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

How Quantum Correlations Enhance Prediction of Complementary Measurements

Radim Filip

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.

AIP conference proceedingsJan 1, 20040 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

Quantum correlations in mutually unbiased bases and non-Markovian dephasing

Hermann L. Albrecht, David M. Bellorin

Wu et al. introduced a symmetric measure $Q^{s}$ in terms of mutually unbiased bases (MUBs) that quantifies residual quantum correlations (RQC). The definition of this measure involves determining two complementary local bases via an optimization of the quantum mutual information. One defines the first local bases, the optimal computational ones, by maximizing the classical correlations measure. Next, one defines a new set of local bases that are complementary to the first ones. In the latter, one also calculates the corresponding measure of quantum correlations by maximization. Considering alternative optimizations of the mentioned measures, one can define other quantifiers. In particular, Mundarain and Ladrón de Guevara introduced local available quantum correlations (LAQC, $\mathcal{L}$ ) in terms of the complementary local bases to the ones defining the least classically correlated state. That is, they characterize LAQC by defining the optimal bases as those that minimize the classical correlations measure. This type of quantum correlation is closely related to an entanglement activation protocol proposed by Piani et al. In previous articles, we derived an exact solution for the LAQC measure for 2-qubit X states. Based on these previous results and methodology, we determine the corresponding exact analytical expression for $Q^s$ of 2-qubit X states. We then analyze the behavior of these two measures for two non-Markovian quantum dephasing channels: Random Telegraph (RT) and Modified Ornstein-Uhlenbeck (MOU) noises. We derive general conditions for sudden death and revival of these measures in X states and illustrate these results with four families of bipartite qubit states: Werner states, Maximally Nonlocal Mixed States (MNMS), Maximally Entangled Mixed States (MEMS), and a mixed symmetric separable state.Wu et al. introduced a symmetric measure $Q^{s}$ in terms of mutually unbiased bases (MUBs) that quantifies residual quantum correlations (RQC). The definition of this measure involves determining two complementary local bases via an optimization of the quantum mutual information. One defines the first local bases, the optimal computational ones, by maximizing the classical correlations measure. Next, one defines a new set of local bases that are complementary to the first ones. In the latter, one also calculates the corresponding measure of quantum correlations by maximization. Considering alternative optimizations of the mentioned measures, one can define other quantifiers. In particular, Mundarain and Ladrón de Guevara introduced local available quantum correlations (LAQC, $\mathcal{L}$) in terms of the complementary local bases to the ones defining the least classically correlated state. That is, they characterize LAQC by defining the optimal bases as those that minimize the classical correlations measure. This type of quantum correlation is closely related to an entanglement activation protocol proposed by Piani et al. In previous articles, we derived an exact solution for the LAQC measure for 2-qubit X states. Based on these previous results and methodology, we determine the corresponding exact analytical expression for $Q^s$ of 2-qubit X states. We then analyze the behavior of these two measures for two non-Markovian quantum dephasing channels: Random Telegraph (RT) and Modified Ornstein-Uhlenbeck (MOU) noises. We derive general conditions for sudden death and revival of these measures in X states and illustrate these results with four families of bipartite qubit states: Werner states, Maximally Nonlocal Mixed States (MNMS), Maximally Entangled Mixed States (MEMS), and a mixed symmetric separable state.

quant-pharXiv:2603.13648Journal of Physics A Mathematical and TheoreticalMar 17, 20260 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.

Wu et al. introduced a symmetric measure

Q^{s}

in terms of mutually unbiased bases (MUBs) that quantifies residual quantum correlations (RQC). The definition of this measure involves determining two complementary local bases via an optimization of the quantum mutual information. One defines the first local bases, the optimal computational ones, by maximizing the classical correlations measure. Next, one defines a new set of local bases that are complementary to the first ones. In the latter, one also calculates the corresponding measure of quantum correlations by maximization. Considering alternative optimizations of the mentioned measures, one can define other quantifiers. In particular, Mundarain and Ladrón de Guevara introduced local available quantum correlations (LAQC,

\mathcal{L}

) in terms of the complementary local bases to the ones defining the least classically correlated state. That is, they characterize LAQC by defining the optimal bases as those that minimize the classical correlations measure. This type of quantum correlation is closely related to an entanglement activation protocol proposed by Piani et al. In previous articles, we derived an exact solution for the LAQC measure for 2-qubit X states. Based on these previous results and methodology, we determine the corresponding exact analytical expression for

Q^s

of 2-qubit X states. We then analyze the behavior of these two measures for two non-Markovian quantum dephasing channels: Random Telegraph (RT) and Modified Ornstein-Uhlenbeck (MOU) noises. We derive general conditions for sudden death and revival of these measures in X states and illustrate these results with four families of bipartite qubit states: Werner states, Maximally Nonlocal Mixed States (MNMS), Maximally Entangled Mixed States (MEMS), and a mixed symmetric separable state.