An entanglement measure for multipartite pure states is formulated using the product of the von Neumann entropy of the reduced density matrices of the constituents. Based on this new measure, all possible ways of the ...An entanglement measure for multipartite pure states is formulated using the product of the von Neumann entropy of the reduced density matrices of the constituents. Based on this new measure, all possible ways of the maximal entanglement of the triqubit pure states are studied in detail and all types of the maximal entanglement have been compared with the result of ‘the average entropy’. The new measure can be used to calculate the degree of entanglement, and an improvement is given in the area near the zero entropy.展开更多
Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems.We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entan...Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems.We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-q entanglement, and Rényi-α entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.展开更多
We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure.We derive the Fubini−Study metric of the projective Hilbert space of a multi-qubit quantum system,endowing it with ...We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure.We derive the Fubini−Study metric of the projective Hilbert space of a multi-qubit quantum system,endowing it with a Riemannian metric structure,and investigate its deep link with the entanglement of the states of this space.As a measure,we adopt the entanglement distance E preliminary proposed in Phys.Rev.A 101,042129(2020).Our analysis shows that entanglement has a geometric interpretation:E(|ψ>)is the minimum value of the sum of the squared distances between|ψ>and its conjugate states,namely the statesυ^(μ).σ^(μ)|ψ>,whereυ^(μ)are unit vectors andμruns on the number of parties.Within the proposed geometric approach,we derive a general method to determine when two states are not the same state up to the action of local unitary operators.Furthermore,we prove that the entanglement distance,along with its convex roof expansion to mixed states,fulfils the three conditions required for an entanglement measure,that is:i)E(|ψ>)=0 iff|ψ>is fully separable;ii)E is invariant under local unitary transformations;iii)E does not increase under local operation and classical communications.Two different proofs are provided for this latter property.We also show that in the case of two qubits pure states,the entanglement distance for a state|ψ>coincides with two times the square of the concurrence of this state.We propose a generalization of the entanglement distance to continuous variable systems.Finally,we apply the proposed geometric approach to the study of the entanglement magnitude and the equivalence classes properties,of three families of states linked to the Greenberger−Horne−Zeilinger states,the Briegel Raussendorf states and the W states.As an example of application for the case of a system with continuous variables,we have considered a system of two coupled Glauber coherent states.展开更多
A new simplified formula is presented to characterize genuine tripartite entanglement of （2 2 n）-dimensional quantum pure states. The formula turns out equivalent to that given in （Quant. Inf. Comp. 7（7） 584 ...A new simplified formula is presented to characterize genuine tripartite entanglement of （2 2 n）-dimensional quantum pure states. The formula turns out equivalent to that given in （Quant. Inf. Comp. 7（7） 584 （2007））, hence it also shows that the genuine tripartite entanglement can be described only on the basis of the local （2 2）-dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang （Phys. Rev. A 71 030302（R） （2005）） are reconsidered by employing the formula. The results show that a discontinuity in the first derivative of the formula or in the formula itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously different from the concurrence.展开更多
Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the g...Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the generalized Smolin state （GSS） in the presence of noise and the two-mode squeezed thermal state. Moreover, we compare their RGME with geometric measure of entanglement （GME） and relative entropy of entanglement （RE）. The results indicate RGME is an appropriate measure of entanglement. Finally, we define the Gaussian GME which is an entangled monotone.展开更多
We propose to use a set of averaged entropies, the multiple entropy measures (MEMS), to partiallyquantify quantum entanglement of multipartite quantum state.The MEMS is vector-like with m = [N/2] components:[S_1, S_2,...We propose to use a set of averaged entropies, the multiple entropy measures (MEMS), to partiallyquantify quantum entanglement of multipartite quantum state.The MEMS is vector-like with m = [N/2] components:[S_1, S_2,..., S_m], and the i-th component S_i is the geometric mean of i-qubits partial entropy of the system.The S_imeasures how strong an arbitrary i qubits from the system are correlated with the rest of the system.It satisfies theconditions for a good entanglement measure.We have analyzed the entanglement properties of the GHZ-state, theW-states, and cluster-states under MEMS.展开更多
Fidelity plays an important role in quantum information processing,which provides a basic scale for comparing two quantum states.At present,one of the most commonly used fidelities is Uhlmann-Jozsa(U-J)fidelity.Howeve...Fidelity plays an important role in quantum information processing,which provides a basic scale for comparing two quantum states.At present,one of the most commonly used fidelities is Uhlmann-Jozsa(U-J)fidelity.However,U-J fidelity needs to calculate the square root of the matrix,which is not trivial in the case of large or infinite density matrices.Moreover,U-J fidelity is a measure of overlap,which has limitations in some cases and cannot reflect the similarity between quantum states well.Therefore,a novel quantum fidelity measure called quantum Tanimoto coefficient(QTC)fidelity is proposed in this paper.Unlike other existing fidelities,QTC fidelity not only considers the overlap between quantum states,but also takes into account the separation between quantum states for the first time,which leads to a better performance of measure.Specifically,we discuss the properties of the proposed QTC fidelity.QTC fidelity is compared with some existing fidelities through specific examples,which reflects the effectiveness and advantages of QTC fidelity.In addition,based on the QTC fidelity,three discrimination coefficients d_(1)^(QTC),d_(2)^(QTC),and d_^(3)^(QTC)are defined to measure the difference between quantum states.It is proved that the discrimination coefficient d_(3)^(QTC)is a true metric.Finally,we apply the proposed QTC fidelity-based discrimination coefficients to measure the entanglement of quantum states to show their practicability.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 10325521 and 60433050) the National Basic Research Program of China(Grant No. 001CB309308).
文摘An entanglement measure for multipartite pure states is formulated using the product of the von Neumann entropy of the reduced density matrices of the constituents. Based on this new measure, all possible ways of the maximal entanglement of the triqubit pure states are studied in detail and all types of the maximal entanglement have been compared with the result of ‘the average entropy’. The new measure can be used to calculate the degree of entanglement, and an improvement is given in the area near the zero entropy.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11805143,11675113Key Project of Beijing Municipal Commission of Education under Grant No.KZ201810028042
文摘Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems.We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-q entanglement, and Rényi-α entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.
基金support from the Research Support Plan 2022-Call for applications for funding allocation to research projects curiosity driven(F CUR)-Project“Entanglement Protection of Qubits’Dynamics in a Cavity”-EPQDCthe support by the Italian National Group of Mathematical Physics(GNFM-INdAM)financial support to this activity.
文摘We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure.We derive the Fubini−Study metric of the projective Hilbert space of a multi-qubit quantum system,endowing it with a Riemannian metric structure,and investigate its deep link with the entanglement of the states of this space.As a measure,we adopt the entanglement distance E preliminary proposed in Phys.Rev.A 101,042129(2020).Our analysis shows that entanglement has a geometric interpretation:E(|ψ>)is the minimum value of the sum of the squared distances between|ψ>and its conjugate states,namely the statesυ^(μ).σ^(μ)|ψ>,whereυ^(μ)are unit vectors andμruns on the number of parties.Within the proposed geometric approach,we derive a general method to determine when two states are not the same state up to the action of local unitary operators.Furthermore,we prove that the entanglement distance,along with its convex roof expansion to mixed states,fulfils the three conditions required for an entanglement measure,that is:i)E(|ψ>)=0 iff|ψ>is fully separable;ii)E is invariant under local unitary transformations;iii)E does not increase under local operation and classical communications.Two different proofs are provided for this latter property.We also show that in the case of two qubits pure states,the entanglement distance for a state|ψ>coincides with two times the square of the concurrence of this state.We propose a generalization of the entanglement distance to continuous variable systems.Finally,we apply the proposed geometric approach to the study of the entanglement magnitude and the equivalence classes properties,of three families of states linked to the Greenberger−Horne−Zeilinger states,the Briegel Raussendorf states and the W states.As an example of application for the case of a system with continuous variables,we have considered a system of two coupled Glauber coherent states.
基金supported by the National Natural Science Foundation of China (Grant Nos 10747112 and 10575017)
文摘A new simplified formula is presented to characterize genuine tripartite entanglement of （2 2 n）-dimensional quantum pure states. The formula turns out equivalent to that given in （Quant. Inf. Comp. 7（7） 584 （2007））, hence it also shows that the genuine tripartite entanglement can be described only on the basis of the local （2 2）-dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang （Phys. Rev. A 71 030302（R） （2005）） are reconsidered by employing the formula. The results show that a discontinuity in the first derivative of the formula or in the formula itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously different from the concurrence.
基金supported by the National Natural Science Foundation of China under Grant No. 60573008
文摘Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the generalized Smolin state （GSS） in the presence of noise and the two-mode squeezed thermal state. Moreover, we compare their RGME with geometric measure of entanglement （GME） and relative entropy of entanglement （RE）. The results indicate RGME is an appropriate measure of entanglement. Finally, we define the Gaussian GME which is an entangled monotone.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10775076,10874098 (GLL)the 973 Program 2006CB921106 (XZ)+1 种基金 the SRFDP Program of Education Ministry of China under Gtant No.20060003048 the Fundamental Research Funds for the Central Universities,DC10040119 (DL)
文摘We propose to use a set of averaged entropies, the multiple entropy measures (MEMS), to partiallyquantify quantum entanglement of multipartite quantum state.The MEMS is vector-like with m = [N/2] components:[S_1, S_2,..., S_m], and the i-th component S_i is the geometric mean of i-qubits partial entropy of the system.The S_imeasures how strong an arbitrary i qubits from the system are correlated with the rest of the system.It satisfies theconditions for a good entanglement measure.We have analyzed the entanglement properties of the GHZ-state, theW-states, and cluster-states under MEMS.
基金supported by the National Natural Science Foundation of China(62003280,61976120)Chongqing Talents:Exceptional Young Talents Project(cstc2022ycjh-bgzxm0070)+2 种基金Natural Science Foundation of Chongqing(2022NSCQ-MSX2993)Natural Science Key Foundation of Jiangsu Education Department(21KJA510004)Chongqing Overseas Scholars Innovation Program(cx2022024)。
文摘Fidelity plays an important role in quantum information processing,which provides a basic scale for comparing two quantum states.At present,one of the most commonly used fidelities is Uhlmann-Jozsa(U-J)fidelity.However,U-J fidelity needs to calculate the square root of the matrix,which is not trivial in the case of large or infinite density matrices.Moreover,U-J fidelity is a measure of overlap,which has limitations in some cases and cannot reflect the similarity between quantum states well.Therefore,a novel quantum fidelity measure called quantum Tanimoto coefficient(QTC)fidelity is proposed in this paper.Unlike other existing fidelities,QTC fidelity not only considers the overlap between quantum states,but also takes into account the separation between quantum states for the first time,which leads to a better performance of measure.Specifically,we discuss the properties of the proposed QTC fidelity.QTC fidelity is compared with some existing fidelities through specific examples,which reflects the effectiveness and advantages of QTC fidelity.In addition,based on the QTC fidelity,three discrimination coefficients d_(1)^(QTC),d_(2)^(QTC),and d_^(3)^(QTC)are defined to measure the difference between quantum states.It is proved that the discrimination coefficient d_(3)^(QTC)is a true metric.Finally,we apply the proposed QTC fidelity-based discrimination coefficients to measure the entanglement of quantum states to show their practicability.
