If there are correlations between two qubits then the results of the measurement on one of them can help to predict measurement results on the other one. It is an interesting question what can be predicted about the results of two complementary projective measurements on the first qubit. To quantify these predictions the complementary knowledge excesses are used. A non-trivial constraint restricting them is derived. For any mixed state and for arbitrary measurements the knowledge excesses are bounded by a factor depending only on the maximal violation of Bell's inequalities. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.If there are correlations between two qubits then the results of the measurement on one of them can help to predict measurement results on the other one. It is an interesting question what can be predicted about the results of two complementary projective measurements on the first qubit. To quantify these predictions the complementary knowledge excesses are used. A non-trivial constraint restricting them is derived. For any mixed state and for arbitrary measurements the knowledge excesses are bounded by a factor depending only on the maximal violation of Bell's inequalities. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEAug 15, 20050 citations

How Quantum Correlations Enhance Prediction of Complementary Measurements

Radim Filip, Miroslav Gavenda, Jan Soubusta +2 more

If there are correlations between two qubits, then the results of the measurement on one of them can help to predict measurement results on the other one. It is an interesting question as to what can be predicted about the results of two complementary projective measurements on the first qubit. To quantify these predictions the complementary knowledge excesses are used. A nontrivial constraint restricting them is derived. For any mixed state and for arbitrary measurements the knowledge excesses are bounded by a factor depending only on the maximal violation of Bell's inequalities. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.If there are correlations between two qubits, then the results of the measurement on one of them can help to predict measurement results on the other one. It is an interesting question as to what can be predicted about the results of two complementary projective measurements on the first qubit. To quantify these predictions the complementary knowledge excesses are used. A nontrivial constraint restricting them is derived. For any mixed state and for arbitrary measurements the knowledge excesses are bounded by a factor depending only on the maximal violation of Bell's inequalities. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.

arXiv:quant-ph/0406110Physical Review LettersOct 27, 20046 citations

KNOWLEDGE EXCESS DUALITY AND VIOLATION OF BELL INEQUALITIES: THEORY AND EXPERIMENT

Miroslav Gavenda, Antonín Černoch, Jan Soubusta +2 more

We analyze correlations between two parties sharing a general mixed two-qubit state ρSM in order to predict measurement outcomes. It is an interesting question as to what can be predicted about the results of two complementary projective measurements on one qubit from the measurement results on the other qubit. To quantify these predictions the complementary knowledge excessesΔK(ΠM→ΠS) and ΔK(Π′M→Π′S) are used, where ΠS, Π′S resp. ΠM, Π′M represent projective measurements on the qubit S resp. M. We derive an inequality ΔK2(ΠM→ΠS) + ΔK2(Π′M→Π′S)≤(B max /2)2, where B max is the maximum violation of Bell inequalities. This inequality restricts our capability to enhance the complementary predictions for any state ρSM and for arbitrary ΠS, Π′S and ΠM, Π′M. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.We analyze correlations between two parties sharing a general mixed two-qubit state ρSM in order to predict measurement outcomes. It is an interesting question as to what can be predicted about the results of two complementary projective measurements on one qubit from the measurement results on the other qubit. To quantify these predictions the complementary knowledge excessesΔK(ΠM→ΠS) and ΔK(Π′M→Π′S) are used, where ΠS, Π′S resp. ΠM, Π′M represent projective measurements on the qubit S resp. M. We derive an inequality ΔK2(ΠM→ΠS) + ΔK2(Π′M→Π′S)≤(B max /2)2, where B max is the maximum violation of Bell inequalities. This inequality restricts our capability to enhance the complementary predictions for any state ρSM and for arbitrary ΠS, Π′S and ΠM, Π′M. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.

Modern Physics Letters BMar 10, 20053 citations

Knowledge excess duality and violation of Bell inequalities

Radim Filip, Miroslav Gavenda

A constraint on two complementary knowledge excesses by maximal violation of Bell inequalities for a single copy of any mixed state of two qubits $S,M$ is analyzed. The complementary knowledge excesses ${\bf ΔK}(Π_{M}\to Π_{S})$ and ${\bf ΔK}(Π'_{M}\to Π'_{S})$ quantify an enhancement of ability to predict results of the complementary projective measurements $Π_{S},Π'_{S}$ on the qubit $S$ from the projective measurements $Π_{M},Π'_{M}$ performed on the qubit $M$ . For any state $ρ_{SM}$ and for arbitrary $Π_{S},Π'_{S}$ and $Π_{M},Π'_{M}$ , the knowledge excesses satisfy the following inequality ${\bf ΔK}^{2}(Π_{M}\to Π_{S})+{\bf ΔK}^{2} (Π'_{M}\to Π'_{S})\leq (B_{max}/2)^2$ , where $B_{max}$ is maximum of violation of Bell inequalities under single-copy local operations (local filtering and unitary transformations). Particularly, for the Bell-diagonal states only an appropriate choice of the measurements $Π_{S},Π'_{S}$ and $Π_{M},Π'_{M}$ are sufficient to saturate the inequality.A constraint on two complementary knowledge excesses by maximal violation of Bell inequalities for a single copy of any mixed state of two qubits $S,M$ is analyzed. The complementary knowledge excesses ${\bf ΔK}(Π_{M}\to Π_{S})$ and ${\bf ΔK}(Π'_{M}\to Π'_{S})$ quantify an enhancement of ability to predict results of the complementary projective measurements $Π_{S},Π'_{S}$ on the qubit $S$ from the projective measurements $Π_{M},Π'_{M}$ performed on the qubit $M$. For any state $ρ_{SM}$ and for arbitrary $Π_{S},Π'_{S}$ and $Π_{M},Π'_{M}$, the knowledge excesses satisfy the following inequality ${\bf ΔK}^{2}(Π_{M}\to Π_{S})+{\bf ΔK}^{2} (Π'_{M}\to Π'_{S})\leq (B_{max}/2)^2$, where $B_{max}$ is maximum of violation of Bell inequalities under single-copy local operations (local filtering and unitary transformations). Particularly, for the Bell-diagonal states only an appropriate choice of the measurements $Π_{S},Π'_{S}$ and $Π_{M},Π'_{M}$ are sufficient to saturate the inequality.

arXiv:quant-ph/0404145Apr 26, 20040 citations

Experimental Certification of Quantum Entanglement Based on the Classical Complementary Correlations of Two-Qubit States

Zhihao Bian, Hui Wu

Quantum entanglement is one of the essential resources in quantum information processing. It is of importance to verify whether a quantum state is entangled. At present, a typical quantum certification focused on the classical correlations has attracted widespread attention. Here, we experimentally investigate the relation between quantum entanglement and the classical complementary correlations based on the mutual information, Pearson correlation coefficient and mutual predictability of two-qubit states. Our experimental results show the classical correlations for complementary properties have strong resolution capability to verify entanglement for two qubit pure states and Werner states. We find that the resolution capability has great performance improvement when the eigenstates of the measurement observables constitute a complete set of mutually unbiased bases. For Werner states in particular, the classical complementary correlations based on the Pearson correlation coefficient and mutual predictability can provide the ultimate bounds to certify entanglement.Quantum entanglement is one of the essential resources in quantum information processing. It is of importance to verify whether a quantum state is entangled. At present, a typical quantum certification focused on the classical correlations has attracted widespread attention. Here, we experimentally investigate the relation between quantum entanglement and the classical complementary correlations based on the mutual information, Pearson correlation coefficient and mutual predictability of two-qubit states. Our experimental results show the classical correlations for complementary properties have strong resolution capability to verify entanglement for two qubit pure states and Werner states. We find that the resolution capability has great performance improvement when the eigenstates of the measurement observables constitute a complete set of mutually unbiased bases. For Werner states in particular, the classical complementary correlations based on the Pearson correlation coefficient and mutual predictability can provide the ultimate bounds to certify entanglement.

PhotonicsNov 23, 20212 citations

Experimental investigation of the relation between measurement uncertainties and non-local quantum correlations

Kengo Matsuyama, Holger Friedrich Hofmann, M. Iinuma

Abstract Bell’s inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell’s inequalities are only possible because the precision of any joint measurement of these observables will be limited by quantum mechanical uncertainty relations. In this paper we explore the relation between the local measurement uncertainties and the magnitude of the correlations by preparing polarization entangled photon pairs and performing joint measurements of non-commuting polarization components at different uncertainty trade-offs. The change in measurement visibility reveals the existence of a non-trivial balance between the measurement uncertainties where the probabilities of a specific pair of measurement outcomes approaches zero because of the particular combination of enhancement and suppression of the experimentally observed correlations. The occurrence of these high-contrast results shows that the quantum correlations between the photons are close to their maximal value, confirming that the Cirel’son bound of Bell’s inequality violations is defined by the minimal uncertainties that limit the precision of joint measurements.Abstract Bell’s inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell’s inequalities are only possible because the precision of any joint measurement of these observables will be limited by quantum mechanical uncertainty relations. In this paper we explore the relation between the local measurement uncertainties and the magnitude of the correlations by preparing polarization entangled photon pairs and performing joint measurements of non-commuting polarization components at different uncertainty trade-offs. The change in measurement visibility reveals the existence of a non-trivial balance between the measurement uncertainties where the probabilities of a specific pair of measurement outcomes approaches zero because of the particular combination of enhancement and suppression of the experimentally observed correlations. The occurrence of these high-contrast results shows that the quantum correlations between the photons are close to their maximal value, confirming that the Cirel’son bound of Bell’s inequality violations is defined by the minimal uncertainties that limit the precision of joint measurements.

arXiv:2106.01052Journal of Physics CommunicationsOct 20, 20214 citations

A constraint on two complementary knowledge excesses by maximal violation of Bell inequalities for a single copy of any mixed state of two qubits

S,M

is analyzed. The complementary knowledge excesses

{\bf ΔK}(Π_{M}\to Π_{S})

and

{\bf ΔK}(Π'_{M}\to Π'_{S})

quantify an enhancement of ability to predict results of the complementary projective measurements

Π_{S},Π'_{S}

on the qubit

S

from the projective measurements

Π_{M},Π'_{M}

performed on the qubit

M

. For any state

ρ_{SM}

and for arbitrary

Π_{S},Π'_{S}

and

Π_{M},Π'_{M}

, the knowledge excesses satisfy the following inequality

{\bf ΔK}^{2}(Π_{M}\to Π_{S})+{\bf ΔK}^{2} (Π'_{M}\to Π'_{S})\leq (B_{max}/2)^2

, where

B_{max}

is maximum of violation of Bell inequalities under single-copy local operations (local filtering and unitary transformations). Particularly, for the Bell-diagonal states only an appropriate choice of the measurements

Π_{S},Π'_{S}

and

Π_{M},Π'_{M}

are sufficient to saturate the inequality.