Distribution Of Quantum Correlations Research Articles

Quantum resource changes and distributions during catalytic transformations

One physical system always evolves from a state of low disorder to another of high disorder. This phenomenon can be identified by increased entropy. As we know, quantum resource theories provide a mathematical framework for examining diverse quantum resources in states, with the primary problem being whether quantum states can be transformed into each other by free operations. Unlike natural transformations, free operations in quantum resource theories never increase the resource measure of a primary system. Generally, the standard approach to this central problem is to study approximate transformations and apply catalysts to broaden the set of possible state transformations. By combining approximate transformations and catalytic transformations, we show that the quantum correlation between the primary system and the catalytic system after approximate catalytic transformations determines quantum resource changes in the primary system as well as the distribution of quantum correlations among different primary systems. We first find and establish that the resource measure of the primary system does not decrease under global free operations on the primary system and the corresponding catalytic system using the universal freezing technology and the catalytic transformation methods. A resource measure is monotonic under free operations, additive on tensor products, and continuous. Using these features, we then access relations between variations in the resource measure of the primary system under global free operations and quantum correlations between the primary and catalytic systems. Therefore, quantum correlations exist between the primary and catalytic systems after catalytic transformations, which are essential for nondecreasing resource measures of the primary system. Finally, we establish relationships among different primary systems after repeatedly applying the same catalyst. The correlation is closely associated with the reuse times of the same catalyst.

Entanglement of formation and quantum discord in multipartite j-spin coherent states

We study the entanglement of formation and the quantum discord contained in even and odd multipartite [Formula: see text]-spin coherent states. The key element of this investigation is the fact that a single [Formula: see text]-spin coherent state is viewed as comprising [Formula: see text] qubit states. We compute the quantum correlations present in the n even and odd [Formula: see text]-spin coherent states by considering all possible bipartite splits of the multipartite system. We discuss the different bi-partition schemes of quantum systems and we examine in detail the conservation rules governing the distribution of quantum correlations between the different qubits of the multipartite system. Finally, we derive the explicit expressions of quantum correlations present in even and odd spin coherent states decomposed in four spin sub-systems. We also analyze the properties of monogamy and we show in particular that the entanglement of the formation and the quantum discord obey the relation of monogamy only for even multipartite [Formula: see text]-spin coherent states.

Restricted distribution of quantum correlations in bilocal network

Analyzing shareability of correlations arising in any physical theory may be considered as a fruitful technique of studying the theory. Our present topic of discussion involves an analogous approach of studying quantum theory. For our purpose, we have deviated from the usual procedure of assessing monogamous nature of quantum correlations in the standard Bell-CHSH scenario. We have considered correlations arising in a quantum network involving independent sources. Precisely speaking, we have analyzed monogamy of nonbilocal correlations by deriving a relation restricting marginals. Interestingly, restrictions constraining distribution of nonbilocal correlations remain same irrespective of whether inputs of the nodal observers are kept fixed (in different bilocal networks) while studying nonbilocal nature of marginal correlations.

Multipartite Einstein-Podolsky-Rosen steering sharing with separable states

Distribution of quantum correlations among remote users is a key procedure underlying many quantum information technologies. Einstein-Podolsky-Rosen steering, which is one kind of such correlations stronger than entanglement, has been identified as a resource for secure quantum networks. We show that this resource can be established between two and even more distant parties by transmission of a system being separable from all the parties. For the case with two parties, we design a protocol allowing to distribute one-way Gaussian steering between them via a separable carrier; the obtained steering can be used subsequently for one-sided device-independent (1sDI) quantum key distribution. Further, we extend the protocol to three parties, a scenario which exhibits richer steerability properties including one-to-multimode steering and collective steering, and which can be used for 1sDI quantum secret sharing. All the proposed steering distribution protocols can be implemented with squeezed states, beam splitters and displacements, and thus they can be readily realized experimentally. Our findings reveal that not only entanglement but even steering can be distributed via communication of a separable system. Viewed from a different perspective, the present protocols also demonstrate that one can switch multipartite states between different steerability classes by operations on parts of the states.

Finer distribution of quantum correlations among multiqubit systems

We study the distribution of quantum correlations characterized by monogamy relations in multipartite systems. By using the Hamming weight of the binary vectors associated with the subsystems, we establish a class of monogamy inequalities for multiqubit entanglement based on the $\alpha$th ($\alpha\geq 2$) power of concurrence, and a class of polygamy inequalities for multiqubit entanglement in terms of the $\beta$th ($0\leq \beta\leq2$) power of concurrence and concurrence of assistance. Moveover, we give the monogamy and polygamy inequalities for general quantum correlations. Application of these results to quantum correlations like squared convex-roof extended negativity (SCREN), entanglement of formation and Tsallis-$q$ entanglement gives rise to either tighter inequalities than the existing ones for some classes of quantum states or less restrictions on the quantum states. Detailed examples are presented.

Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems**Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20171397), the National Natural Science Foundation of China (Grant Nos. 11535004, 11375086, 1175085, and 11120101005), the Foundation for Encouragement of College of Sciences (Grant No. LYLZJJ1616), and the Pre-research Foundation of Army Engineering University

We investigate the role of quantum correlation around the quantum phase transitions by using quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can efficiently detect the quantum critical point in the two-dimensional XY systems. The nonanalytic behavior of the first derivative of quantum correlation is observed at the critical point as the size of the model increases. Furthermore, we discuss the quantum correlation distribution in this system based on the square of concurrence (SC) and square of quantum discord (SQD). The monogamous properties of SC and SQD are obtained. Particularly, we prove that the quantum critical point can also be achieved by monogamy score.

Multipartite monogamous relations for entanglement and discord

The distribution of quantum correlations in multipartite systems play a significant role in several aspects of the quantum information theory. While it is well known that these quantum correlations can not be freely distributed, the way that it is shared in multipartite system is an open problem even for small set of qubits. Based on new monogamylike relations between entanglement and discord for $n$-partite systems, we show how these correlations are distributed in general, determining distinct equalities and inequalities to the quantum discord and the entanglement of formation for arbitrary multipartite pure states.

Solid-State Source of Nonclassical Photon Pairs with Embedded Multimode Quantum Memory.

The generation and distribution of quantum correlations between photonic qubits is a key resource in quantum information science. For applications in quantum networks and quantum repeaters, it is required that these quantum correlations be stored in a quantum memory. In 2001, Duan, Lukin, Cirac, and Zoller (DLCZ) proposed a scheme combining a correlated photon-pair source and a quantum memory in atomic gases, which has enabled fast progress towards elementary quantum networks. In this Letter, we demonstrate a solid-state source of correlated photon pairs with embedded spin-wave quantum memory, using a rare-earth-ion-doped crystal. We show strong quantum correlations between the photons, high enough for performing quantum communication. Unlike the original DLCZ proposal, our scheme is inherently multimode thanks to a built-in rephasing mechanism, allowing us to demonstrate storage of 11 temporal modes. These results represent an important step towards the realization of complex quantum networks architectures using solid-state resources.

Quantum correlations generation and distribution in a universal covariant quantum cloning circuit

We discussed the distribution and generation of quantum correlations in a universal covariant quantum cloning circuit. Specifically, we first considered the distribution of quantum correlation, i.e., quantum discord, among the four qubits of the circuit. Then, we analyzed the generation of genuine 3- or 4-qubit entanglement in the cloning process. It is found that the circuit generates genuine 4-qubit GHZ (Greenberger-Horne-Zeilinger)-type state while only W-type 3-qubit state could be generated. These results illustrate the special quantum correlation manipulation capabilities of the cloning circuit.

Forbidden regimes in the distribution of bipartite quantum correlations due to multiparty entanglement

Monogamy is a nonclassical property that limits the distribution of quantum correlation among subparts of a multiparty system. We show that monogamy scores for different quantum correlation measures are bounded above by functions of genuine multipartite entanglement for a large majority of pure multiqubit states. The bound is universal for all three-qubit pure states. We derive necessary conditions to characterize the states that violate the bound, which can also be observed by numerical simulation for a small set of states, generated Haar uniformly. The results indicate that genuine multipartite entanglement restricts the distribution of bipartite quantum correlations in a multiparty system.

Anisotropic Invariance and the Distribution of Quantum Correlations.

We report the discovery of two new invariants for three-qubit states which, similarly to the three-tangle, are invariant under local unitary transformations and permutations of the parties. These quantities have a direct interpretation in terms of the anisotropy of pairwise spin correlations. Applications include a universal ordering of pairwise quantum correlation measures for pure three-qubit states; trade-off relations for anisotropy, three-tangle and Bell nonlocality; strong monogamy relations for Bell inequalities, Einstein-Podolsky-Rosen steering inequalities, geometric discord and fidelity of remote state preparation (including results for arbitrary three-party states); and a statistical and reference-frame-independent form of quantum secret sharing.

Nonmaximally Entangled States can be Better for Quantum Correlation Distribution and Storage

For carrying out many quantum information protocols entanglement must be established in advance between two distant parties. Practically, inevitable interaction of entangled subsystems with their environments during distribution and storage will result in degradation of entanglement. Here we investigate the decoherence of two-qubit entangled states in the local amplitude noise. We show that there exists a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction, and quantum discord. This result indicates that nonmaximally entangled states can outperform maximally entangled states for quantum correlation distribution and storage under the amplitude damping. It also educes a notable consequence that the ordering of states under quantum correlation monotones can be reversed even by local trace-preserving and completely positive maps.

Propagation of nonclassical correlations through one-dimensional quantum networks

We investigate transfer of nonclassical correlations through one-dimensional quantum networks for several schemes by employing concurrence and local quantum uncertainty as the measures and the extended Werner-like states as the initial resources. The exact dynamics of quantum correlations are derived, and the differences of dynamics between concurrence and local quantum uncertainty are analyzed. Besides, the influences of node number and initial parameters on the generation of quantum correlations between the two end nodes are discussed. Moreover, we explore the effects of duplex encodings and double channels on distribution of quantum correlations.

Distribution of quantum correlations and conditional entropy in Heisenberg spin chains

The quantum discord, which quantifies the amount of quantum correlation present between parts of a system, is investigated for spin systems. The discord for a pair of spins in the many-spin ground state, computed by minimizing the conditional entropy of the two spins, is related to the diagonal and off-diagonal spin–spin correlation functions and the local magnetization. We show that for isotropic and translationally invariant states, the discord depends only on the diagonal spin correlation function. Thus, near a thermal/quantum critical point, the pairwise discord exhibits long-range behavior, analogously to the correlation function. The discord exhibits a kink singularity as a function of the anisotropy parameter for the ground state of the anisotropic Heisenberg model, for both nearest-neighbor spins as well as for well-separated spins. The preferred measurement basis for the minimum conditional entropy, which determines the discord, changes discontinuously across the critical point. We also investigate, from exact numerical diagonalization, the distribution of conditional entropies as the measurement basis is varied. For the isotropic model, the conditional entropy distribution is a δ-function, whereas it has a twin-peak structure for the anisotropic model. It is shown that the average value and the mean-square fluctuation of the conditional entropy also show a signature of the critical-point behavior.

Systems with stationary distribution of quantum correlations: open spin-1/2 chains with $$XY$$ X Y interaction

Although quantum correlations in a quantum system are characterized by the evolving quantities (which are entanglement and discord usually), we reveal such basis (i.e. the set of virtual particles) for the representation of the density matrix that the entanglement and/or discord between any two virtual particles in such representation are stationary. In particular, dealing with the nearest neighbor approximation, this system of virtual particles is represented by the $$\beta $$s-fermions of the Jordan---Wigner transformation. Such systems are important in quantum information devices because the evolution of quantum entanglement/discord leads to the problems of realization of quantum operations. The advantage of stationary entanglement/discord is that they are completely defined by the initial density matrix and by the Hamiltonian governing the quantum dynamics in the system under consideration. Moreover, using the special initial condition together with the special system's geometry, we construct large cluster of virtual particles with the same pairwise entanglement/discord. In other words, the measure of quantum correlations is stationary in this system and correlations are uniformly "distributed" among all virtual particles. As examples, we use both homogeneous and non-homogeneous spin-1/2 open chains with XY-interaction although other types of interactions might be also of interest.

QUANTUM CORRELATIONS DYNAMICS OF QUASI-BELL CAT STATES

A model of dynamics of quantum correlations of two modes quasi-Bell cat states, based on Glauber coherent states, is considered. The analytic expressions of pairwise entanglement of formation, quantum discord and its geometrized variant are explicitly derived. We analyze the distribution of quantum correlations between the two modes and the environment. We show that, in contrast with squared concurrence, entanglement of formation, quantum discord and geometric quantum discord do not follow the property of monogamy except in some particular situations that we discuss.

Propagation and distribution of quantum correlations in a cavity QED network

We study the propagation and distribution of quantum correlations through two chains of atoms inside cavities joined by optical fibres. This system is interesting because it can be used as a channel for quantum communication or as a network for quantum computation. In order to quantify those correlations, we used two different measurements: entanglement and quantum discord. We also use tangle for multipartite entanglement. We consider an effective Hamiltonian for the system and cavity losses, in the dressed atom picture, using the generalized master equation. We found a case where the quantum discord and the classical correlation are almost constant, and we also found multipartite entanglement, starting with only one excitation per chain. Finally, we propose a way to select the initial condition so that we can optimize the results for different purposes.

Exploring multipartite quantum correlations with the square of quantum discord

We explore the quantum correlation distribution in multipartite quantum states based on the square of quantum discord (SQD). For tripartite quantum systems, we derive the necessary and sufficient condition for the SQD to satisfy the monogamy relation. Particularly, we prove that the SQD is monogamous for three-qubit pure states, based on which a genuine tripartite quantum correlation measure is introduced. In addition, we also address the quantum correlation distributions in four-qubit pure states. As an example, we investigate multipartite quantum correlations in the dynamical evolution of multipartite cavity-reservoir systems.

Impact of Turbulence in Long Range Quantum and Classical Communications

The study of the free-space distribution of quantum correlations is necessary for any future application of quantum and classical communication aiming to connect two remote locations. Here we study the propagation of a coherent laser beam over 143km (between Tenerife and La Palma Islands of the Canary archipelagos). By attenuating the beam we also studied the propagation at the single photon level. We investigated the statistic of arrival of the incoming photons and the scintillation of the beam. From the analysis of the data, we propose the exploitation of turbulence to improve the signal to noise ratio of the signal.

Generation of maximally entangled atom pairs in driven dissipative cavity QED systems

We investigate the entanglement of an open tripartite system where a cavity field mode in thermal equilibrium is off-resonantly coupled with two atoms that are simultaneously driven by a resonant coherent field. For moderately detuned atom-field coupling and strong atomic driving we show the generation, at given interaction times and for low enough cavity decay rates, of atomic Bell states and of Bell state superpositions relevant for quantum gates implementation. The system can oscillate between bi-separable and fully separable states. Also we describe the distribution of quantum correlations between the atom-atom and the two atom-field subsystems. In the dispersive coupling regime with strongly driven atoms we show the generation of nearly stationary Bell states which remain protected from cavity dissipation.