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Entanglement swapping and quantum teleportation Talk at: Institute of Applied Physics Johannes Kepler University Linz 10 Dec Johannes Kofler Max Planck Institute of Quantum Optics (MPQ) Garching / Munich, Germany

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Outlook Quantum entanglement Foundations: Bells inequality Application: quantum information (quantum cryptography & quantum computation) Entanglement swapping Quantum teleportation

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Light consists of… Christiaan Huygens (1629–1695) Isaac Newton (1643–1727) James Clerk Maxwell (1831–1879) Albert Einstein (1879–1955) …waves….particles …electromagnetic waves …quanta

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The double slit experiment Picture: ParticlesWavesQuanta Superposition: | = |left + |right

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Superposition and entanglement 1 photon in (pure) polarization quantum state: superposition states (in chosen basis) | = | Pick a basis, say: horizontal | and vertical | Examples: | = (| + | ) / 2 | = | | = (| + i| ) / 2 2 photons (A and B): Examples: | AB = | A | B | AB | AB = | AB product (separable) states: | A | B | AB = (| AB + | AB ) / 2 | AB = (| AB + i| AB – 3| AB ) / n entangled states, i.e. not of form | A | B Example: | AB = (| AB + | AB + | AB + | AB ) / 2= | AB = | = |

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Quantum entanglement Entanglement: | AB = (| AB + | AB ) / 2 = (| AB + | AB ) / 2 BobAlice locally:random / : globally:perfect correlation basis: result Picture:

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Entanglement Erwin Schrödinger Total knowledge of a composite system does not necessarily include maximal knowledge of all its parts, not even when these are fully separated from each other and at the moment are not influencing each other at all. (1935) What is the difference between the entangled state | AB = (| AB + | AB ) / 2 and the (trivial, classical) fully mixed state probability ½: | AB which is also locally random and globally perfectly correlated? = (| AB | + | AB |) / 2

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Local Realism Realism:objects possess definite properties prior to and independent of measurement Locality:a measurement at one location does not influence a (simultaneous) measurement at a different location Alice und Bob are in two separated labs A source prepares particle pairs, say dice. They each get one die per pair and measure one of two properties, say color and parity measurement 1:colorresult:A 1 (Alice), B 1 (Bob) measurement 2:parityresult:A 2 (Alice), B 2 (Bob) possible values:+1 (even / red) –1 (odd / black) A 1 (B 1 + B 2 ) + A 2 (B 1 – B 2 ) = ±2 A 1 B 1 + A 1 B 2 + A 2 B 1 – A 2 B 2 2 A 1 B 1 + A 1 B 2 + A 2 B 1 – A 2 B 2 = ±2 for all local realistic (= classical) theories Alice Bob CHSH version (1969) of Bells inequality (1964)

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Quantum violation of Bells inequality John S. Bell A 1 B 1 + A 1 B 2 + A 2 B 1 – A 2 B 2 2 With the entangled quantum state | AB = (| AB + | AB ) / 2 and for certain measurement directions a 1,a 2 and b 1,b 2, the left hand side of Bells inequality Conclusion: entangled states violate Bells inequality (fully mixed states cannot do that) they cannot be described by local realism (Einstein: Spooky action at a distance) experimentally demonstrated for photons, atoms, etc. (first experiment: 1978) becomes A1A1 A2A2 B1B1 B2B2

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Interpretations Copenhagen interpretationquantum state (wave function) only describes probabilities objects do not possess all properties prior to and independent of measurements (violating realism) individual events are irreducibly random Bohmian mechanicsquantum state is a real physical object and leads to an additional force particles move deterministically on trajectories position is a hidden variable & there is a non-local influence (violating locality) individual events are only subjectively random Many-worlds interpretationall possibilities are realized parallel worlds

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Einstein vs. Bohr Albert Einstein (1879–1955) Niels Bohr (1885–1962) What is nature? What can be said about nature?

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Cryptography plain textencryptioncipher textdecryptionplain text Symmetric encryption techniques Asymmetric (public key) techniques: eg. RSA

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Secure cryptography One-time pad Idea: Gilbert Vernam (1917) Security proof: Claude Shannon (1949) [only known secure scheme] Criteria for the key: - random and secret - (at least) of length of the plain text - is used only once (one-time pad) Quantum physics can precisely achieve that: Quantum Key Distribution (QKD) Idea: Wiesner 1969 & Bennett et al. 1984, first experiment 1991 With entanglement: Idea: Ekert 1991, first experiment 2000 Gilbert VernamClaude Shannon

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Quantum key distribution (QKD) Basis: / / / / / / / … Result: … Basis: / / / / / / / … Result: … -Alice and Bob announce their basis choices (not the results) -if basis was the same, they use the (locally random) result -the rest is discarded -perfect correlation yields secret key: 0110… -in intermediate measurements, Bob chooses also other bases (22.5°,67.5°) and they test Bells inequality -violation of Bells inequality guarantees that there is no eavesdropping -security guaranteed by quantum mechanics

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First experimental realization (2000) First quantum cryptography with entangled photons Key length: bit Bit error rate: 0,4% T. Jennewein et al., PRL 84, 4729 (2000)

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8 km free space above Vienna (2005) K. Resch et al., Opt. Express 13, 202 (2005) Millennium Tower Twin Tower Kuffner Sternwarte

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Tokyo QKD network (2010) Partners: Japan: NEC, Mitsubishi Electric, NTT NICT Europe: Toshiba Research Europe Ltd. (UK), ID Quantique (Switzerland) and All Vienna (Austria). Toshiba-Link (BB84): 300 kbit/s over 45 km

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The next step ISS (350 km Höhe)

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Moores law (1965) Gordon Moore Transistor size nm nm nm (?)

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Computer and quantum mechanics David Deutsch 1985:Formulation of the concept of a quantum Turing machine Richard Feynman 1981:Nature can be simulated best by quantum mechanics

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Quantum computer Classical input 01101… preparation of qubits measurement on qubits Classical Output 00110… evolution 1 0 |Q = (|0 + |1 ) Bit: 0 or 1Qubit: 0 and 1

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Qubits General qubit state: Physical realizations: photon polarization: |0 = | |1 = | electron/atom/nuclear spin: |0 = |up |1 = |down atomic energy levels: |0 = |ground |1 = |excited superconducting flux:|0 = |left |1 = |right etc… P(0) = cos 2 /2, P(1) = sin 2 /2 … phase (interference) | = |0 + |1 |R = |0 + i |1 Bloch sphere: Gates: Operations on one ore more qubits

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Quantum algorithms Deutsch algorithm (1985) checks whether a bit-to-bit function is constant, i.e. f(0) = f(1), or balanced, i.e. f(0) f(1) cl: 2 evaluations, qm: 1 evaluation Shor algorithm (1994) factorization of a b-bit integer cl: super-poly. O{exp[(64b/9) 1/3 (logb) 2/3 ]}, qm: sub-poly. O(b 3 ) [exp. speed-up] b = 1000 (301 digits) on THz speed: cl: years, qm: 1 second Grover algorithm (1996) search in unsorted database with N elements cl: O(N), qm: O( N) [quadratic speed-up]

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Possible implementations NV centersQuantum dotsSpintronics Trapped ionsNMRPhotons SQUIDs

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Quantum teleportation C AB initial state (Charlie) source entangled pair Alice Bob classical channel teleported state C Idea: Bennett et al. (1992/1993) First realization: Zeilinger group (1997) Bell-state measurement

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Quantum teleportation Entangled pair (AB): | – AB = (|HV AB – |VH AB ) / 2 | + AB = (|HV AB + |VH AB ) / 2 | – AB = (|HH AB – |VV AB ) / 2 | + AB = (|HH AB + |VV AB ) / 2 Bell states: Unknown input state (C): | C = |H C + |V C Total state (ABC): | – AB | C = (1/ 2) (|HV AB – |VH AB ) ( |H C + |V C ) = [ | – AC ( |H B + |V B ) + | + AC (– |H B + |V B ) + | – AC ( |H B + |V B ) + | + AC (– |H B + |V B ) ] if A and C are found in | – AC then B is in input state if A and C are found in another Bell state, then a simple trans- formation has to be performed

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Bell-state measurement BS PBS CA H1H1 H2H2 V1V1 V2V2 | – AC = (|HV AC – |VH AC ) / 2 | + AC = (|HV AC + |VH AC ) / 2 singlet state, anti-bunching: H 1 V 2 or V 1 H 2 triplet state, bunching: H 1 V 1 or H 2 V 2 | – AC = (|HH AC – |VV AC ) / 2 | + AC = (|HH AC + |VV AC ) / 2 cannot be distinguished with linear optics

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Entanglement swapping Idea: Zukowski et al. (1993) First realization: Zeilinger group (1998) Picture: PRL 80, 2891 (1998) initial state factorizes into 1,2 x 3,4 if 2,3 are projected onto a Bell state, then 1,4 are left in a Bell state … … … quantum repeater

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Delayed-choice entanglement swapping X. Ma et al., Nature Phys. 8, 479 (2012) Bell-state measurement (BSM): Entanglement swapping Mach-Zehnder interferometer and QRNG as tuneable beam splitter Separable-state measurement (SSM): No entanglement swapping

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Delayed-choice entanglement swapping A later measurement on photons 2 & 3 decides whether photons 1 & 4 were in a separable or an entangled state If one viewed the quantum state as a real physical object, one would get the seemingly paradoxical situation that future actions appear as having an influence on past events X. Ma et al., Nature Phys. 8, 479 (2012)

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Quantum teleportation over 143 km Towards a world-wide quantum internet X. Ma et al., Nature 489, 269 (2012)

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Quantum teleportation over 143 km X. Ma et al., Nature 489, 269 (2012) 605 teleportation events in 6.5 hours State-of-the-art technology: - frequency-uncorrelated polarization-entangled photon-pair source - ultra-low-noise single-photon detectors - entanglement-assisted clock synchronization

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Acknowledgments A. Zeilinger X. Ma R. Ursin B. Wittmann T. Herbst S. Kropascheck

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