We study the properties of coherence concurrence and present a physical explanation analogous to the coherence of assistance. We give an optimal pure state decomposition which attains the coherence concurrence for qubit states. We prove the additivity of coherence concurrence under direct sum operations in another way. Using these results, we calculate analytically the coherence concurrence for X states and show its optimal decompositions. Moreover, we show that the coherence concurrence is exactly twice the convex roof extended negativity of the Schmidt correlated states, thus establishing a direct relation between coherence concurrence and quantum entanglement.
Quantum coherence is a fundamental manifestation of the quantum superposition principle. Recently, Baumgratz \emph{et al}. [Phys. Rev. Lett. \textbf{113}, 140401 (2014)] presented a rigorous framework to quantify coherence from the view of theory of physical resource. Here we propose a new valid quantum coherence measure which is a convex roof measure, for a quantum system of arbitrary dimension, essentially using the generalized Gell-Mann matrices. Rigorous proof shows that the proposed coherence measure fulfills all the requirements dictated by the resource theory of quantum coherence measur…
Based on a proposed coherence measure, we show that the local coherence of a bipartite quantum pure state (coherence of its reduced density matrix) is exactly the same as the minimal average co- herence with all potential pure-state realizations under consideration. In particular, it is shown that bipartite concurrence of pure states just captures the maximal difference between local coherence and the average coherence of one subsystem induced by local operations on the other subsystem with the assistance of classical communications, which provides an alternative operational meaning for bipart…
Entanglement and coherence are two essential quantum resources for quantum information processing. A natural question arises of whether there are direct link between them. And by thinking about this question, we propose a new measure for quantum state that contains concurrence and is called intrinsic concurrence. Interestingly, we discover that the intrinsic concurrence is always complementary to coherence. Note that the intrinsic concurrence is related to the concurrence of a special pure state ensemble. In order to explain the trade-off relation more intuitively, we apply it in some composit…
We provide detailed proofs of triangle inequalities in coherence measures and entanglement concurrence. If a rank-$2$ state $\varrho$ can be expressed as a convex combination of two pure states, i.e., $\varrho=p_{1}|ψ_{1}\rangle\langleψ_{1}|+p_{2}|ψ_{2}\rangle\langleψ_{2}|$, a triangle inequality can be established as $\big{|}E(|Ψ_{1}\rangle)-E(|Ψ_{2}\rangle)\big{|}\leq E(\varrho)\leq E(|Ψ_{1}\rangle)+E(|Ψ_{2}\rangle)$, where $|Ψ_{1}\rangle=\sqrt{p_{1}}|ψ_{1}\rangle$ and $|Ψ_{2}\rangle=\sqrt{p_{2}}|ψ_{2}\rangle$, $E$ can be considered either coherence measures or entanglement concurrence. This…
We study the entanglement of tripartite quantum states and provide analytical lower bound of concurrence in terms of the concurrence of sub-states. The lower bound may improve all the existing lower bounds of concurrence. The approach is generalized to arbitrary dimensional multipartite systems.
We obtain Lewenstein-Sanpera decomposition of iso-concurrence decomposable states of $2\otimes 2$ quantum systems. It is shown that in these systems average concurrence of the decomposition is equal to the concurrence of the state and also it is equal to the amount of violation of positive partial transpose criterion. It is also shown that the product states introduced by Wootters in [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245 (1998)] form the best separable approximation ensemble for these states.
It is well known that fringe contrast is not a good quantifier of the wave nature of a quanton in multipath interference. A new interference visibility, based on the Hilbert-Schmidt coherence is introduced. It is demonstrated that this visibility is a good quantifier of wave nature, and can be experimentally measured. A generalized path predictability is introduced, which reduces to the predictability of Greenberger and Yasin, for the case of two paths. In a multipath, which-way interference experiment, the new visibility, the predictability and the I-concurrence (quantifying the entanglement …
We propose a new family of coherence monotones, named the \emph{generalized coherence concurrence} (or coherence $k$-concurrence), which is an analogous concept to the generalized entanglement concurrence. The coherence $k$-concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than $k$, and a state can be converted to a state with nonzero entanglement $k$-concurrence via incoherent operations if and only if the state has nonzero coherence $k$-concurrence. We apply the coherence concurrence family to…
It is shown that for a given bipartite density matrix and by choosing a suitable separable set (instead of product set) on the separable-entangled boundary, optimal Lewenstein-Sanpera (L-S) decomposition can be obtained via optimization for a generic entangled density matrix. Based on this, We obtain optimal L-S decomposition for some bipartite systems such as $2\otimes 2$ and $2\otimes 3$ Bell decomposable states, generic two qubit state in Wootters basis, iso-concurrence decomposable states, states obtained from BD states via one parameter and three parameters local operations and classical …
We give explicit expressions for entanglement measures of Werner states in arbitrary dimensions in terms of concurrence and tangle. We show that an optimal ensemble decomposition for a joint density matrix of a Werner state can achieve the minimum average concurrence and tangle simultaneously. Furthermore, the same decomposition also attains entanglement of formation for Werner states.
We propose a simple geometrical approach for finding the Lewenstein-Sanpera decomposition of Bell decomposable states of 2 otimes 2 quantum systems. We show that in these systems, the weight of the pure entangled part in the decomposition is equal to the concurrence of the state. It is also shown that the optimized separable part of L-S decomposition minimizes the von Neumann relative entropy. We also obtain the decomposition for a class of mixed states by using some LQCC actions. It is also shown that for these states the average concurrence of L-S decomposition is equal to their concurrence.
For n an even number of qubits and v a unitary evolution, a matrix decomposition v=k1 a k2 of the unitary group is explicitly computable and allows for study of the dynamics of the concurrence entanglement monotone. The side factors k1 and k2 of this Concurrence Canonical Decomposition (CCD) are concurrence symmetries, so the dynamics reduce to consideration of the a factor. In this work, we provide an explicit numerical algorithm computing v=k1 a k2 for n odd. Further, in the odd case we lift the monotone to a two-argument function, allowing for a theory of concurrence dynamics in odd qubits.…
The two-qubit canonical decomposition SU(4) = [SU(2) \otimes SU(2)] Delta [SU(2) \otimes SU(2)] writes any two-qubit quantum computation as a composition of a local unitary, a relative phasing of Bell states, and a second local unitary. Using Lie theory, we generalize this to an n-qubit decomposition, the concurrence canonical decomposition (C.C.D.) SU(2^n)=KAK. The group K fixes a bilinear form related to the concurrence, and in particular any computation in K preserves the tangle |<phi^*|(-i sigma^y_1)...(-i sigma^y_n)|phi>|^2 for n even. Thus, the C.C.D. shows that any n-qubit quantum compu…
Quantum coherence and entanglement orignate from the superposition principle. We derive a rigorous relation between the ${l_1}$-norm of coherence and concurrence, in that we show that the former is always greater than the latter. This result highlights the hierarchical relationship between coherence and concurrence, and proves coherence to be a fundamental and ubiquitous resource. We derive an analogous form of monogamy inequality which is based on the partial coherence of the reduced two-qubit and reduced single qubit of the particular class of three-qubit state. Moreover, we provide coherenc…
Quantum resources play crucial roles for displaying superiority in many quantum communication and computation tasks. To reveal the intrinsic relations hidden in these quantum resources, many efforts have been made in recent years. In this work, we investigate the correlations of the tripartite W-type states based on bipartite quantum resources. The interrelations among the degree of coherence, concurrence, Bell nonlocality and purity are presented. Considering Bell nonlocal and Bell local (satisfied the Clauser-Horne-Shimony-Holt inequality) states for the two-qubit subsystems derived from the…
In this report, a scheme different from the PT and Wootters concurrence is developed to acquire a criterion to investigate the bipartite separability of the Werner state.
We introduce a new discrete coherence monotone named the \emph{coherence number}, which is a generalization of the coherence rank to mixed states. After defining the coherence number in a similar manner to the Schmidt number in entanglement theory, we present a necessary and sufficient condition of the coherence number for a coherent state to be converted to an entangled state of nonzero $k$-concurrence (a member of the generalized concurrence family with $2\le k \le d$). It also turns out that the coherence number is a useful measure to understand the process of Grover search algorithm of $N$…
We discuss in this letter Lewenstein-Sanpera (L-S) decomposition for a specific Werner state. Compared with the optimal case, we propose a quasi-optimal one which in the view of concurrence leads to the same entanglement measure for the entangled mixed state discussed. We think that in order to obtain entanglement of given state the optimal L-S decomposition is not necessary.
We prove some new properties of fidelity (transition probability) and concurrence, the latter defined by straightforward extension of Wootters notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on conjugated pairs of density operators. These functions turn out to be concave or convex roofs. Optimal decompositions are constructed. Some applications to two- and tripartite systems illustrate the general theorem.
We study the average quantum coherence over the pure state decompositions of a mixed quantum state. An upper bound of the average quantum coherence is provided and sufficient conditions for the saturation of the upper bound are shown. These sufficient conditions always hold for two and three dimensional systems. This provides a tool to estimate the average coherence experimentally by measuring only the diagonal elements, which remarkably requires less measurements compared with state tomography. We then describe the pure state decompositions of qubit state in Bloch sphere geometrically. For an…
We present a detailed study of the entanglement dynamics of a two-qubit system coupled to independent non-Markovian environments, employing hierarchy equations. This recently developed theoretical treatment can conveniently solve non-Markovian problems and take into consideration the correlation between the system and bath in an initial state. We concentrate on calculating the death and rebirth time points of the entanglement to obtain a general view of the concurrence curve and explore the behavior of entanglement dynamics with respect to the coupling strength, the characteristic frequency of…
Properties of weak spatio-spectral twin beams in paraxial approximation are analyzed using the decomposition into appropriate paired modes. Numbers of paired modes as well as numbers of modes in the signal (or idler) field in the transverse wave-vector and spectral domains are analyzed as functions of pump-beam parameters. Spatial and spectral coherence of weak twin beams is described by auto- and cross-correlation functions. Relation between the numbers of modes and coherence is discussed.
The present methods for obtaining the optimal Lewenestein- Sanpera decomposition of a mixed state are difficult to handle analytically. We provide a simple analytical expression for the optimal Lewenstein-Sanpera decomposition by using semidefinite programming. Specially, we obtain the optimal Lewenstein-Sanpera decomposition for some examples such as: Bell decomposable state, Iso-concurrence state, generic two qubit state in Wootters's basis, $2\otimes 3$ Bell decomposable state, $d\otimes d$ Werner and isotropic states, a one parameter $3\otimes 3$ state and finally multi partite isotropic s…
Imaginarity as a Resource within Quantum Coherence: Geometric Decomposition and Operational Conversion
School of Science, East China University of Technology（华东交通大学理学院）；School of Computer and Computing Science, Hangzhou City University（杭州城市大学计算机与计算科学学院）；School of Mathematical Sciences, Capital Normal University（首都师范大学数学科学学院）
We investigate the factorization, coherence and asymmetry properties of the 1d Heisenberg spin-1/2 XXZ chain with Dzyaloshinskii-Moriya interaction (DMI) and a transverse magnetic field using quantum information measures. Both longitudinal and transverse DM vectors are considered. Using numerical DMRG, we compute the one-tangle, two-spin concurrence and the Wigner-Yananse-skew information. We show that a longitudinal DMI destroys the factorizability property while a transverse DMI preserves it. We relate the absence of factorizability to the breaking of the $U(1)$ rotation symmetry about the l…
Quantum coherence is the most fundamental of all quantum quantifiers, underlying other well-known quantities such as entanglement, quantum discord, and Bell correlations. It can be distributed in a multipartite system in various ways -- for example, in a bipartite system it can exist within subsystems (local coherence) or collectively between the subsystems (global coherence) and exhibits a trade-off relation. In quantum systems with more than two subsystems, there are more trade-off relations, due to the various decomposition ways of the coherence. In this paper, we experimentally verify thes…
The quantum teleportation with noisy EPR state is discussed. Using an optimal decomposition technique, we compute the concurrence, entanglement of formation and Groverian measure for various noisy EPR resources. It is shown analytically that all entanglement measures reduce to zero when $\bar{F} \leq 2/3$, where $\bar{F}$ is an average fidelity between Alice and Bob. This fact indicates that the entanglement is a genuine physical resource for the teleportation process. This fact gives valuable clues on the optimal decomposition for higher-qubit mixed states. As an example, the optimal decompos…
Using the type-I SPDC process in BBO nonlinear crystal (NLC), we generate a polarization-entangled state near to the maximally-entangled Bell-state with high-visibility (high-brightness) $ 98.50 \pm 1.33 ~ \% $ ($ 87.71 \pm 4.45 ~ \% $) for HV (DA) basis. We calculate the CHSH version of the Bell inequality, as a nonlocal realism test, and find a strong violation from the classical physics or any hidden variable theory (HVT), $ S= 2.71 \pm 0.10 $. Via measuring the coincidence count (CC) rate in the SPDC process, we obtain the quantum efficiency of single-photon detectors (SPDs) around $ (25.5…
We employ ptychography, a phase-retrieval imaging technique, to show experimentally for the first time that a partially coherent high-energy matter (electron) wave emanating from an extended source can be decomposed into a set of mutually independent modes of minimal rank. Partial coherence significantly determines the optical transfer properties of an electron microscope and so there has been much work on this subject. However, previous studies have employed forms of interferometry to determine spatial coherence between discrete points in the wavefield. Here we use the density matrix to deriv…
Quantum-limited estimation of atmospheric turbulence via spatial mode decomposition
Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine（乌克兰国家科学院博戈留博夫理论物理研究所）；Laboratoire d’Optique Appliqué (LOA), CNRS, École polytechnique, ENSTA, Institut Polytechnique de Paris（巴黎理工学院应用光学实验室（CNRS、巴黎综合理工学院、ENSTA））；Laboratoire Kastler Brossel, Sorbonne Université, ENS-Université PSL, CNRS, Collège de France（索邦大学卡斯勒布罗塞尔实验室（ENS-巴黎文理研究大学、法国国家科学研究中心、法兰西学院））；Department of Theoretical and Mathematical Physics, Kyiv Academic University（基辅学术大学理论与数学物理系）；Department of Mathematics, Kyiv School of Economics（基辅经济学院数学系）
Finite-temperature entanglement and coherence in asymmetric bosonic Josephson junctions
Università di Padova（帕多瓦大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Scuola Internazionale Superiore di Studi Avanzati（国际高等研究院）；Padua QTech Center, Università di Padova（帕多瓦量子技术中心）；Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche（意大利国家研究委员会光学研究所）
