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

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

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

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

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

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

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

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

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 Idler photon spectrum Type-I and II quasi-phase matching in Nonlinear wave guides

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

Type II BBO, centered at 800nm (shows typical spectral correlations present in SPDC. S=1.228 Type II ADP, centered at 800nm (note that spectral correlations have been eliminated) Type II BBO, centered at 1600nm (note that spectral correlations have been eliminated). S=0 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. Engineering the entropy of entanglement

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

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

Generating downconversion economically Economy figure of merit: 465mW1250 kHzType-II 2mm BBO crystal Weinfurter [2] [1] Kwiat et al, Phys. Rev. A 48 R867 (1993) [2] Weinfurter et al, quant-ph/ (2001) [3] Banaszek, U’Ren et al, Opt. Lett (2001) 10  W 65 kHzType-I 10cm KDP crystal Kwiat, Steinberg [1] 720 kHz 22  W Type-I 1mm KTP QPM waveguide Banaszek, U’Ren, Walmsley [3] PUMP POWER COUNTSDOWNCOVERTERGROUP

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

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

Possibility for efficient wave-based computation Classical quantum Particles WavesWaves Entangled Particles

Science, January 2000 Computations based on quantum interference

Scaling Criticisms “Exponential overhead required for measurement”

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

Equivalence of single-particle QIP and CWIP

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 Collective manipulations on several particles cannot be made efficiently through a single -particle degree of freedom (implications for error-correcting protocols) Issues in single-particle quantum manipulation There’s nothing quantum about single particle processors w/ counting readout, even using several degrees of freedom

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

Implications for atomic and molecular-based QIP Isotope separation Control of chemical reactions: –molecular dissociation –product ratio Carrier dynamics in semiconductors Information processing Averbukh et al., PRL (1996) Charron et al., PRL (1993) Shnitman et al., PRL (1997) Heberle et al., PRL (1995) Ahn et al., Science (2000) Amitay et al., Chem. Phys. (2001) Howell et al., PRA (2000) Database search Multilevel quantum simulator Graph connectivity analysis 2 N x2 N NxN 2N2N 2N2N ? 2N2N ? Non-orthogonal orthogonal N ln 2 N Coding Particles N ln 2 N (N) CNOT gate Tesch and De Vivie-Riedle, CPL (2001) How to efficiently address the processor Hlibert space using only one or two degrees of freedom?

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 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 Plan: future work