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 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

A quantum computer Input Classical information Output Classical information

• Resources for preparing and reading register are important

The structure of quantum fields

Quantum field ˆ (



)

      

ˆ



Mode function

Size of computer

Particle annihilation operator Quantum state

    

N

   1  

n



vac

Number of Particles

Mode amplitude Vacuum

Quantum state characterized by classical and quantum parts Field-theoretic view Provides a natural measure of resources

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

Generating Entangled States Entangled state: multi-mode, multi-particle  

1 2



ˆ †

1 

ˆ †

2  

†

1 

ˆ †

2  

vac

  

;

   

,

 •

N

-particles •

2N

-modes (inc. hyper-entangled states) • 2N pathways for creating particles in 2N modes • Non-observed degrees of freedom must be identical

Classical mode structure mode engineering: Distinguishing information destroys interference Braunstein-Mann Bell-state analyzer

Coincidence detection implies input photons are entangled

g d Bell-state measurements are a requirement for teleportation, a computational primitive

Classical mode structure Even a single photon can have a complicated shape e.g. localized in space and time

I

(

t

)

t

2  2  1 4

I

(  )  (

t

) Time (fs)  (  ) Wavelength (nm)

A. Baltuska et al, Opt. Lett.

23

, 1474 (1998)

Generation of entangled photons Spontaneous parametric downconversion generates pairs of photons that may be entangled in frequency, time of emission and polarization

Pulsed pump

 p  s  i

Signal photon spectrum Idler photon spectrum

Q Q  s Type-I and II quasi-phase matching in Nonlinear wave guides  i

Generation of entangled photons   

d



s d



i

 

s

 

i

  

s

, 

i

 

s SIGNAL



i IDLER

Pump Envelope Phase-Matching Function Product of One-Photon Fock States 

s



i



s



i

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

Interfering the two-photon state with itself



y



y

+ e i

 

x



x

BBO   Spectral entanglement is robust against decoherence But Bell measurements difficult

Engineering the entropy of entanglement

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

S=1.228

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

S=0

Type II ADP, centered at 800nm (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 .

Generating Correlated, unentangled photons Why no entanglement?

1. Dispersion cancellation to all orders: Erdmann et al, Phys. Rev. A 62 53810 (2000)  System immune to dispersion 2. Multiple-source experiments: Grice, U’Ren at al, Phys. Rev. A 64 63815 (2001) Spectral uncorrelation  Unwanted distinguishing Information eliminated How to attain positive correlation?

Group velocity matching condition: Rubin et al, Phys. Rev. A 56 1534 (1997) KTP phase matching function at 1.58

m m: KTP spectral Intensity at 1.58

m m:

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

Generating downconversion economically Economy figure of merit: GROUP DOWNCOVERTER Kwiat, Steinberg [1] Type-I 10cm KDP crystal Weinfurter [2] Type-II 2mm BBO crystal Banaszek, U’Ren, Walmsley [3] Type-I 1mm KTP QPM waveguide PUMP POWER 10 465mW 22 m m W W COUNTS 65 kHz 1250 kHz 720 kHz R [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)  7  Hz 6  10

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

Particles W a v e s Entangled Particles Classical quantum

Science, January 2000 Computations based on quantum interference

Scaling Criticisms “Exponential overhead required for measurement”

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

Equivalence of single-particle QIP and CWIP

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)

Anything better than Pentiums without QIP?

Meyer-Bernstein-Vazirani Circuit

H H g a H H X H • 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. Since nowhere are the qubits entangled, they can be replaced by the modes of an optical field.

Implications for atomic and molecular-based QIP

Database search Graph connectivity analysis Multilevel quantum simulator CNOT gate Ahn et al., Science (2000) Amitay et al., Chem. Phys. (2001) Howell et al., PRA (2000) Tesch and De Vivie-Riedle, CPL (2001) • How to efficiently address the processor Hlibert space using only one or two degrees of freedom?

Coding 2 N Non-orthogonal Particles N ln 2 N

?

2 N x2 N 2 N orthogonal (N)

?

2 N Non-orthogonal N ln 2 N

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