Entanglement is the key resource in quantum information processing,and an entanglement witness(EW)is designed to detect whether a quantum system has any entanglement.However,prior knowledge of the target states should...Entanglement is the key resource in quantum information processing,and an entanglement witness(EW)is designed to detect whether a quantum system has any entanglement.However,prior knowledge of the target states should be known first to design a suitable EW,which weakens this method.Nevertheless,a recent theory shows that it is possible to design a universal entanglement witness(UEW)to detect negative-partial-transpose(NPT)entanglement in unknown bipartite states with measurement-device-independent(MDI)characteristic.The outcome of a UEW can also be upgraded to be an entanglement measure.In this study,we experimentally design and realize an MDI UEW for two-qubit entangled states.All of the tested states are well-detected without any prior knowledge.We also show that it is able to quantify entanglement by comparing it with concurrence estimated through state tomography.The relation between them is also revealed.The entire experimental framework ensures that the UEW is MDI.展开更多
In the measurement-based model of quantum computing, a one-way quantum computer consisting of many qubits can be immersed in a common environment as a simple decoherence mechanism. This paper studies the dynamics of e...In the measurement-based model of quantum computing, a one-way quantum computer consisting of many qubits can be immersed in a common environment as a simple decoherence mechanism. This paper studies the dynamics of entanglement witness for 3-qubit cluster states in the common environment. The result shows that environment can induce an interesting feature in the time evolution of the entanglement witness： i.e., the periodical collapse and revival of the entanglement dynamics.展开更多
Motivated by the wise idea of entanglement witness （EW）, we present an inequivalent entanglement witness （IEEW） that can analogously classify certain eigenstates entangled in inequivalent ways under stochastic loc...Motivated by the wise idea of entanglement witness （EW）, we present an inequivalent entanglement witness （IEEW） that can analogously classify certain eigenstates entangled in inequivalent ways under stochastic local operations and classical communication （SLOCC） in the Heisenberg spin chain. Since the IEEW is the absolute value of magnetization （M） that is a macroscopically measurable quantity, our conclusions provide a macroscopic method to detect inequivalent entanglement between microscopic spins, on the one hand, and clearly show that inequivalent entanglement can yield different macroscopic effects, on the other hand.展开更多
For n≥3,we construct a class{Wn,π1,π2}of n^(2)×n^(2) hermitian matrices by the permutation pairs and show that,for a pair{π1,π2}of permutations on(1,2,…,n),Wn,π1,π2 is an entanglement witness of the n⊗n s...For n≥3,we construct a class{Wn,π1,π2}of n^(2)×n^(2) hermitian matrices by the permutation pairs and show that,for a pair{π1,π2}of permutations on(1,2,…,n),Wn,π1,π2 is an entanglement witness of the n⊗n system if{π1,π2}has the property(C).Recall that a pair{π1,π2}of permutations of(1,2,…,n)has the property(C)if,for each i,one can obtain a permutation of(1,…,i−1,i+1,…,n)from(π1(1),…,π1(i−1),π1(i+1),…,π1(n))and(π2(1),…,π2(i−1),π2(i+1),…,π2(n)).We further prove that Wn,π1,π2 is not comparable with Wn,π,which is the entanglement witness constructed from a single permutationπ;Wn,π1,π2 is decomposable ifπ1π2=id orπ21=π22=id.For the low dimensional cases n∈{3,4},we give a sufficient and necessary condition onπ1,π2 for Wn,π1,π2 to be an entanglement witness.We also show that,for n∈{3,4},Wn,π1,π2 is decomposable if and only ifπ1π2=id orπ21=π22=id;W3,π1,π2 is optimal if and only if(π1,π2)=(π,π2),whereπ=(2,3,1).As applications,some entanglement criteria for states and some decomposability criteria for positive maps are established.展开更多
Energy is introduced as an entanglement witness to describe the entanglement property of a quantum system. The thermal equilibrium system is guaranteed to be entangled when system is cooled down below the entanglement...Energy is introduced as an entanglement witness to describe the entanglement property of a quantum system. The thermal equilibrium system is guaranteed to be entangled when system is cooled down below the entanglement temperature TE. By virtue of this concept we exploit the minimum separable state energy and entanglement temperature TE of the bilinear-biquadratic antiferromagnetic spin-1 chain model. We numerically calculate TE for arbitrary values of the strength of biquadratic exchange interaction Q up to N=7. We find TE decreases with Q for fixed N when Q is between -3 and 1/3 （J = 1）. In this regime TE also decreases with N for fixed Q and varies slowly for large N. While the thermal system is always entangled when Q is smaller than -3.展开更多
We use the generalized Wootters formula, the positive partial transpose(PPT) criterion and the matched entanglement witness, to detect entanglement of three-qubit GHZ and W superposition state and its decayed states. ...We use the generalized Wootters formula, the positive partial transpose(PPT) criterion and the matched entanglement witness, to detect entanglement of three-qubit GHZ and W superposition state and its decayed states. It shows that the results of the generalized Wootters formula in the part near the W state are tight. In the other parts, the PPT criterion is superior to the generalized Wootters formula. Furthermore, we investigate the relationship between entanglement and coherence.展开更多
Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build famili...Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with a Schmidt number less than k.展开更多
A quantum entangled state is easily disturbed by noise and degenerates into a separable state.Compared to the entanglement with bipartite quantum systems,less progress has been made for the entanglement with multipart...A quantum entangled state is easily disturbed by noise and degenerates into a separable state.Compared to the entanglement with bipartite quantum systems,less progress has been made for the entanglement with multipartite quantum systems.For tripartite separability of a four-qubit system,we propose two entanglement witnesses,each of which corresponds to a necessary condition of tripartite separability.For the four-qubit GHZ state mixed with a W state and white noise,we prove that the necessary conditions of tripartite separability are also sufficient at W states side.展开更多
We analytically investigate Multiple Quantum(MQ) NMR dynamics in a mixed-three-spin(1/2,1,1/2)system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property...We analytically investigate Multiple Quantum(MQ) NMR dynamics in a mixed-three-spin(1/2,1,1/2)system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders(zeroth and second orders) for two pairs of spins(1,1/2) and(1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite(sub)systems(1,1/2) and(1/2,1/2)permanently coupled by, respectively, coupling constants J_1 and J_2, by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins(1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins(1,1/2) as an entanglement witness at some special time intervals.展开更多
We propose a method of constructing the separability criteria for multipartite quantum states on the basis of entanglement witnesses. The entanglement witnesses are obtained by finding the maximal expectation values o...We propose a method of constructing the separability criteria for multipartite quantum states on the basis of entanglement witnesses. The entanglement witnesses are obtained by finding the maximal expectation values of Hermitian operators and then optimizing over all possible Hermitian operators. We derive a set of tripartite separability criteria for the four-qubit Greenberger-Horne-Zeilinger （GHZ） diagonal states. The derived criterion set contains four criteria that are necessary and sufficient for the tripartite separability of the highly symmetric four-qubit GHZ diagonal states; the criteria completely account for the numerically obtained boundaries of the tripartite separable state set. One of the criteria is just the tripartite separability criterion of the four-qubit generalized Werner states.展开更多
基金the National Key Research and Development Program of China(Grant No.2016YFA0302700)the National Natural Science Foundation of China(Grant Nos.11674304,11822408,11774335,61490711,11474267,11821404,and 91321313)+3 种基金the Youth Innovation Promotion Association of Chinese Academy of Sciences(Grant No.2017492)the Foundation for Scientific Instrument and Equipment Development of Chinese Academy of Sciences(Grant No.YJKYYQ20170032)the Key Research Program of Frontier Sciences of the Chinese Academy of Sciences(Grant No.QYZDY-SSW-SLH003)the Fundamental Research Funds for the Central Universities,China(Grant No.WK2470000026)。
文摘Entanglement is the key resource in quantum information processing,and an entanglement witness(EW)is designed to detect whether a quantum system has any entanglement.However,prior knowledge of the target states should be known first to design a suitable EW,which weakens this method.Nevertheless,a recent theory shows that it is possible to design a universal entanglement witness(UEW)to detect negative-partial-transpose(NPT)entanglement in unknown bipartite states with measurement-device-independent(MDI)characteristic.The outcome of a UEW can also be upgraded to be an entanglement measure.In this study,we experimentally design and realize an MDI UEW for two-qubit entangled states.All of the tested states are well-detected without any prior knowledge.We also show that it is able to quantify entanglement by comparing it with concurrence estimated through state tomography.The relation between them is also revealed.The entire experimental framework ensures that the UEW is MDI.
基金Project supported by the Natural Science Foundation of Shandong Province, China （Grant No Y2006 A05）.
文摘In the measurement-based model of quantum computing, a one-way quantum computer consisting of many qubits can be immersed in a common environment as a simple decoherence mechanism. This paper studies the dynamics of entanglement witness for 3-qubit cluster states in the common environment. The result shows that environment can induce an interesting feature in the time evolution of the entanglement witness： i.e., the periodical collapse and revival of the entanglement dynamics.
基金Project supported by the National Natural Science Foundation of China (Grant No 10404039)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No 200524)Program for New Century Excellent Talents (NCET) of China (Grant No NCET-06-0920)
文摘Motivated by the wise idea of entanglement witness （EW）, we present an inequivalent entanglement witness （IEEW） that can analogously classify certain eigenstates entangled in inequivalent ways under stochastic local operations and classical communication （SLOCC） in the Heisenberg spin chain. Since the IEEW is the absolute value of magnetization （M） that is a macroscopically measurable quantity, our conclusions provide a macroscopic method to detect inequivalent entanglement between microscopic spins, on the one hand, and clearly show that inequivalent entanglement can yield different macroscopic effects, on the other hand.
基金partially supported by National Natural Science Foundation of China(11671294,12071336)。
文摘For n≥3,we construct a class{Wn,π1,π2}of n^(2)×n^(2) hermitian matrices by the permutation pairs and show that,for a pair{π1,π2}of permutations on(1,2,…,n),Wn,π1,π2 is an entanglement witness of the n⊗n system if{π1,π2}has the property(C).Recall that a pair{π1,π2}of permutations of(1,2,…,n)has the property(C)if,for each i,one can obtain a permutation of(1,…,i−1,i+1,…,n)from(π1(1),…,π1(i−1),π1(i+1),…,π1(n))and(π2(1),…,π2(i−1),π2(i+1),…,π2(n)).We further prove that Wn,π1,π2 is not comparable with Wn,π,which is the entanglement witness constructed from a single permutationπ;Wn,π1,π2 is decomposable ifπ1π2=id orπ21=π22=id.For the low dimensional cases n∈{3,4},we give a sufficient and necessary condition onπ1,π2 for Wn,π1,π2 to be an entanglement witness.We also show that,for n∈{3,4},Wn,π1,π2 is decomposable if and only ifπ1π2=id orπ21=π22=id;W3,π1,π2 is optimal if and only if(π1,π2)=(π,π2),whereπ=(2,3,1).As applications,some entanglement criteria for states and some decomposability criteria for positive maps are established.
基金The project supported by the National Fundamental Research Program of China under Grant No. 2001CB309310 and National Natural Science Foundation of China under Grant No. 60573008.We are grateful to MA Xiao-San and CA0 Ya for helpful discussions.
文摘Energy is introduced as an entanglement witness to describe the entanglement property of a quantum system. The thermal equilibrium system is guaranteed to be entangled when system is cooled down below the entanglement temperature TE. By virtue of this concept we exploit the minimum separable state energy and entanglement temperature TE of the bilinear-biquadratic antiferromagnetic spin-1 chain model. We numerically calculate TE for arbitrary values of the strength of biquadratic exchange interaction Q up to N=7. We find TE decreases with Q for fixed N when Q is between -3 and 1/3 （J = 1）. In this regime TE also decreases with N for fixed Q and varies slowly for large N. While the thermal system is always entangled when Q is smaller than -3.
基金supported by the National Natural Science Foundation of China (Grant No. 61871347)。
文摘We use the generalized Wootters formula, the positive partial transpose(PPT) criterion and the matched entanglement witness, to detect entanglement of three-qubit GHZ and W superposition state and its decayed states. It shows that the results of the generalized Wootters formula in the part near the W state are tight. In the other parts, the PPT criterion is superior to the generalized Wootters formula. Furthermore, we investigate the relationship between entanglement and coherence.
基金supported by the National Natural Science Foundation of China (Grant No. 12301580)the Funds of the College of Information Science and Technology, Beijing University of Chemical Technology (Grant No. 0104/11170044115)。
文摘Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with a Schmidt number less than k.
基金Supported by the National Natural Science Foundation of China(Grant No:61871347)。
文摘A quantum entangled state is easily disturbed by noise and degenerates into a separable state.Compared to the entanglement with bipartite quantum systems,less progress has been made for the entanglement with multipartite quantum systems.For tripartite separability of a four-qubit system,we propose two entanglement witnesses,each of which corresponds to a necessary condition of tripartite separability.For the four-qubit GHZ state mixed with a W state and white noise,we prove that the necessary conditions of tripartite separability are also sufficient at W states side.
文摘We analytically investigate Multiple Quantum(MQ) NMR dynamics in a mixed-three-spin(1/2,1,1/2)system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders(zeroth and second orders) for two pairs of spins(1,1/2) and(1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite(sub)systems(1,1/2) and(1/2,1/2)permanently coupled by, respectively, coupling constants J_1 and J_2, by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins(1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins(1,1/2) as an entanglement witness at some special time intervals.
文摘We propose a method of constructing the separability criteria for multipartite quantum states on the basis of entanglement witnesses. The entanglement witnesses are obtained by finding the maximal expectation values of Hermitian operators and then optimizing over all possible Hermitian operators. We derive a set of tripartite separability criteria for the four-qubit Greenberger-Horne-Zeilinger （GHZ） diagonal states. The derived criterion set contains four criteria that are necessary and sufficient for the tripartite separability of the highly symmetric four-qubit GHZ diagonal states; the criteria completely account for the numerically obtained boundaries of the tripartite separable state set. One of the criteria is just the tripartite separability criterion of the four-qubit generalized Werner states.
