Engineering entanglement:How and how much?

Alfred U’renPablo Londero

Konrad BanaszekSascha Wallentowitz

Matt AndersonChristophe DorrerIan 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

InputClassical

information

OutputClassical

information

• Resources for preparing and reading register are important

The structure of quantum fields

ˆ E (+) x,t( ) = φλ x,t( )ˆ a λλ∑

Quantum field

Mode function Particle annihilation operator

Quantum state

Mode amplitude Vacuum

Quantum state characterized by classical and quantum parts

Size of computer

Number of Particles

Field-theoretic view Provides a natural measure of resources

ψ = c nλ{ }( )

nλ{ }

∑ ) a λ( )

nλ

λ=1

N

∏ vac†

Detection of quantum systems via particle counting

Particle physics

Quantum Computation Optics

Atomic physics

Generating Entangled States

Entangled state: multi-mode, multi-particle

ψ =12

ˆ a 1↑† ˆ a 2→

† +ˆ a 1→† ˆ a

2↑†

( )vac

λ =αβ; α ∈1,2( ),β ∈ ↑,→( )

• 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

)(ωI)(tI

)(ωϕ

)(tϕ

Wavelength (nm)Time (fs)

Inst

anta

neou

s po

wer

Spec

tral

den

sity

A. Baltuska et al, Opt. Lett. 23, 1474 (1998)

Even a single photon can have a complicated shapee.g. localized in space and time

t2 ω2 ≥14

Classical mode structure

ωp

ωs

ωi

Q

Q

ωs

ωi

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 inNonlinear wave guides

Pump Envelope

Phase-Matching Function

Product of

One-Photon

Fock States

ψ = d ωs∫∫

d ωi

φ ωs

, ωi

( )α ωs

+ ωi

( ) ωs SIGNAL

ωi IDLER

ωi

ωs

ωi

ωs

Generation of entangled photons

Interfering the two-photon state with itself

+ e iθ

ωx

ωy

λ/4

θ

BBO

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 decoherenceBut Bell measurements difficult

Type II BBO, centered at 800nm (shows typicalspectral correlations present in SPDC.

S=1.228

Type II ADP, centered at 800nm (note thatspectral correlations have been eliminated)

Type II BBO, centered at 1600nm (note thatspectral correlations have been eliminated).

S=0

S=0

By appropriately choosing:

i) the crystal materialii) the central wavelengthiii) the pump bandwidthiv) the crystal length

it is possible to engineer a two-photonstate with zero spectral correlation.

Engineering the entropy of entanglement

Generating Correlated, unentangled photons

Why no entanglement? How to attain positive correlation?

KTP phase matchingfunction at 1.58m:

KTP spectral Intensity at 1.58m:

2. Multiple-source experiments:

Grice, U’Ren at al, Phys. Rev. A 64 63815 (2001)

Unwanted distinguishingInformation eliminated

Spectral uncorrelation⇓

1. Dispersion cancellation to all orders:

Erdmann et al, Phys. Rev. A 62 53810 (2000)

System immune to dispersion

⇓ Group velocity matching condition:

Rubin et al, Phys. Rev. A 56 1534 (1997)

Wave guide QPM downconversion

Towards a useful source of heralded photons

Compact NL structuresLow pump powers

Photons from independent sources will interfere

High repetition rates

STP operation

Conditioned generation

Generating downconversion economically

Economy figure of merit:

465mW 1250 kHzType-II 2mm BBO crystal

Weinfurter [2]62.710×

[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)

10 W 65 kHzType-I 10cm

KDP crystal

Kwiat, Steinberg [1]

76.510×

720 kHz22WType-I 1mm KTP QPM waveguide

Banaszek,

U’Ren,

Walmsley [3]

103.310×

HzR mmW⎛⎞⎜⎟•⎝⎠PUMP

POWER

COUNTSDOWNCOVERTERGROUP

Proposed Type II Polarization Entanglement Setup

FD: frequency doublerSWP DICH: short-wave-pass dichroic mirrorKTP II WG: waveguideLWP DICH: long-wave-pass dichroic mirrorPBS: polarizing beam splitterPOL1 and POL2: polarizersDET1 and DET2: detectors

+Ψ −Ψ

+Φ −Φ

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 WavesEntangledParticles

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

HX

H

H

ga

• 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.

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

Ahn et al., Science (2000)

Amitay et al., Chem. Phys. (2001)

Howell et al., PRA (2000)

Database search

Multilevel quantum simulator

Graph connectivity analysis

2Nx2N

NxN

2N 2N

? NxN

2N

?

Non-orthogonal Non-orthogonalorthogonal

N ln2 N

Coding

Particles N ln2 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