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Monogamy of Quantum Correlations. Aditi Sen (De) Harish-Chandra Research Institute, India. Monogamy of Quantum Correlations. Aditi Sen (De) Harish-Chandra Research Institute, India. Co-workers: Asutosh , Salini , Arun , Prabhu , Ujjwal. Outline. - PowerPoint PPT Presentation

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Monogamy of Quantum CorrelationsAditi Sen (De)Harish-Chandra Research Institute, India

Monogamy of Quantum CorrelationsAditi Sen (De)Harish-Chandra Research Institute, India

Co-workers: Asutosh, Salini, Arun, Prabhu, UjjwalWhat is monogamy of quantum correlations?

Quantum Correlations Entanglement-Separability paradigm Information-theoretic paradigm

Info-theoretic measures: nonmonogamous (3-qubits)

R quantum correlations monogamous? Powers of QC r monogamous QC r monogamous for higher no of partiesOutline

What is monogamy of quantum correlations?

Quantum Correlations Entanglement-Separability paradigm Information-theoretic paradigm

Info-theoretic measures: nonmonogamous (3-qubits)

R quantum correlations monogamous? Powers of QC r monogamous QC r monogamous for higher no of partiesOutline

What is monogamy of quantum correlations?

Quantum Correlations Entanglement-Separability paradigm Information-theoretic paradigm

Info-theoretic measures: nonmonogamous (3-qubits)

R quantum correlations monogamous? Powers of QC r monogamous QC r monogamous for higher no of partiesOutline

What is monogamy of quantum correlations?

Quantum Correlations Entanglement-Separability paradigm Information-theoretic paradigm

Info-theoretic measures: nonmonogamous (3-qubits)

What is monogamy of quantum correlations?

Quantum Correlations Entanglement-Separability paradigm Information-theoretic paradigm

Info-theoretic measures: nonmonogamous (3-qubits)

What is monogamy of quantum correlations?

Quantum Correlations Entanglement-Separability paradigm Information-theoretic paradigm

Info-theoretic measures: nonmonogamous (3-qubits)

What is monogamy of QC?

Quantum Correlations Entanglement-Separability paradigm Information-theoretic paradigm

Info-theoretic measures: nonmonogamous (3-qubits)

What is monogamy?

What is monogamy?

Scene from Mahabharata

What is monogamy?

MonogamyScene from Mahabharata

Is sharing QCs between several parties restricted? What is monogamy?

What is monogamy?

BAC

What is monogamy?

BACMaximal QC

What is monogamy?

BACMaximal QCNo QC

What is monogamy?BACMaximal QCNo QCIf A and B have maximal QC,they cannot be quantum correlated, at all with CEkert, PRL91; Bennett, Brassard, Mermin, PRL92C.H. Bennett, et al., PRA 53, 2046 (96)

What is monogamy?BACMaximal QCNo QC

If A and B have maximal QC,they cannot be quantum correlated, at all with CWhat is monogamy?BACHighly QCWeakly QC

What is monogamy?BACHighly QCMain ingredient of quantum cryptography

SenderReceiverEavesdropper

What is monogamy?BACHigh CCHigh CCClassical correlations do not follow!!

What is monogamy?BACHighly QCWeakly QC Trade-off between the amount of QCs between A-B and A-C -- Monogamy

Monogamy-QuantificationBAC Monogamy relation for QC measure

Monogamy-QuantificationBAC Monogamy relation for QC measure

Monogamy-QuantificationBAC Monogamy relation for QC measure

Monogamy-QuantificationBAC Monogamy relation for QC measure

If is monogamous, thenMonogamy-QuantificationBAC

Coffman, Kundu, Wootters, PRA 61, 052306 (00)

If is monogamous, thenMonogamy-QuantificationB1ABN

B2N+1-party case

Squared Concurrence is monogamousMonogamy of concurrenceB1ABN

B2CKW,PRA00; Osborne, Verstraete, PRL 06

Monogamy-QuantificationB1ABN

B2

Multiparty Properties by bipartite measures

What is monogamy of quantum correlations?

QC measures Entanglement-Separability paradigm Information-theoretic paradigm

Info-theoretic measures: nonmonogamous (3-qubits)

Entanglement measures

Is it entangled?

3232Entanglement measures

Is it entangled?

Qualitative query3333Entanglement measures

Is it entangled?How much?

Qualitative queryQuantitative query3434Entanglement measures

Is it entangled?How much?

For 2 spin-1/2 particles, Entanglement: well understoodqualitatively, quantitatively

3535Entanglement MeasuresEnt of Formation, Concurrence

Logarithmic NegativityWootters, PRL 80, 2245 (98)Vidal, Werner, PRA 65, 2245 (1998)

Ent of Formation

Concurrence:

s are the square root of the eigen values of

Ent of Formation

Concurrence:

s are the square root of the eigen values of

Ent of Formation

Concurrence:

s are the square root of the eigen values of

Computable measure

: absolute sum of negative eigenvalues of

Partial transpose:Log Neg

: absolute sum of negative eigenvalues of

Partial transpose:Log NegComputable measure

Information-theoretic MeasuresQuantum Discord

Quantum Work-deficitOlliver&Zurek, Henderson & Vedral 01Oppenheim. Horodeccy, ASD, Sen 03H(X|Y)Quantum discordH(X)H(Y)H(Y|X)H(X,Y)H(X) + H(Y) H(X,Y)H(X) H(X|Y)orMutual informationfor classical random variables.H = Shannon Entropy

434083 (manab) 4055 (nju verma)H(X|Y)H(X)H(Y)H(Y|X)H(X,Y)H(X) + H(Y) H(X,Y)H(X) H(X|Y)orQuantizing them producesinequivalent quantitiesfor bipartite quantum states.Quantum discord

444083 (manab) 4055 (nju verma)H(X|Y)H(X)H(Y)H(Y|X)H(X,Y)H(X) + H(Y) H(X,Y)H(X) H(X|Y)orQuantizing them producesinequivalent quantitiesfor bipartite quantum states.The difference is called Discord.Quantum discord

454083 (manab) 4055 (nju verma)H(X|Y)H(X)H(Y)H(Y|X)H(X,Y)S(X) + S(Y) S(X,Y)S(X) S(X|Y)orThe difference is called Discord.Total CorrClassical CorrDiscordQuantum discord

464083 (manab) 4055 (nju verma)Quantum Work-deficit

H(X|Y)H(Y|X)The difference is called WDGlobal workLocal WorkWD

Quantum Work-deficit

H(X|Y)H(Y|X)The difference is called WDGlobal workLocal WorkWD

Quantum Work-deficit

H(X|Y)H(Y|X)The difference is called WDGlobal workLocal WorkWD

What is monogamy of quantum correlations?

Quantum Correlations Entanglement-Separability paradigm Information-theoretic paradigm

Info-theoretic measures: nonmonogamous (3-qubits)

Does quantum discord satisfy monogamy relation?

Does the sharing of quantum discord follow the same broad guidelines that are followed by entanglement?Questions

51Does quantum discord satisfy monogamy relation?

Does the sharing of quantum discord follow the same broad guidelines that are followed by entanglement?Questions

52

For tripartite state

Monogamy of Q DiscordDoes it hold?

53

For tripartite state

Monogamy of Q DiscordDoes it hold?a000 + b111 generalized GHZ

54

For tripartite state

Monogamy of Q DiscordDoes it hold?a000 + b111 generalized GHZ

55

For tripartite state

Monogamy of Q DiscordDoes it hold?c001 + d010 + e100 generalized W

56

Monogamy of Q DiscordDoes it hold?c001 + d010 + e100 generalized W

57

Monogamy of Q DiscordDoes it hold?c001 + d010 + e100 generalized WPrabhu, Pati, ASD, Sen, PRA 86 040102(R)12

58Quantum discord is nonmonogamous

Quantum discord is nonmonogamous

What is it useful for?a000 + b111 generalized GHZ

c001 + d010 + e100 generalized W

GHZ vs W

a000 + b111 generalized GHZ

c001 + d010 + e100 generalized W

GHZ vs WSLOCC

a000 + b111 generalized GHZ

c001 + d010 + e100 generalized W

GHZ vs WMonogamy of discord can distinguish them.

a000 + b111 generalized GHZ

c001 + d010 + e100 generalized W

GHZ vs WMonogamy of discord can distinguish them.GHZs are monogamous.Ws are polygamous.

GHZ vs WMonogamy of discord test{Gen GHZ, Gen W}

Positive portNegative portS

GHZ vs WMonogamy of discord test{Gen GHZ, Gen W}

>00SatisfyGen W< 0ViolateGHZ class90%-->010%--