Max Planck Institute of Quantum Optics MPQ Garching

Max Planck Institute of Quantum Optics (MPQ) Garching / Munich, Germany Entanglement swapping and quantum teleportation Johannes Kofler Talk at: Institute of Applied Physics Johannes Kepler University Linz 10 Dec. 2012

Outlook • Quantum entanglement • Foundations: Bell’s inequality • Application: “quantum information” (quantum cryptography & quantum computation) • Entanglement swapping • Quantum teleportation

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

The double slit experiment Particles Waves Quanta Superposition: | = |left + |right Picture: http: //www. blacklightpower. com/theory/Double. Slit. shtml

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

Quantum entanglement Entanglement: | AB = (| AB + | AB) / 2 Alice Bob basis: result / : / : / : locally: random globally: perfect correlation / : Picture: http: //en. wikipedia. org/wiki/File: SPDC_figure. png

Entanglement “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 Erwin Schrödinger probability ½: | AB = (| AB | + | AB |) / 2 which is also locally random and globally perfectly correlated?

Local 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: measurement 2: color result: parity result: possible values: +1 (even / red) – 1 (odd / black) A 1 (Alice), B 1 (Bob) A 2 (Alice), B 2 (Bob) 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 Bob Alice for all local realistic (= classical) theories CHSH version (1969) of Bell’s inequality (1964)

Quantum violation of Bell’s inequality 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 Bell’s inequality A 1 B 1 + A 1 B 2 + A 2 B 1 – A 2 B 2 ≤ 2 becomes 2 2 2. 83. A 2 A 1 John S. Bell B 1 B 2 Conclusion: entangled states violate Bell’s 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)

Interpretations Copenhagen interpretation quantum 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 mechanics quantum 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 interpretation all possibilities are realized parallel worlds

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

Cryptography Symmetric encryption techniques plain text encryption cipher text Asymmetric („public key“) techniques: eg. RSA decryption plain text

Secure cryptography One-time pad Idea: Gilbert Vernam (1917) Security proof: Claude Shannon (1949) [only known secure scheme] Criteria for the key: Gilbert Vernam Claude Shannon - 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

Quantum key distribution (QKD) 0 0 1 1 0 1 1 0 Basis: Result: / / 0 1 / / 0 1 0 / … 1 … Basis: Result: / / 0 0 / / 1 - Alice and Bob announce their basis choices (not the results) - violation of Bell’s inequality guarantees that there is no eavesdropping / … 0 0 … 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 Bell’s inequality security guaranteed by quantum mechanics

First experimental realization (2000) First quantum cryptography with entangled photons Key length: 51840 bit Bit error rate: 0, 4% T. Jennewein et al. , PRL 84, 4729 (2000)

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

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 (BB 84): 300 kbit/s over 45 km http: //www. uqcc 2010. org/highlights/index. html

The next step ISS (350 km Höhe)

Moore’s law (1965) Gordon Moore Transistor size 2000 200 nm 2010 20 nm 2020 2 nm (? )

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

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

Qubits Bloch sphere: General qubit state: P(„ 0“) = cos 2 /2, P(„ 1“) = sin 2 /2 … phase (interference) 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 - etc… Gates: Operations on one ore more qubits |1 = |right | = |0 + |1 |R = |0 + i |1

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[(64 b/9)1/3(logb)2/3]}, qm: sub-poly. O(b 3) [“exp. speed-up”] b = 1000 (301 digits) on THz speed: cl: 100000 years, qm: 1 second - Grover algorithm (1996) search in unsorted database with N elements cl: O(N), qm: O( N) [„quadratic speed-up“]

Possible implementations NMR SQUIDs Trapped ions NV centers Quantum dots Photons Spintronics

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

Quantum teleportation Entangled pair (AB): Bell states: | – AB = (|HV AB – |VH AB) / 2 | + AB = (|HV AB + |VH AB) / 2 Unknown input state (C): | C = |H C + |V C | – AB = (|HH AB – |VV AB) / 2 | + AB = (|HH AB + |VV AB) / 2 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 transformation has to be performed

Bell-state measurement H 1 H 2 PBS BS V 1 V 2 C A | – AC = (|HV AC – |VH AC) / 2 singlet state, anti-bunching: H 1 V 2 or V 1 H 2 | + AC = (|HV AC + |VH AC) / 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

Entanglement swapping Idea: Zukowski et al. (1993) First realization: Zeilinger group (1998) ……… “quantum repeater” 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 Picture: PRL 80, 2891 (1998)

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

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)

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

Quantum teleportation over 143 km State-of-the-art technology: - frequency-uncorrelated polarization-entangled photon-pair source - ultra-low-noise single-photon detectors - entanglement-assisted clock synchronization 605 teleportation events in 6. 5 hours X. Ma et al. , Nature 489, 269 (2012)

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