1 / 28

JOB OPENING

ERATO-SORST, JST is hiring theorists and an experimentalist for a Quantum Computation and Information Project.

ivonnee
Download Presentation

JOB OPENING

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. JOB OPENING • PD position in Quantum Computation and Information Project, ERATO-SORST,JST • Theorists (1-2, working in Tokyo, Japan) • Quantum computing: HSP, communication complexity,interacting proof, … • Quantum Cryptography • Experimentalist (1, working in Tsukuba, Japan) • entangled photons, quantum cryptography,… • Contact: • Akihisa Tomita (tomita@qci.jst.go.jp)

  2. Self-teleportation and its applications to LOCC state estimation and cloning Keiji Matsumoto NII, ERATO-SORST,JST

  3. Motivation, Background Characterization of quantum non-locality by the best LOCCvs.collective operations in the efficiency of state estimation Known: non-entangled states can be non-local 1. Holevo, Belavkin etc (1970s): State detection ρ⊗n vs σ⊗n 2. Bennett et al. “nonlocality without entanglement”, 1999 A set of pure orthogonal separable states with non-zero detection error Message of the talk entangled pure states are not nonlocal, at all separable states are nonlocal, but small exceptions

  4. The Challenge There is no good characterization of LOCC Optimization is awfully hard • Past researches • restrict to special case • weak statements • lowerboud only, • perfect detection only • This talk : • 1. arbitrary pure state family • optimal figure of merit • 3. n copies of the same state. (n≫10)

  5. LOCC Estimation • Given n-copies of unknown bipartite pure state, shared by A and Bwith n≒20or more. {|φθi } : a parameterized family of pure states • Error measure: mean distance E(D(|φθi, |φθesti)2) = a/n +b/n3/2 +c/n2 + … want to minimize a, b, c, …. except for exponentially small order. Question: Can we do as good as global measurement? YES for entangled state, No for separable state (some exceptions)

  6. Self-teleportation |φi 1. A and B share given n copies of an unknown pure entangled state. 2. By LOCC, A sends her quantum info to B. No quantum channel, No extra entangled states Without sacrificing any of pairs Error:p1n LOCC |φiABsn |φiBBsn＋ε

  7. Difference from teleportation, remote state preparation,and entanglement swapping • Teleportation, remote state preparation requires additional entanglement other than the state teleported • Self-teleportation uses its own entanglement to teleport oneself.

  8. Caution : Measurement based protocol does not work! 1. A and B measure the state, compute the estimate |φesti 2. B locally fabricate |φestisn |hφest|φi|2≦1-O(1/n) ∴ |hφest|φi|2n ≦const. <1 very bad You have to do something non-trivial.

  9. LOCC estimation by Self-teleportation • Self-teleportation: |φθiABsn ⇒ |φθi BBsn+ε If entangled, |ε|=O(p1n) : exponentially small If not entangled, p1=1: |ε|=1 Totally fail 2. If succeed, B does globally optimal measurement. Separable states suffers from quantum non-locality. (Counter intuitive)

  10. A standard form [MH00] Ul⊗Vl H⊗n = Representation of permutation Representation of GL Asn |φi |φ’i |φ’’i |φi ⊗n = al|φli⊗|Φl i Vl,A⊗ Vl,B Ul,A⊗ Ul,B Independent of |φi Max. ent Depends on |φi dim Ul≦ poly(n) dim Vl : Typically exponential Necessary quantum information for estimation is negligibly small

  11. Why necessary quantum information for estimation is negligibly small ? • Consider n-times (biased) coin flip. • Want to estimate prob. of tail. • For that, we only need the frequency of tail, and can forget when tail occurred. • # of tails is 0,1,2, …,n, • Information = log(n+1) bits = o(n)-bits • Similar for quantum case. H H T H H T T T

  12. Not-so bad protocol |φi ⊗n = al|φli⊗|Φl i • Alice and Bob measures l • Teleport |φli using |Φl i Coherence between λ’s will be distroyed (but optimal so long as O(1/n) is concerned) Ul,A⊗ Ul,B Vl,A⊗ Vl,B |φli⊗|Φl i Vl,A⊗ Vl,B Ul,A⊗ Ul,B

  13. Self-teleportation Protocol 1. A & B project onto 2. A measures by basis 3. A sends 4. B does upon al|φli 5. B creates max. ent locally al|φli⊗|Φl i≒ |φi ⊗n

  14. Failure probability Failure Prob = p1 :the largest Schmidt coefficient ≒p1n p1<1 for entangled state p1=1 for separable state So long as the state is not separable, Failure probvanishes exponentially fast!

  15. If the state is separable … Self-teleportation fails with certainty, so our protocol does not work. Ex. |ai： coherent state Global optimal: q 1 by XA + XB q 2 by YA - YB (commute) Locally : q 1 by XA, XB at each site q 2 by YA, YB at each site Estimation is harder for separable states!

  16. First order asymptotic theory of probability distributions Asymptotic Cramer-Rao: Fisher Information:

  17. Quantum : non-collective measurement Theorem[Nagaoka 1989, GillMassar 2000,HM 1998] • Measurement on n-copy, • Construction is independent of θ CR-type bound • Measurement on single copy, • Construction depends on θ

  18. Quantum: Collective measurement Theorem[HM 1998] ρ⊗m ρ⊗m ρ⊗m ρ⊗m ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ

  19. tensor-product (mixed or pure) state, LOCC & collective measurement A-B A-B Between copies • minimization is only over LO. • Can by-pass characterization of LOCC • Doesn’t mean asymptotically optimal protocol is LO. ( corresponding protocol requires 2 times of 2 way communications)

  20. Cor.ρθ=ρθA⊗ρθB Can be mixed states ⇔　ρθA’s and ρθB’s tangent space have to has the same structure tr ρθA LAθ,i LAθ,j=c tr ρθB LBθ,i LBθ,j independent of i, j LAθ,i LBθ,i(SLD): defined as a solution to: ≒ρθA⊗ρθB ∴　Typically,LOCC estimation < global operation

  21. Self- teleprot-concentration LOCC |φisn |jisn+ε |ε|=O(log2n/ n) |ji : unknown c.f. Haydn-Winter’s “mother protocol” 1. |ji：　known 2. use zero-rate quantum channel Bell pairs nE(|ji)+o(n) gentle tomography Not gentle enough

  22. Self-teleport-concentration • Intrinsic maximally entangled state : O(n) • Quantum information to be teleported : O(log n) Therefore, without damaging intrinsic maximally entanglement, we can teleport All necessary quantum information! …..But with average fidelity 1-O(log2n /n)

  23. An application: Local copying LOCC |jisn rn, rn≒|jis rn r nEc (rn, rn ) – n E(|ji)+o(n) F(rn, rn,|jis rn) is close to global optimal if n>>1

  24. Challenges in application tolocal copying 1. Ec (ρn,m ) : how to characterize? since this is not tensored-product state, we need Te-Sun Han’s INFORMATION SPECTRUM(=smooth Reny entropy, In qic jargon) 2. In general, Ec (ρ) ebits is not enough to teleport half of ρ. In addition, in our case, ρis unknown ⇒　anonymous entanglement dilution for symmetric states

  25. Entanglement of optimal clone • Given n copies of |φi. E(|φi): entropy measure • Want to inflate to r× n copies. (r:const) • What will be the entanglement of this approximate clone? Suppose we know |φi’s Schmidt basis, except for the phases. ρn,rn: optimal n→rn clone not close to |φisrn at all. Same in entanglement as |φisrn Ec (ρn,rn )= E(|φisr)= r E(|φi)

  26. END • By Self-Teleportation, LOCC estimate = Global estimate Cloning =Global cloning By Self-Teleportation + universal concentration, Local copying = Global cloning 3bodies ? Mixed states? Zero-rate QC?

  27. An optimal adaptive strategy 1 2

  28. An optimal strategy 1 2 The bound is almost achieved if m>>1

More Related