1、Experimental Assisted Distillation of Quantum Coherence&Inter-conversion Between Coherence and DiscordOutline Experimentally Obtaining Maximal Coherence Via Assisted Distillation Process Experimental Cyclic Inter-conversion between Coherence and Quantum Correlation ConclusionQuantum resource theorie
2、s seek to quantify sources of non-classicality that bestow quantum technologies their operational advantage.Chief among these are studies of quantum correlations and quantum coherence.The former to isolate non-classicality in how quantum systems can correlate,the latter to formalize non-classicality
3、 of quantum superposition states within a single physical systemExperimentally Obtaining Maximal Coherence Via Assisted Distillation ProcessBasic ConceptI IK KK Kl ll ll lI IIKIKK Kl ll l0 0i ip pi ii i1 1p pi ii ii ii ip p i ii id d1 1d d2 2:Coherence Measure Relative Entropy of Quantum Coherence:w
4、here and The denotes the dephasing operation in the reference basis：)(minmin()S SC CI I RERE)loglog Tr(Tr(loglog)(2 22 2S S()()()S SS SC CREREi ii i i ii i()i i)(Coherence Measure L1-Norm Measure of Quantum Coherence:where denote the trace norm,we have:The above two measures are most popular among a
5、ll quantifiers l1l1l1l1 I I minmin()C CA AA ATrTrA Al1l1 j ji iij ijl1l1|()C CAssisted Distillation Protocol Condition:At least two subsystems Alice and Bob Task:Obtaining maximal distillable coherence on Bobs side with the assistance of Alice Restriction:Local Quantum Incoherent Operations and Clas
6、sical Communication(LQICC):Arbitrary operations can be performed on Alices side and classical information is allowed,while Bob is restricted only to incoherent operations Distillable Coherence of Collaboration:Quantum-Incoherent State:QI-Relative Entropy of Quantum Coherence:where:set of quantum-inc
7、oherent statesB Bi iA Ai ii ii i)(minmin()S SC CB B|A ARERE 0 0)(limlim:RR()RnRnn n infinfn nB B|A Ad d supsupC CTheoretical Results()()B B|A AR RE EB B|A Ad dC CC C)()(ABABB B|A AREREABABB B|A Ad dC CC CExperimental SetupExperimentally obtaining maximal coherence via assisted distillation process，O
8、ptica Vol.4,Issue 4,pp.454-459(2017),Kang-Da Wu,et al In the experiments,we respectively tested pure and mixed state Two classes of pure states were generated as and Mixed states were generated as Werner states:with arbitrary purity.VVVV2 2 HHHH2 2 sinsin coscosABAB)V VV V2 2 V VHH2 2 HHV V2 2 HHHH2
9、 2(1 1 s si in n s si in n c co os s c co os s2 2A AB BI I 4 4)(1 1p pp pExperimental ResultsExperimentally obtaining maximal coherence via assisted distillation process，Optica Vol.4,Issue 4,pp.454-459(2017),Kang-Da Wu,et alExperimental results for the pure states(a)Experimental results for the pure
10、 states(b)Experimentally obtaining maximal coherence via assisted distillation process，Optica Vol.4,Issue 4,pp.454-459(2017),Kang-Da Wu,et alExperimental results for the mixed statesExperimentally obtaining maximal coherence via assisted distillation process，Optica Vol.4,Issue 4,pp.454-459(2017),Kan
11、g-Da Wu,et alCyclic Inter-conversion between Quantum Coherence and Quantum CorrelationTheoretical Framework Two subsystems A and B Correlation measure:Relative Entropy of Quantum Discord:The operation represents projection into arbitrary but orthogonal basis in subsystem A and B Coherence measure:Re
12、lative Entropy of Quantum Coherence.)(minmin)(ABABABABABABABABRERES SD DABABB Bj jB Bj jA Ai iA Ai iABABe ee ee ee eTheoretical FrameworkExperimental cyclic inter-conversion between Coherence and Quantum Correlations arXiv:1710.01738 quant-ph，Kang-Da Wu et al.Theoretical FrameworkExperimental cyclic
13、 inter-conversion between Coherence and Quantum Correlations arXiv:1710.01738 quant-ph，Kang-Da Wu et al.Converting coherence to discord In single-shot Let ,and where is incoherent operation and is an incoherent ancilla.We have (1)The bound can always be saturated by first replacing B with an incoher
14、ent pure state，following a generalized controlled-NOT gate。)(B BA AABABI IABAB)()(A AREREI IABABREREC CD DA AB Bd dd d ABAB B B B B0 0B B0 0i ii iRecycling discord back to coherence Under single-shot LQICC operation For the full-conversion case of We have (2)The bound can be saturated by application
15、 of optimal single-shot LQICC operations。Thus we establish cyclic inter-conversion between quantum coherence and discord with out loss.)()(ImaxImaxABABRERELQICCLQICCA AREREDDC CImaxImaxABAB Recycling discord back to coherence The optimal LQICC can be constructed as projections on the basis of B，toge
16、ther with a feed forward incoherent operation on A.The resulting state of A is ，the same as the initial state.1 1d d1 1k k2 2 ijkijkk ke ei ik kk ke ei i1 1d d1 1k k2 2 ikikA ALQICCLQICCA A General CaseIn general,the protocol in each conversion hold for the basis-dependent discord defined as We have
17、 for the first conversion under incoherent operations andfor the second conversion under LQICC protocol.)()(ABABA AABABABABA A|B BRERES SD D)()(A AREREI IABABA A|B BREREC CD D)()(I IA AB BA A|B BR RE EL LQ QI IC CC CA AR RE ED DC CExperimental SetupExperimental cyclic inter-conversion between Cohere
18、nce and Quantum Correlations arXiv:1710.01738 quant-ph，Kang-Da Wu et al.In the experiments,we respectively tested pure and mixed states of A Pure states:where is an adjustable parameter.Mixed states:Where ，a is a complex number represents dephasing strength that can be tuned.B BA AA AABAB0 0)1 12 2
19、0 02 2 (sinsincoscosB BA AABAB0 00 0 )0 01 1*1 10 0(2 21 1a aa aI I 2 2A AExperimental Results Pure statesExperimental cyclic inter-conversion between Coherence and Quantum Correlations arXiv:1710.01738 quant-ph，Kang-Da Wu et al.Mixed states:Experimental cyclic inter-conversion between Coherence and
20、 Quantum Correlations arXiv:1710.01738 quant-ph，Kang-Da Wu et al.The simulation curves are plotted based on the Quantum Process Tomography of our CNOT gate.The Process fidelity is 0.885.arXiv:1710.01738 quant-ph，Kang-Da Wu et al.A full understanding of these connections is still inprogress.Quantum c
21、omputation:deterministic quantum computation with one quantum bit(DQC1),factoring,measurement based computation.Quantum resource theory:quantum coherence,quantumthermodynamics,quantum correlation which is beyond entanglement.Conclusion Much progress in the physical sciences has been catalysed by the
22、 capacity to transform resources into each other.Help:Unify quantum resources Establishes operational meaning of one resource in the context of the otherFuture Work Manuscript in Preparation:Non-Markovian influence the coherence generating rate at a distant party together with local measurement.Collective measurement in reducing measurement back-action due to quantum coherence and cohering power of quantum process Future Work:Coherence effect in quantum thermodynamics,PT-symmetry evolution.
