Physics, information, and the new quantum technologies. Luiz Davidovich Instituto de Física Universidade Federal do Rio de Janeiro

Transcription

1 Physics, information, and the new quantum technologies Luiz Davidovich Instituto de Física Universidade Federal do Rio de Janeiro

2 WHAT IS INFORMATION? In+form: form inside, organize Claude Shanon (1948): Anything that reduces uncertainty Difference in organization or uncertainty before and after getting a message Shannon entropy for a set X = x, p(x) H (X) = x X p(x)log p(x) { } : Claude Shannon

3 CLASSICAL INFORMATION Information can be discretized: the elementary unit of information is the bit (or cbit, from classical bit), which has only two states 0 and 1 (true of false, yes or not, etc) Any text can be codified by a sequence of bits Bits can be physically stored (state on or off of a transistor, magnetic domain)

4 CLASSICAL INFORMATION The two states are robust, they are not destroyed when read and can be easily copied (or cloned") Quantum revolution: a new perspective on information

5 THE QUANTUM REVOLUTION Planck Einstein Planck, 1900, Einstein, 1905: Light behaves in some experiments as if it were a stream of particles (photons)

6 PHYSICS AND INFORMATION "It is not unreasonable to imagine that information sits at the core of physics, just as it sits at the core of a computer every physical quantity, every it, derives its ultimate significance from bits, binary yes-or-no indications, a conclusion which we epitomize in the phrase, it from bit John Wheeler (1989)

7 PHYSICS AND INFORMATION Information is physical. Information is not a disembodied abstract entity; it is always tied to a physical representation. It is represented by engraving on a stone tablet, a spin, a charge, a hole in a punched card, a mark on paper, or some other equivalent. Rolf Landauer

8 QUANTUM TECHNOLOGY: END OF XX CENTURY Trapped atoms and ions R. Blatt, D. Wineland Cavity Quantum Electrodynamics Courtesy of R. Blatt Single-photon devices Chapman, Haroche, Kimble, Rempe, Walther Optical chips Morandotti, O Brien, Sciarrino

9 PHOTONS: FLYING QUBITS Polarization of a single photon as a classical bit: H 0, V 1 H 0 1 V General direction of polarization: qubit superposition of H and V ψ = a H + b V, a and b complex Polarized beam splitter

10 PHOTONS AND POLARIZERS Each photon has a probability of going through, which depends on the angle Small probability > low intensity Direction of polarization changes

11 PECULIARITIES OF QUANTUM INFORMATION: BITS X QUBITS If we do not know a priori the direction of the polarization of a photon, measurement along any other direction changes photon polarization It is not possible to measure the polarization of a single photon? It is not possible to clone a qubit (Wooters and Zurek, Dieks, 1982) Intriguing implications on the foundations of quantum mechanics

12 APPLICATION TO KEY DISTRIBUTION Original message: Random key: Coded message: Key: Recovered message: Summation rule 1+1=0 1+0=1 0+1=1 0+0=0

13 Quantum key distribution Bennett and Brassard, 84: Four-state protocol Polarizers Alice Horizontal-Vertical Diagonal (45 0,-45 0 ) Bit sequence Photon sequence Bob sequence Compatibility Key Detection results Compatibility Key

14 QUANTUM CRYPTOGRAPHY

15 1935

16 ENTANGLED STATES Individual state of each system is not known: only global state is known!

17 SCHRÖDINGER ON ENTANGLEMENT Naturwissenschaften 23, 807 (1935) This is the reason that knowledge of the individual systems can decline to the scantiest, even zero, while that of the combined system remains continually maximal. Best possible knowledge of a whole does not include best possible knowledge of its parts and that is what keeps coming back to haunt us.

18 PHOTONIC ENTANGLED STATES Ultraviolet light beam crosses a crystal and generates two infrared light beams: each ultraviolet photon generates two photons twin photons Under some conditions, the two photons have orthogonal polarizations, but the polarization of each photon is unknown (( ) / ) 2/ 2 ψ = HHV V VH V H Measurement of polarization of photon 1 determines polarization of photon 2!

19 Spooky actions at a distance I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance. Letter from Einstein to Born, March 3, 1947 (The Born-Einstein Letters, Macmillan, NY, 2005) Max Born

20 Faster than light communication? ψ = ( HV VH ) / 2 I measured Therefore?

21 Multiphotonic entanglement

22 Multi-particle entanglement

23 ENTANGLEMENT AS A RESOURCE Entanglement is useful for quantum communication and computation

24 Entanglement as a resource

25 ENTANGLEMENT AS A RESOURCE

26 LIMITS OF CLASSICAL COMPUTATION 10-CORE XEON (2011): 2,600,000,000 transistors Moore s law (1965): number of transistors in CPU doubles every two years! Around 2020: aprox. one atom per bit

27 OTHER MOTIVATIONS... Factoring problem: difficult! Best known algorithm for factorization of an integer N : n h exp O n 1/3 (log n) 2/3io, n = log N RSA public key cryptographic method (banks, internet...) Shor s algorithm (quantum computing): O[(n) 2+ε ] Code breaking! Data bank search (Grover): classic α N, quantum α

28 QUANTUM COMPUTATION

29 Google and quantum simulations

30 Business initiatives

31 Business initiatives

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34 SUPERPOSITION PRINCIPLE Two qbits: N atoms: 2 N inputs! All possible values of two bits in a single state! Using this for parallel computing: 1 ψ = 1 i 2 N 1 i 2!i N U ψ = 1 f (i 2 N 1 i 2!i N ) i 1 i 2!i N =0 1 i 1 i 2!i N =0

35 UNIVERSAL GATES FOR QUANTUM COMPUTATION Universal gates: single-qubit unitary transformations + controlled not (DiVincenzo et al., 1995) Controlled not: Control bit Target bit Entangled state

36 QUANTUM COMPUTATION

37 QUANTUM COMPUTATION ENVIRONMENT

38 FROM QUANTUM TO CLASSICAL Lighted cavity + Dark cavity Quantum superposition

39 RESILIENCE OF ENTANGLEMENT Environment

40 Collaborators: dynamics of entanglement Leandro Aolita Fernando de Melo Rafel Chaves Malena Hor-Meyll Alejo Salles Osvaldo Jiménez-Farías Gabriel Aguillar Marcelo P. de Almeida Andrea Valdés-Hernandéz Paulo Souto Ribeiro Stephen Walborn Daniel Cavalcanti Antonio Acín Joe Eberly Xiao-Feng Qian 40

41 Collaborators: quantum metrology, quantum sensors Gabriel Bié Marcio Taddei Camille Latune Bruno Escher Nicim Zagury Ruynet Matos Filho

42 Quantum Information in Brazil UFC UFAL UFPE UNICAMP UFU UFMG CEFET-MG UFSCar UFF UFRJ USP-SÃO CARLOS UFABC PUC-RIO UEPG USP-SP UFSC CBPF

43 THANKS!