Introduction to PhotonicQuantum Logic QUAMP Summer School SEPT 2006J. G. RarityUniversity of Bristoljohn.rarity@bristol.ac.uk EU FET: QAPBristol: Daniel Ho, J. Fulconis, J. Duligall, C. Hu, R. Gibson, O Alibart, J. OBrien Bath: William Wadsworth, Sheffield: M. Skolnick, D. Whittaker, M. Fox, J. TimpsonHP Labs: W. Munro, T. Spiller, K. Harrison

EPSRC1-photFP6:IP SECOQCwww.ramboq.org

StructureWhat is light?Decoherence of photonsSingle photon detectionEncoding bits with single photons and single bit manipulation.Linear logicEntangled state sourcesSingle photon sourcesQuantum Cryptography

The electro-magnetic spectrumOptical Photon energy Eph=hf>>KT=1.5umEph=0.8eV=0.33umEph=4eVV+ParticlelikeWave-like during propagationParticlelike

Decoherence of photons: associated with lossStorage time in fibre 5s/km, loss 0.17 dB/km (96%)Polarised light from stars==Storage for 6500 years!

Photon counting using avalanche photodiodesPhoton is absorbed in the avalanche region to create an electron hole pairElectron and hole are accelerated in the high electric fieldCollide with other electrons and holes to create more pairsWith high enough field the device breaks down when one photon is absorbedPhoton absorbed

Commercial actively quenched detector module using Silicon APDEfficiency ~70% (at 700nm)Timing jitter~400ps (latest

Other detectorsThe Geiger mode avalanche diodes count one photon then switch off for a dead time before they are ready to detect another-NOT PHOTON NUMBER RESOLVINGPhoton number resolving detectors may become available in the near future: Cryogenic superconducting to resistive transitions Jaspan et al APL 89, 031112, 2006 Impurity transitions in heavily doped silicon (Takeuchi)

Interference effectswith single photonsSingle photon can only be detected in one detectorHowever interference pattern built up from many individual countsP. Grangier et al, Europhysics Letters 1986LUIn the interferometer we have superposition state

After the interferometer:

Encoding one bit per photon and single qubit rotationsEncoding single photons using two polarisation modes Superposition states of 1 and 0|>= |0> +|1> Probability amplitudes , Detection Probability: ||2 Single photon encoding showing QBER

2QUBIT logic: Photonic CNOT Gate.QR is a quantum polarisation rotatorRotates polarisation if control is vertically polarisedDoes nothing if control is Horizontally polarisedRequires non-linearity at single photon level: Atoms: Turchette and Kimble PRL1995, Solid state: J. P. Reithmaier/ A. Forchel, NATURE 432, Nov 2004.

Bennett and Brassard 1984Secure key exchange using quantum cryptographySendsno. bit pol.1 1 452 0 453 0 04 1 455 1 06 0 457 1 451004 0 451005 1 0.3245 1 45Receivesno. Bit Pol.246 1 451004 0 452134 0 03245 0 04765 1 05698 0 45

Multi-qubit gates

Hong Ou Mandel interference effectHong, Ou, MandelPRL 1987

KLM gate

Demonstration of an all-optical quantum controlled-NOT gateKnill et al Nature 409, 4652 (2001)J L OBrien et al, Nature 426, 264 (2003) / quant-ph/0403062

Polarisation KLM gate

Parity Measurement

Parity and conditional CNOTKnill et al Nature 409, 4652 (2001)Pittman et al (2002) PRL 88, 257902 Not 100% efficient but Up to 50%NotesTarget V-->H+V Control V-->H+VParity-->HH+VV -45--> H(H+V)-V(H-V) Confirm click is H-->(H-V) out -45--> |H>Confirm click is V-->(H+V) out -45--> |V>Target V-->H+V Control H-->H-VParity-->HH-VV -45--> H(H+V)+V(H-V) Confirm click is H-->(H+V) out -45--> |V>

A scalable 2-qubit CNOT gateIn the proposalActual realisationTruth tableFidelity ~0.8S. Gasparoni, J-W Pan, P. Walther, T. Rudolph, and A. Zeilinger, Phys. Rev. Lett. 93, 020504 (2004)IST-2001-38864: RAMBOQ

Optical Cluster State ComputingP. Walther et al Nature 434, 169-176 (2005)