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Teleporting an Unknown Quantum State Via Dual Classical and
Einstein‐Podolsky‐Rosen ChannelsCharles H. Bennet, Gilles Brassard, Claude Crépeau,Richard Jozsa, Asher Peres, and William K. Wootters
Teleporting an Unknown Quantum State Via Dual Classical and Einstein‐Podolsky‐Rosen Channels 1
Team 10
Sheikh, MohammedSteiner, CharlesTsang, Chi Hang BoyceTiwari, Apoorv
*C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
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
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 7
Quantum teleportation from Alice to Bob
Measures her qubits in the Bell Basis
Classical signal of result
Quantum operation on
qubit 3Teleportation Procedure
Putting the problem in the Bell basis
If Alice measures
Bob’s qubit
becomes3‐particle state becomes
Teleportation Procedure 9
Alice and Bob again
MeasureΨ+
Ψ-
Φ+
Φ-
Qubitbecomesα|0>+β|1>α|0>‐β|1>α|1>+β|0>α|1>‐β|0>
Result
Recovery operation
Teleportation Procedure 10
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 11
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 (almostbroadcasting!)
“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– 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
100110011101…
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 14
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. Mixed‐state 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
Thank you for your attention!
Teleporting an Unknown Quantum State Via Dual Classical and Einstein‐Podolsky‐Rosen Channels 19
BB84 Protocol• Quantum Key Distribution (BB84)*
– Shared Private Key is crucial to cryptography1. Alice prepare two particles with some basis ( or )2. Alice measure the state of particle with same basis3. Bob measure the particle with random basis4. Choices of axes are then made public5. Measurement in same axis: Results become shared key6. Compare subset of string to detect eavesdropper
Teleporting an Unknown Quantum State Via Dual Classical and Einstein‐Podolsky‐Rosen Channels 20
*Table extracted on 10/12/2011, from Wikipedia, “Quantum key distribution”