( Qubit) Classical Computation Quantum Computation Data unit: bit = 1 = 0 Data unit: qubit = 1 = 0 Valid states: Valid states: x = 0 or 1 ψ = c 1 0 + c 2 1 x = 0 x = 1 ψ = 0 ψ = 1 ψ = ( 0 + 1 )/ 2 0 1 0 1
Postulate 2: The Schrödinger Equation Postulate 2: The wavefunction of a system follows the Schrödinger Equation: ih t Ψ= h 2 2m 2 Ψ+VΨ Combined with the Pauli exclusion principle and electron spin, the Schrödinger equation predicts the structure of all atoms
The strangeness of Postulate 2 Quantum trajectories: quantum particles take all paths. Classical mouse Quantum mouse Takes one path. Takes all paths, even forbidden ones!
Postulate 3: Measurement Postulate 3: Measurement of a quantum mechanical system is associated with some linear, Hermitian operator Ô. Measurement leads to a collapse of the wavefunction, leading to indeterminacy and nonlocality in quantum mechanics. Interesting facts about the measurement postulate: 1. It implies that measurement is inherently probabilistic. 2. It implies that measurement necessarily alters the observed system.
The strangeness of Postulate 3 Measurement: Deterministic versus probabilistic Classical Elephant: Quantum Elephant: Before measurement or After measurement For a known state, outcome is deterministic. For a known state, outcome is probabilistic.
Classical vs. Quantum Classical bits: can be measured completely, are not changed by measurement, can be copied, can be erased. Quantum bits: can be measured partially, are changed by measurement, cannot be copied, cannot be erased.
Postulate 4: Composite systems Postulate 4: The state space of a composite physical system is the tensor product of the state space of the component physical System. Ψ = Ψ1 Ψ2 Ψm Interesting facts about the composite systems postulate: It enable us to define one of the most interesting and puzzling ideas associated with composite quantum systems, Quantum entanglement
Quantum entanglement Consider the two qubit state Ψ = ϕ 1 2 ( + ) This state has the remarkable property that there are no single qubit State and such that ψ Ψ = ψ ϕ Bell (1964) and Aspect (1982): Entanglement can be used to show that no locally realistic (that is, classical) theory of the world is possible.
Quantum entanglement ψ α β = 0 + 1 A A ϕ α β = 0 + 1 A B Ψ = ψ ϕ Separable state 1 Φ = ( 0 0 + 1 1 ) 2 Entangled state
Using entanglement to do stuff Entanglement-based Superdense coding quantum cryptography Quantum teleportation Quantum computing Entanglement is a useful resource that can be used to accomplish tasks that would otherwise be difficult or impossible. Given an information-processing goal, we can always ask What would I gain by throwing some entanglement into the problem?
Quantum Computation & Quantum Information Study of information processing tasks that can be accomplished using quantum mechanical systems Cryptography Quantum Mechanics Computer Science Information Theory
Physical implementations Quantum information and quantum computation Quantum measurements Quantum circuits Quantum error correction Quantum computation Quantum control Quantum communication Quantum simulation Quantum Entanglement Decoherence Quantum games Quantum algorithms
Quantum Cryptography A secure way of exchanging keys such that eavesdropping can always be detected. Public key cryptography is conditionally secure Sharing key via qubits guarantees security unconditionally according to quantum physics. Magiq Tech ID Quantique
Quantum Teleportation Transfer of information using quantum entanglement. Teleportation experiments so far: Light onto light: Innsbruck(97), Rome(97), Caltech(98), Geneva, Tokyo, Canberra Single ion onto single ion: Boulder (04), Innsbruck (04) Teleportation of light onto a macroscopic atomic sample Niels Bohr Institute(06)
I think I can safely say that nobody understands quantum mechanics. Richard Feynman Nobel Prize (1965)
Thank You!