M. Markham, D.J. Twitchen

C. Abellán, W. Amaya, V. Pruneri, M.W. Mitchell

B. Hensen, H. Bernien, A.E. Dréau, A. Reiserer, N. Kalb, M.S. Blok, J. Ruitenberg, R.F.L. Vermeulen, R.N. Schouten, D. Elkouss, S. Wehner, T.H. Taminiau, R. Hanson

Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km arXiv:1508.05949

• Introduction • Setup at TU Delft • Data evaluation • Discussion

• Introduction • Setup at TU Delft • Data evaluation • Discussion

Bell’s theorem

1. 2. 3.

Communication is limited to speed of light Settings a,b can be freely chosen Local hidden variable model (LHVM) governs the experiment

3’. Quantum theory predicts

Bell’s game Game score 1 if −1 𝑎𝑎𝑎𝑎 𝑥𝑥𝑥𝑥 = 1 C= 0 else 1. 2. 3.

Communication is limited to speed of light Settings a,b can be freely chosen uniformly at random Local hidden variable model (LHVM) governs the experiment

P(𝐶𝐶 = 1) ≤ 3/4

3’. Quantum theory predicts

P(𝐶𝐶 = 1) ≤(√2+2)/4≈0.85

Unless…

Locality loophole

Time t

x ∈ {−1,1}

A

a ∈ {0,1}

y ∈ {−1,1} Distance L

B

b ∈ {0,1}

- If L is so short that Alice can signal to Bob before y is produced then y=f(a,b) - Strategy with winning probability one: x=1, 𝑦𝑦 = −1

𝑎𝑎𝑏𝑏

Detection loophole

A

a ∈ {0,1}

y ∈ {−1,1} Distance L

B

b ∈ {0,1}

- Outcomes are not always conclusive  data discarded - Strategy with winning probability one: if a=0 output x=1, if b=0 output y=1 else no output

efficiency η

Time t

x ∈ {−1,1}

Bell experiments Locality loophole addressed (photons)

Aspect (1982), Weihs (1998), Tittel (1999)

Detection loophole closed (ions, atoms, superconducting qubits, photons)

Rowe (2001), Matsukevich (2008), Ansmann (2009), Giustina (2013), Christensen (2013)

Detection loophole closed AND locality loophole addressed = “loophole-free” Bell test

• Introduction • Setup at TU Delft • Data evaluation • Discussion

Time

Setup for closing the loopholes

Space

Bell, J. Phys. (Paris) Colloq. C2, 41 (1981).

GO / NOT GO

𝑥𝑥 ∈ {−1,1}

𝑥𝑥 ∈ {−1,1}

Matter qubits: “easy” high fidelity readout

𝑎𝑎 ∈ {0,1}

L=? limited by 3 us readout  L>1 km

𝑏𝑏 ∈ {0,1}

Phys. Rev. Lett. 91, 110405 (2003).

Loophole-free Bell test campus ✗

Bob lab Alice lab ✗



Beamsplitter lab

Experimental scheme Alice

time

space

Beam splitter station

Bob

Experimental scheme Initialization Initialization of the qubits into a well defined state Nature 477, 574 (2011)

time

space

Alice

Beam splitter station

Bob

Experimental scheme Spin-photon entanglement Create spin-photon entanglement on both sides. Send photons to beam splitter.

Alice

Beam splitter station

Bob

Experimental scheme Alice Entanglement generation

* click!

Photon detection projects spins into entangled state Barrett and Kok, PRA 71, 060310 (2005) Nature 497, 86 (2013)

time

space

Beam splitter station

Bob

Experimental scheme Random basis choice

1! Fresh Quantum Random Number Generator Optics Express 22, 1645 (2014) arXiv:1506.02712 (2015)

time

space

Alice

Beam splitter station

Bob

Experimental scheme Readout Distance such that signaling is not possible:

Locality loophole addressed

Alice

Beam splitter station

Bob

end

Efficient Readout:

Detection loophole closed Nature 477, 574 (2011)

start

• Introduction • Setup at TU Delft • Data evaluation • Discussion

Statistical analysis LHVM imply limitations in probability or expectation

Finite number of events

Hypothesis test - Null hypothesis: the experiment was governed by a LHVM - p-value: Probability of data at least as extreme as that observed given a LHVM maximized over all LHVMs. - p-value is not the probability that our experiment is ruled by a LHVM

Rigorous bound • No unfounded assumptions: i.i.d. • No approximations: Gaussian

Gill, Found. of Prob. and Phy., 179-206 (2003) Zhang, Glancy, Knill, PRA 84 062118 (2011) Bierhorst, Found. Phys. 44, 736-761 (2014)

Challenges for modelling the experiment t=1(YES) or 0(NO)

T

go?

1 if t −1 C= 0 else

𝑎𝑎𝑎𝑎 𝑥𝑥𝑥𝑥

=1

Local hidden variable model (LHVM) governs the experiment: 1. Setting choices are independent conditioned on the history 2. Inputs have a bias from uniform 𝝉𝝉 (𝟏𝟏𝟏𝟏−𝟓𝟓 ) 3. Settings and outcomes at both sites are conditionally independent on the history 4. Arbitrary statistics at heralding station

P(𝐶𝐶 = 1) ≤ 3/4+3(𝜏𝜏 + 𝜏𝜏 2 )

Upper bound on the p-value Experimental Data - n = number of GO rounds - k = number of wins - 𝜏𝜏 = bias of the RNGs

p-value ≔ max 𝑃𝑃 𝑎𝑎𝑎𝑎 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑖𝑖𝑖𝑖 𝑛𝑛 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿) 𝐿𝐿𝐻𝐻𝐻𝐻𝑀𝑀

Remarks - Upper bound is the tail of an i.i.d. distribution -

Elkouss, Wehner in preparation (2015)

Evaluation of the experiment Gathered data - 1 event per hour - 245 events over more than 220 hours - 196 “wins” over the 245 events

How do we interpret it?

Hypothesis test - Null hypothesis: the experiment was governed by a LHVM - p-value: probability of data at least as extreme as that observed given a LHVM maximized over all LHVMs.

p-value ≔ max 𝑃𝑃 𝑎𝑎𝑎𝑎 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 196 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑖𝑖𝑖𝑖 245 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿) ≤ 0.039 𝐿𝐿𝐻𝐻𝐻𝐻𝑀𝑀

• Introduction • Setup at TU Delft • Data evaluation • Discussion

Conclusions

First loophole-free Bell inequality violation arXiv:1508.05949 (2015)

Next: • Independent confirmation • Proof-of-principle of device-independent security … • Quantum networks

Thank you!

どうもありがとうございます!

march meeting

Experimental loophole-free violation of a Bell inequality ... Communication is limited to speed of light. 2. Settings a,b can ... addressed = “loophole-free” Bell test.

2MB Sizes 2 Downloads 599 Views

Recommend Documents

170320 March Community Meeting Update.pdf
Sosan Schaller, Chief Financial Officer. • Ariel Ramos, Operations Supervisor. • Mandy Braun, Director of Safety and Security. Project Management - CBRE.

City Council Meeting – March 7, 2017 1439th REGULAR MEETING ...
[840-OR]. 10. ADJOURNMENT. Agenda prepared by Nancy A. Vincent, City Clerk for Jack Ethredge, City Manager. Agenda & items subject to change.

March.22.2016 Community Meeting Minutes.docx.pdf
Others Present: Emma Buechs, Don Greeley, Joseph Spangler, Lt. Gary Nelson, Robert Thunder, ... Abubakar Masjid Open House – Wednesday April 6th.

March.22.2016 Community Meeting Minutes.docx.pdf
March.22.2016 Community Meeting Minutes.docx.pdf. March.22.2016 Community Meeting Minutes.docx.pdf. Open. Extract. Open with. Sign In. Main menu.

Meeting materials March 1_Brown University.pdf
Meeting materials March 1_Brown University.pdf. Meeting materials March 1_Brown University.pdf. Open. Extract. Open with. Sign In. Main menu. Whoops!

TIP Platform Committee Meeting - March 16.pdf
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. TIP Platform ...

APS -APS March Meeting 2016 - Top Scheduler Events
Mar 14, 2016 - APS -APS March Meeting 2016 - Top Scheduler Events. Página 1 de 2 http://meetings.aps.org/Meeting/MAR16/TopEvent. APS Meetings Home ...

Minutes of Special Meeting of Future Nillumbik Committe - 22 March ...
Mar 22, 2018 - Special Meeting of Future Nillumbik Committee minutes. 22 March 2018. Nillumbik Shire Council. Contents. 1. Welcome and apologies. 1. 2.

March 8, 2016 Board Meeting Agenda.pdf
Page 1 of 1. America's Finest Charter School. 730 45th Street, San Diego, CA 92102. Phone: 619-694-4809 Fax: 619-794-2762. 2015-2016. GOVERNING BOARD AGENDA. REGULAR BOARD MEETING. March 8, 2016 at 1:00 p.m. / Office of the Director at AFCS. Roll Cal

Minutes of the CHMP meeting 20-23 March 2017 - European ...
May 4, 2017 - Re-examination of initial application procedures under Article 9(2) of ...... scientific advice given to companies during the development of ...

SEAF Meeting Minutes March 2016.pdf
o Update for candidate forum for City Council elections. Determined that at this time we will not be hosting or partnering with anyone to host a candidate.

March 21, 2017 BON Stakeholder Meeting Notice.pdf
Mar 21, 2017 - meeting via webinar at https://attendee.gotowebinar.com/register/7519774807821750017. What is this about? The State Board of Nursing will ...

Economic Development Committee Meeting Minutes of March 20 ...
Economic Development Committee Meeting Minutes of March 20, 2018.pdf. Economic Development Committee Meeting Minutes of March 20, 2018.pdf. Open.

Economic Development Committee Meeting Minutes of March 16 ...
Economic Development Committee Meeting Minutes of March 16, 2017.pdf. Economic Development Committee Meeting Minutes of March 16, 2017.pdf. Open.

Notice, Council Meeting Public Hearing, March 17, 2017.pdf
Notice/Council Meeting Public Hearing/17-03-30v.1/ms. Page 1 of 1. Notice, Council Meeting Public Hearing, March 17, 2017.pdf. Notice, Council Meeting ...

HPC, SOLA Regular Meeting, March 27, 2017.pdf
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. HPC, SOLA ...

Voting Modernization Board: Actions from the March 26, 2015, Meeting
May 21, 2015 - State Alex Padilla. These actions and a copy of the meeting minutes for this meeting are available on the Prop. 41 website at:.

Meeting Minutes - March 23, 2015 Budget Work Session.pdf ...
Councilman Bradley Doughty-Present. Councilman Bryon ... The Byrne Grant fluctuates, ... Meeting Minutes - March 23, 2015 Budget Work Session.pdf. Meeting ...

Minutes of the CHMP meeting 20-23 March 2017 - European ...
May 4, 2017 - Send a question via our website www.ema.europa.eu/contact ... Additional details on some of these procedures will ...... Any other business. 47.

Minutes of Special Meeting of Future Nillumbik Committe - 22 March ...
Mar 22, 2018 - held at the Civic Centre, Civic Drive, Greensborough on Thursday 22 March 2018. Minutes. Mark Stoermer. Chief Executive Officer. Monday 26 ...

ECS Board Meeting - March 2016.pdf
Sign in. Page. 1. /. 1. Loading… Page 1 of 1. Page 1 of 1. ECS Board Meeting - March 2016.pdf. ECS Board Meeting - March 2016.pdf. Open. Extract. Open with.

March 14, 2009 Place of Meeting: Meeting held at Winterhaven Minute
Trice Benge – Secretary (present via conference call). ○ Judy Hoops - Treasurer. ○ Roy Shrewsbury. ○ Mary Cox. ○ Laurie Pate (present via conference call).

AESGP hearing at MLWP meeting, March 2017 - European Medicines ...
Jun 1, 2017 - An agency of the European Union ... clarified that new information was collected which will shortly be taken into account in the 5-year revision.

CNRAC Business Meeting Agenda for March 2016.pdf
... DEP Secretary John Quigley. Matt Keefer, Assistant State Forester. Bureau of Forestry. 6. PA Explorer Conservation Tool Ellen Shultzabarger, Division Chief.