Teleporting an Unknown Quantum State Via Dual Classical and Einstein Podolsky Rosen Channels 1

Teleporting an Unknown Quantum State Via Dual Classical and Einstein Podolsky Rosen Channels Charles H. Bennet, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters Team 10 Sheikh, Mohammed Steiner, Charles Tsang, Chi Hang Boyce Tiwari, Apoorv *C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993). Teleporting an Unknown Quantum State Via Dual Classical and Einstein Podolsky Rosen Channels 1

Outline The problem and required background Teleportation procedure Critical review Experimental realization and summary Teleporting an Unknown Quantum State Via Dual Classical and Einstein Podolsky Rosen Channels 2

A modern problem in gift giving We have two people, Alice and Bob. Alice wants to send Bob a particle as a gift. The problem is she doesn t know what the state of the particle is. And unfortunately she can t give it to Bob directly. We ll call the state of the particle How does she get the particle to Bob? The problem and required background

Quantum Entanglement Entangled states are states such that measurement of one particle s state also collapses the other particle s state. Measuring 0 A for particle A will collapse particle B s state to 1 B. The problem and required background 4

Can particle A s state be measured in an arbitrary basis? Apply a unitary transformation to the ( 0 A, 1 A ) basis. For example: ( 0 A, 1 A ) ( 0 A + 1 A, 0 A 1 A) = ( ψ +, ψ ) Then my entangled state will be: 0 B + 1 B ) ψ + + 0 B 1 B ) ψ The problem and required background

The Bell basis is the basis of a two particle entangled state The Bell basis has a total of four possible basis vectors. In quantum teleportation, three states are needed, two of which are entangled. The Bell basis serves are the measurement basis for Alice. The problem and required background

Quantum teleportation from Alice to Bob Measures her qubits in the Bell Basis Classical signal of result Teleportation Procedure Quantum operation on qubit 3

Putting the problem in the Bell basis 3 particle state becomes If Alice measures Bob s qubit becomes Teleportation Procedure 9

Alice and Bob again Measure Ψ + Ψ - Φ + Φ - Qubit becomes α 0>+β 1> α 0> β 1> α 1>+β 0> α 1> β 0> Result Recovery operation Teleportation Procedure 10

What is expected from this paper? Reminded that the following were impossible at the beginning Superluminal information transfer Quantum state cloning Broadcast of quantum state Showed interesting point of the procedure Teleportation is still possible without knowing State being teleported Location of receiver (almost broadcasting!) It is known that instantaneous information transfer is impossible. Critical Review 12

Why is this procedure important? Paper mentioned relevance to quantum cryptography, quantum parallel computation Quantum Key Distribution 100110011101 Shared Private Key is crucial to cryptography Use quantum teleportation to generate shared keys Eavesdropper will destroy entanglement and hence be detected Critical Review 13

Experimental Quantum Teleportation First experiments with photons: D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, Experimental Quantum Teleportation, Nature 390, 6660, 575 579 (1997). D. Boschi, S. Branca, F. De Martini, L. Hardy, & S. Popescu, Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual classical and Einstein Podolsky Rosen channels, Phys. Rev Lett. 80, 6, 1121 1125 (1998) I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, N. Gisin, Long Distance Teleportation of Qubits at Telecommunication Wavelengths, Nature, 421, 509 (2003) Experimental Realization and Summary 15

Photon Entanglement Parametric Down Conversion Inside a nonlinear crystal, an incoming pump photon can decay spontaneously into two photons. Experimental Realization and Summary 16

Experimental Quantum Teleportation Experiments with Atoms: M. Riebe, H. Häffner, C. F. Roos, W. Hänsel, M. Ruth, J. Benhelm, G. P. T. Lancaster, T. W. Körber, C. Becher, F. Schmidt Kaler, D. F. V. James, R. Blatt, Deterministic Quantum Teleportation with Atoms, Nature 429, 734 737 (2004) M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, D. J. Wineland, Deterministic Quantum Teleportation of Atomic Qubits, Nature 429, 737 (2004). S. Olmschenk, D. N. Matsukevich, P. Maunz, D. Hayes, L. M. Duan, and C. Monroe, Quantum Teleportation between Distant Matter Qubits, Science 323, 486 (2009). Experimental Realization and Summary 17

Citation Report Total Citations : 4977 Top Cited articles: Quantum Cryptography Author(s): Gisin N; Ribordy GG; Tittel W; et al. Quantum Cryptography,REVIEWS OF MODERN PHYSICS 74,145 195 (JAN 2002) Bouwmeester D; Pan JW; Mattle K; et al., Experimental quantum teleportation NATURE 390,6660,575 579,1997 Times Cited: 2,074 Bennett CH; DiVincenzo DP; Smolin JA; et al. Mixedstate entanglement and quantum error correction PHYSICAL REVIEW A, 54, 5. 3824 3851.1996 Times Cited: 2,043 Knill E; Laflamme R; Milburn GJ A scheme for efficient quantum computation with linear optics NATURE 409,6816, 46 52, 2001 Times Cited: 1,668 Experimental Realization and Summary 18

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BB84 Protocol Quantum Key Distribution (BB84)* Shared Private Key is crucial to cryptography 1. Alice prepare two particles with some basis ( or ) 2. Alice measure the state of particle with same basis 3. Bob measure the particle with random basis 4. Choices of axes are then made public 5. Measurement in same axis: Results become shared key 6. Compare subset of string to detect eavesdropper *Table extracted on 10/12/2011, from Wikipedia, Quantum key distribution Teleporting an Unknown Quantum State Via Dual Classical and Einstein Podolsky Rosen Channels 20