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Transcript
MIT OpenCourseWare http://ocw.mit.edu 6.453 Quantum Optical Communication Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. October 28, 2008 6.453 Quantum Optical Communication Lecture 14 Jeffrey H. Shapiro Optical and Quantum Communications Group www.rle.mit.edu/qoptics 6.453 Quantum Optical Communication - Lecture 14 ! Announcements ! Turn in problem set 7 ! Pick up problem set 7 solutions, problem set 8, lecture notes, slides ! Teleportation ! Polarization entanglement and qubit teleportation ! Quadrature entanglement and continuous-variable teleportation 2 www.rle.mit.edu/qoptics Polarization-Entangled Photon Pairs ! Post-Selected Bi-Photon State from Dual-Paramp Source ! Measure Outputs 1 and 2 in Conjugate Polarizations wave plates Output k 3 www.rle.mit.edu/qoptics Polarization-Entangled Photon Pairs ! Classical Theory: correlated, randomly-polarized photons where ! Quantum Theory: polarization-entangled photons 4 www.rle.mit.edu/qoptics The Four Steps of Qubit Teleportation from Charlie Alice Bob 5 www.rle.mit.edu/qoptics What’s Under the Teleportation Hood ! Step 1: Alice and Bob share and store an entangled state ! Bob’s state intimately tied to result of Alice’s measurement ! Step 2: Alice measures her state ƒ message state ! she obtains two bits of classical information ! she learns nothing about her state or the message ! Step 3: Alice sends her measurement bits to Bob… ! using classical communication: nothing moves faster than light speed ! Step 4: Bob applies polarization transformation… ! chosen in accordance with Alice’s measurement bits ! entanglement guarantees that Bob has recovered the message 6 www.rle.mit.edu/qoptics And Now the Details… ! Step 1: Alice and Bob share and store an entangled state ! Step 2: Alice measures the Bell observable 7 www.rle.mit.edu/qoptics Here’s the Magic of Entanglement… ! Alice’s Measurement Result Determines Bob’s State ! Step 3: Alice sends her two measurement bits to Bob ! Step 4: Bob makes the appropriate state transformation 8 www.rle.mit.edu/qoptics Quadrature Entanglement: Vacuum-Input Paramp Type-II Phase-Matched Degenerate Parametric Amplifier ! Quadrature Variances: ! Quadrature-Difference Variances: 9 www.rle.mit.edu/qoptics Continuous-Variable Teleportation: the Xmtr vacuum-input paramp loss to rcvr loss message input homodyne homodyne to rcvr to rcvr 10 www.rle.mit.edu/qoptics Continuous-Variable Teleportation: the Rcvr from xmtr coherent state EO modulator from xmtr 11 www.rle.mit.edu/qoptics Coming Attractions: Lectures 15 and 16 ! Lecture 15: Quadrature Teleportation ! Fidelity analysis for coherent-state inputs ! Lecture 16: Quantum Cryptography ! Bennett-Brassard protocol ! Ekert protocol 12 www.rle.mit.edu/qoptics