Engineering entanglement: How and how much?

1. The Center for Quantum Information Engineering entanglement: How and how much? Alfred U’ren Pablo Londero Konrad Banaszek Sascha Wallentowitz Matt Anderson Christophe Dorrer Ian A. Walmsley

2. Approaches • Manipulating quantum fields Engineering indistinguishability and entanglement • Scaling issues for QIP readout based on experiment Quantum field theoretic model of resources Outcomes • Developed engineered photon Sources • Experimentally demonstrated resource scaling for Interference-based information processing Objectives Develop “Quantum Toolbox” of elementary protocols Determine resources needed for each element

3. A quantum computer Input Classical information Output Classical information •Resources for preparing and reading register are important

4. The structure of quantum fields Quantum field Size of computer Mode function Particle annihilation operator Quantum state Number of Particles † Mode amplitude Vacuum Quantum state characterized by classical and quantum parts Field-theoretic view Provides a natural measure of resources

5. Detection of quantum systems via particle counting Atomic physics Particle physics Optics Quantum Computation

6. Generating Entangled States Entangled state: multi-mode, multi-particle • N-particles • 2N-modes (inc. hyper-entangled states) • 2N pathways for creating particles in 2N modes • Non-observed degrees of freedom must be identical

7. g d Classical mode structure mode engineering: Distinguishing information destroys interference Braunstein-Mann Bell-state analyzer Coincidence detection implies input photons are entangled Bell-state measurements are a requirement for teleportation, a computational primitive

8. Classical mode structure Even a single photon can have a complicated shape e.g. localized in space and time Spectral density Instantaneous power Time (fs) Wavelength (nm) A. Baltuska et al, Opt. Lett. 23, 1474 (1998)

10. Generation of entangled photons Spontaneous parametric downconversion generates pairs of photons that may be entangled in frequency, time of emission and polarization Pulsed pump Signal photon spectrum Type-I and II quasi-phase matching in Nonlinear wave guides Idler photon spectrum

11. Generation of entangled photons

12. Generation of entangled photons Supply two pathways for the generation of a pair of photons with no distinguishing information in the unmeasured degree of freedom Spectral entanglement is robust against decoherence But Bell measurements difficult

13. Engineering the entropy of entanglement Type II BBO, centered at 800nm (shows typical spectral correlations present in SPDC. Type II BBO, centered at 1600nm (note that spectral correlations have been eliminated). S=1.228 S=0 Type II ADP, centered at 800nm (note that spectral correlations have been eliminated) By appropriately choosing: i) the crystal material ii) the central wavelength iii) the pump bandwidth iv) the crystal length it is possible to engineer a two-photon state with zero spectral correlation. S=0

14. 1. Dispersion cancellation to all orders: Erdmann et al, Phys. Rev. A62 53810 (2000) Group velocity matching condition: System immune to dispersion Rubin et al, Phys. Rev. A56 1534 (1997) 2. Multiple-source experiments: KTP phase matching function at 1.58mm: KTP spectral Intensity at 1.58mm: Grice, U’Ren at al, Phys. Rev. A64 63815 (2001) Spectral uncorrelation Unwanted distinguishing Information eliminated Generating Correlated, unentangled photons How to attain positive correlation? Why no entanglement?

15. Towards a useful source of heralded photons Wave guide QPM downconversion Compact NL structures Low pump powers Photons from independent sources will interfere High repetition rates STP operation Conditioned generation

16. Kwiat, Steinberg [1] Type-I 10cm KDP crystal 10 mW 65 kHz GROUP DOWNCOVERTER PUMP POWER COUNTS Weinfurter [2] Type-II 2mm BBO crystal 465mW 1250 kHz Banaszek, U’Ren, Walmsley [3] Type-I 1mm KTP QPM waveguide 22mW 720 kHz Generating downconversion economically Economy figure of merit: [1] Kwiat et al, Phys. Rev. A 48 R867 (1993) [2] Weinfurter et al, quant-ph/0101074 (2001) [3] Banaszek, U’Ren et al, Opt. Lett. 26 1367 (2001)

17. Proposed Type II Polarization Entanglement Setup FD: frequency doubler SWP DICH: short-wave-pass dichroic mirror KTP II WG: waveguide LWP DICH: long-wave-pass dichroic mirror PBS: polarizing beam splitter POL1 and POL2: polarizers DET1 and DET2: detectors

18. Applications to quantum-enhanced precision measurement Accuracy doubling in phase measurement using local entanglement only No nonclassical light enters probed region - enhanced accuracy for lossy systems e.g. near-field microscopy

20. Entangled Particles Waves Possibility for efficient wave-based computation Particles Classical quantum

21. Computations based on quantum interference Science, January 2000

22. Scaling Criticisms “Exponential overhead required for measurement”

23. Particle-counting readout Definition of distinguishable detector modes • Each state of the system mapped to a specific space-time mode

24. Equivalence of single-particle QIP and CWIP

25. Issues in single-particle quantum manipulation • Single-particle systems do not scale poorly in readout - Binary coding possible even for single particle systems (No increase in number of detectors or particles required over entangled register) - No advantage to using several different degrees of freedom • There’s nothing quantum about single particle processors w/ counting readout, even using several degrees of freedom • Collective manipulations on several particles cannot be made efficiently through a single -particle degree of freedom (implications for error-correcting protocols)

26. H H ga H H H X Anything better than Pentiums without QIP? Meyer-Bernstein-Vazirani Circuit • Each line represents a single qubit. • H is a Hadamard transformation and X a bit-flip operation • ga is a controlled-NOT transformation acting on all bits simultaneously. • The top n qubits are measured at the end of the circuit. Since nowhere are the qubits entangled, they can be replaced by the modes of an optical field.

27. Isotope separation Control of chemical reactions: molecular dissociation product ratio Carrier dynamics in semiconductors Information processing Implications for atomic and molecular-based QIP Ahn et al., Science (2000) Database search Amitay et al., Chem. Phys. (2001) Graph connectivity analysis Howell et al., PRA (2000) Multilevel quantum simulator Tesch and De Vivie-Riedle, CPL (2001) CNOT gate Averbukh et al., PRL (1996) • How to efficiently address the processor Hlibert space using only one or two degrees of freedom? Charron et al., PRL (1993) Shnitman et al., PRL (1997) ? ? NxN 2Nx2N NxN Heberle et al., PRL (1995) 2N 2N 2N Coding Non-orthogonal orthogonal Non-orthogonal N ln2 N N ln2 N (N) Particles

28. Summary: work to date • New Methods developed for Generating entangled biphotons • Model for resource analysis proposed based on experimental realization Resources for single-particle readout scaling analyzed and experimentally verified Plan: future work • Develop waveguide sources as “entanglement factories” • make use of low decoherence rates of spectrally entangled biphotons • Design classical implementation of MBV circuit • Look at measures of nonclassicality based on scaling associated with quantum logic