• Chinese Optics Letters
  • Vol. 15, Issue 5, 052701 (2017)
Lianwu Yang1、2 and Yunjie Xia1、*
Author Affiliations
  • 1Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165, China
  • 2Department of Physics and Information Engineering, Jining University, Qufu 273155, China
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    DOI: 10.3788/COL201715.052701 Cite this Article Set citation alerts
    Lianwu Yang, Yunjie Xia. Freezing quantum coherence with weak measurement[J]. Chinese Optics Letters, 2017, 15(5): 052701 Copy Citation Text show less

    Abstract

    We show how to optimally protect quantum states and freeze coherence under incoherent channels using a quantum weak measurement and quantum measurement reversal. In particular, we present explicit formulas for the conditions for freezing quantum coherence in a given quantum state.
    δ=i1,,iNdi1,,iN|i1,,iNi1,,iN|.(1)

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    K0A=[1001q],K1A=[0q00].(2)

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    ΛqN(ρ)=j1,,jN(Kj1KjN)ρ(Kj1+KjN+).(3)

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    ρfw=NΛq(MρM+)N+,(4)

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    ρfw=1T[n2(cos2θ+m2qsin2θ)mn1qcosθsinθmn1qcosθsinθm2(1q)sin2θ],(5)

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    Ps=T·min{1,1/m2}·min{1,1/n2}.(6)

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    ρ12=ρ21=mn1qcosθsinθn2cos2θ+m2(1q+n2q)sin2θ.(7)

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    m=f1(θ)/q,n=(1q)/qf1(θ)tanθ,(8)

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    M1=[100m1][100m2],N1=[n1001][n2001].(9)

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    ρMN=1T1[a100e10b10000c10e100d1],(10)

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    Ps1=T1Πx={m1,m2,n1,n2}min{1,1/x2}.(11)

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    m1m2=f2(θ)/q,n1=n2=[(1q)f2(θ)tanθ]/q,(12)

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    E0=p[1001q],E1=p[0q00],E2=1p[1q001],E3=1p[00q0],(13)

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    ρGADw=1T2[a2c2d2b2],(14)

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    Ps2=T2·min{1,1/m2}·min{1,1/n2}.(15)

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    m=(1q+pq)(1p)(1pq)p4cotθ,n=(1pq)(1p)p(1q+pq)4.(16)

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    Lianwu Yang, Yunjie Xia. Freezing quantum coherence with weak measurement[J]. Chinese Optics Letters, 2017, 15(5): 052701
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