Bipartite Correlations Research Articles

Protecting quantum correlations of the XXZ model by topological boundary conditions

The differences between the XXZ model with topological and periodical boundary conditions were compared by studying their entanglement, quantum discord, and critical temperature above which the entanglement vanishes. It shows that the different boundary conditions mainly affect bipartite quantum correlations of the boundary spins rather than that of other spin pairs. The topological boundary spins can protect entanglement and discord against strong magnetic fields while the periodical boundary spins can protect them against nonuniform magnetic fields. Compared with the periodical XXZ model, the critical temperature is significantly improved for the topological XXZ model. The topological XXZ model also allows us to improve significantly its critical temperature by increasing the strength of magnetic field, which is not feasible for the periodical XXZ model. It is therefore more promising for preparing entangled states at high temperature in the topological XXZ model.

Decoherence of quantum systems sequentially interacting with a common environment

A composite quantum channel is derived for two independent quantum systems that interact sequentially with a common environment. One of the two quantum systems first interacts with the environment for a finite time, and after that the other one interacts with the same environment. In the process, the environment does not simultaneously interact with the two quantum systems. It is important to note that the second quantum system interacts with the environment that has been disturbed by the first one. As a result, the correlation between the two quantum systems, not directly interacting with each other, is created through the environment. An approximation to the composite quantum channel is also provided, which is applicable if a correlation time of the environment is not so long. When two independent qubits interact sequentially with a common bosonic environment via a dephasing coupling, it is explicitly shown that the time evolution of the second qubit can be non-Markovian due to the disturbance effect caused by the first qubit, even if the time evolution of the first qubit is Markovian. Entanglement, total, classical, and quantum correlations are calculated to find how the disturbance affects bipartite correlations. Furthermore, in state transmission through the composite quantum channel, it is found that the fidelity of quantum states can be enhanced by the disturbance effect.

Necessarily transient quantum refrigerator

We show that it is possible to construct a quantum absorption refrigerator that provides refrigeration only in the transient regime, by using three interacting qubits, each of which is also interacting with a local heat bath. Though the machine does not provide any effective cooling in the steady state, significant cooling of a qubit can be achieved much before the system reaches its steady state. We also demonstrate a scenario where the temperature of the qubit that has to be cooled, decreases monotonically to its minimum steady-state temperature. This facilitates bypassing of precise time control in cooling. We study the behaviour of the ratio of the heat currents of the machine for both the scenarios. The results remain qualitatively unchanged for different models of thermal baths. We also comment on the temporal behaviour of bipartite and multipartite quantum correlations present in the system, when transient cooling without steady-state cooling takes place.

Creation of bipartite steering correlations by a fast damped auxiliary mode

We consider a three-mode system and show how steering correlations can be created between two modes of the system using the fast dissipation of the third mode. These correlations result in a directional form of entanglement, called quantum or Einstein–Podolsky–Rosen steering. We illustrate this on examples of the interactions among damped radiation modes in an optomechanical three-mode system. By assuming that one of the modes undergoes fast dissipation, we show that the coupling of that mode to one or two other modes of the system may result in one- or two-way quantum steering. Explicit analytical results are given for the steering parameters. We find that two modes coupled by the parametric-type interaction and damped with the same rates can be entangled but cannot exhibit quantum steering. When, in addition, one of the modes is coupled to a fast damped mode, steering correlations are created and the modes then exhibit one-way steering. The creation of the steering correlations is interpreted in the context of the variances of the quadrature components of the modes that the steering correlations result from an asymmetry in the variances of the quadrature components of the modes induced by the auxiliary mode. It is found that the fluctuations act directionally that quantum steering may occur only when the variance of the steering mode is larger that the variance of the steered mode. The scheme is shown to be quite robust against the thermal excitation of the modes if the fluctuations of the steering mode are larger than the fluctuations of the steered mode.

Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization

In this paper we study optimization problems related to bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. First we consider the problem of finding the minimal entanglement dimension of such correlations. We construct a hierarchy of semidefinite programming lower bounds and show convergence to a new parameter: the minimal average entanglement dimension, which measures the amount of entanglement needed to reproduce a quantum correlation when access to shared randomness is free. Then we study optimization problems over synchronous quantum correlations arising from quantum graph parameters. We introduce semidefinite programming hierarchies and unify existing bounds on quantum chromatic and quantum stability numbers by placing them in the framework of tracial polynomial optimization.

Analytical solution and applications of three qubits in three coupled modes without rotating wave approximation

We study the dynamics of the three-qubit system interacting with multi-mode without rotating wave approximation (RWA). A physical realization of the system without direct qubits interactions with dephasing bath is proposed. It is shown that non-Markovian characters of the purity of the three qubits and the coupling strength of modes are stronger enough the RWA is no longer valid. The influences of the dephasing of qubits and interactions of modes on the dynamics of genuine multipartite entanglement and bipartite correlations of qubits are investigated. The multipartite and bipartite quantum correlations could be generated faster if we increase the coupling strength of modes and the RWA is not valid when the coupling strength is strong enough. The unitary transformations approach adopted here can be extended to other systems such as circuit or cavity quantum electrodynamic systems in the strong coupling regime.

Einstein-Podolsky-Rosen steering and coherence in the family of entangled three-qubit states

Considering the system of three interacting qubits, we analyze four families of states from the point of view of bipartite correlations appearing in two-qubit subsystems of a three-qubit model, such as Einstein-Podolsky-Rosen steering, entanglement, and coherence. We reveal mutual relations among the steering parameter, concurrence, and three measures of coherence (degree of coherence, first-, and second-order correlation functions). Analyzing in parallel the steerable and unsteerable states, we derive analytical formulas giving the maximal and minimal values of coherence measures as concurrence varies.

Entanglement degradation in the presence of the Kerr–Newman black hole

We investigate bipartite quantum correlations in the presence of the four-dimensional Kerr–Newman black hole using the negativity as a measure for the entanglement. We assume Alice and Rob initially share a maximally entangled state, and then Rob accelerates toward the event horizon \(h_{+}\). We find that when Rob accelerates uniformly toward the external horizon, the entanglement degrades for the Alice–Rob system and this degradation increases as Rob gets closer to the horizon. It is found that for the case Alice–AntiRob, no creation of quantum correlation occurs. Finally, we investigate the bipartite entanglement using an alternative entanglement measure, namely generalized concurrence, and we show that the results are in consistent with those obtained by negativity.

Bipartite non-classical correlations for a lossy two connected qubit–cavity systems: trace distance discord and Bell’s non-locality

In this paper, some non-classical correlations are investigated for bipartite partitions of two qubits trapped in two spatially separated cavities connected by an optical fiber. The results show that the trace distance discord and Bell’s non-locality introduce other quantum correlations beyond the entanglement. Moreover, the correlation functions of the trace distance discord and the Bell’s non-locality are very sensitive to the initial correlations, the coupling strengths, and the dissipation rates of the cavities. The fluctuations of the correlation functions between their initial values and gained (loss) values appear due to the unitary evolution of the system. These fluctuations depend on the chosen initial correlations between the two subsystems. The maximal violations of Bell’s inequality occur when the logarithmic negativity and the trace distance discord reach certain values. It is shown that the robustness of the non-classical correlations, against the dissipation rates of the cavities, depends on the bipartite partitions reduced density matrices of the system, and is also greatly enhanced by choosing appropriate coupling strengths.

Generation and robustness of bipartite non-classical correlations in two nonlinear microcavities coupled by an optical fiber

We explore the bipartite non-classical correlations of two quantum wells coupled to two spatially separated microcavities. The microcavities are filled by linear optical media and linked by a single-mode optical fiber. We prove that it is possible to generate a correlation from the initially uncorrelated state. With particular coupling constants of the cavity-exciton and the fiber-cavity coupling, the maximum correlations can be generated periodically, and sudden changes occur only in the local quantum uncertainty. The optical susceptibility and coupling constants control the regularity, amplitudes, and frequencies of the correlation functions. When the system initially starts with a maximally correlated state, we show that the correlation robustness of the Wigner-Yanase skew information and Bell’s inequality depends not only on the coupling strengths and optical susceptibility but also on the dissipation rates. Deterioration of the correlations is substantially associated with the dissipation.

Reliable computation from contextual correlations

An operational approach to the study of computation based on correlations considers black-boxes with one-bit inputs and outputs, controlled by a limited classical computer capable only of performing sums modulo-2. In this setting, it was shown that non-contextual correlations do not provide any extra computational power, while contextual correlations were found to be necessary for the deterministic evaluation of non-linear Boolean functions. Here we investigate the requirements for reliable computation in this setting, that is, the evaluation of any Boolean function with success probability bounded away from 1/2. We show that bipartite CHSH quantum correlations suffice for reliable computation. We also prove that an arbitrarily small violation of a multipartite GHZ non-contextuality inequality also suffices for reliable computation.

Quantum Correlations and Coherence of Polar Symmetric Top Molecules in Pendular States

We consider two ultracold polar symmetric top molecules coupled by dipole-dipole interaction in an external electric field with appreciable intensity gradient, serving as the physical carrier of quantum information. Each molecule is induced to undergo pendular oscillations under the strong static electric field. Based on the pendular states of polar symmetric top molecules as candidate qubits, we investigate the bipartite quantum correlations of the two polar molecular system for the thermal equilibrium states, characterized by negativity and quantum discord, and then analyze the corresponding coherence, measured by relative entropy and l1 norm. Furthermore, we also examine the dynamics of the entanglement and coherence of the system in the presence of intrinsic decoherence, and explore the relations of their temporal evolution with various physical system parameters for two different initial Bell states. It is found that quantum correlations and coherence of the two polar molecules in pendular states can be manipulated by adjusting appropriate reduced variables including external electric field, dipole-dipole interaction, ambient temperature and decoherence factor. Our findings could be used for molecular quantum computing based on rotational states.

Random Quantum Correlations are Generically Non-classical

It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random instances of such bipartite correlations. The main question we are interested in is: given a quantum correlation, taken at random, how likely is it that it is truly non-explainable by a classical model? We show that, under very general assumptions on the considered distribution, a random correlation which lies on the border of the quantum set is with high probability outside the classical set. What is more, we are able to provide the Bell inequality certifying this fact. On the technical side, our results follow from (i) estimating precisely the "quantum norm" of a random matrix, and (ii) lower bounding sharply enough its "classical norm", hence proving a gap between the two. Along the way, we need a non-trivial upper bound on the $\infty{\rightarrow}1$ norm of a random orthogonal matrix, which might be of independent interest.

Tripartite and bipartite quantum correlations in the XXZ spin chain with three-site interaction

Tripartite and bipartite quantum correlations in the three-qubit XXZ Heisenberg spin chain with two types of three-site interactions and an external magnetic field are investigated. We show that the increase in XZY − YZX interaction can enhance the robustness of both tripartite and bipartite correlations, whereas the increase in XZX $$+$$ YZY interaction could improve the robustness of tripartite quantum correlations, but diminish the robustness of bipartite quantum correlations. Tripartite measurement-induced disturbance is the most robust against temperature, and bipartite entanglement is the most fragile. Tripartite entanglement is even more robust than bipartite quantum discord when XZX $$+$$ YZY or XZY − YZX interaction is relatively large. The cooperative effect of XZX $$+$$ YZY and XZY − YZX interaction could induce bipartite entanglement even at high temperature. The cooperative effect of XZX $$+$$ YZY and XZY − YZX interaction is the most optimal to improve the robustness of all quantum correlations when the magnetic field is negative. When the magnetic field is positive, the effective of XZY − YZX interaction alone is more ideal to preserve different quantum correlations.

Quantifying Genuine Multipartite Correlations and their Pattern Complexity.

We propose an information-theoretic framework to quantify multipartite correlations in classical and quantum systems, answering questions such as what is the amount of seven-partite correlations in a given state of ten particles? We identify measures of genuine multipartite correlations, i.e., statistical dependencies that cannot be ascribed to bipartite correlations, satisfying a set of desirable properties. Inspired by ideas developed in complexity science, we then introduce the concept of weaving to classify states that display different correlation patterns, but cannot be distinguished by correlation measures. The weaving of a state is defined as the weighted sum of correlations of every order. Weaving measures are good descriptors of the complexity of correlation structures in multipartite systems.

Quantum-correlated twin-atom laser from a Bose-Hubbard system

We propose and evaluate a method to construct a quantum correlated twin atom laser using a pumped and damped Bose-Hubbard inline trimer which can operate in a stationary regime. With pumping via a source condensate filling the middle well and damping using either an electron beam or optical means at the two end wells, we show that bipartite quantum correlations build up between the ends of the chain, and that these can be measured either in situ or in the outcoupled beams. While nothing similar to our system has yet been achieved experimentally, recent advances mean that it should be practically realisable in the near future.

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.

Activation of monogamy in nonlocality using local contextuality

A unified view on the phenomenon of monogamy exhibited by Bell inequalities and non-contextuality inequalities arising from the no-signaling and no-disturbance principles is presented using the graph-theoretic method introduced in \textit{Phys. Rev. Lett. 109, 050404 (2012)}. We propose a novel type of trade-off, namely Bell inequalities that do not exhibit monogamy features of their own can be activated to be monogamous by the addition of a local contextuality term. This is illustrated by means of the well-known $\mathcal{I}_{3322}$ inequality, and reveals a resource trade-off between bipartite correlations and the local purity of a single system. In the derivation of novel no-signaling monogamies, we uncover a new feature, namely that two-party Bell expressions that are trivially classically saturated can become non-trivial upon the addition of an expression involving a third party with a single measurement input.

Reexamination of strong subadditivity: A quantum-correlation approach

The strong subadditivity inequality of von Neumann entropy relates the entropy of subsystems of a tripartite state $\rho_{ABC}$ to that of the composite system. Here, we define $\boldsymbol{T}^{(a)}(\rho_{ABC})$ as the extent to which $\rho_{ABC}$ fails to satisfy the strong subadditivity inequality $S(\rho_{B})+S(\rho_{C}) \le S(\rho_{AB})+S(\rho_{AC})$ with equality and investigate its properties. In particular, by introducing auxiliary subsystem $E$, we consider any purification $|\psi_{ABCE}\rangle$ of $\rho_{ABC}$ and formulate $\boldsymbol{T}^{(a)}(\rho_{ABC})$ as the extent to which the bipartite quantum correlations of $\rho_{AB}$ and $\rho_{AC}$, measured by entanglement of formation and quantum discord, change under the transformation $B\rightarrow BE$ and $C\rightarrow CE$. Invariance of quantum correlations of $\rho_{AB}$ and $\rho_{AC}$ under such transformation is shown to be a necessary and sufficient condition for vanishing $\boldsymbol{T}^{(a)}(\rho_{ABC})$. Our approach allows one to characterize, intuitively, the structure of states for which the strong subadditivity is saturated. Moreover, along with providing a conservation law for quantum correlations of states for which the strong subadditivity inequality is satisfied with equality, we find that such states coincides with those that the Koashi-Winter monogamy relation is saturated.

On the closure of the completely positive semidefinite cone and linear approximations to quantum colorings

We investigate structural properties of the completely positive semidefinite cone $\mathcal{CS}_+$, consisting of all the $n \times n$ symmetric matrices that admit a Gram representation by positive semidefinite matrices of any size. This cone has been introduced to model quantum graph parameters as conic optimization problems. Recently it has also been used to characterize the set $\mathcal Q$ of bipartite quantum correlations, as projection of an affine section of it. We have two main results concerning the structure of the completely positive semidefinite cone, namely about its interior and about its closure. On the one hand we construct a hierarchy of polyhedral cones covering the interior of $\mathcal{CS}_+$, which we use for computing some variants of the quantum chromatic number by way of a linear program. On the other hand we give an explicit description of the closure of the completely positive semidefinite cone by showing that it consists of all matrices admitting a Gram representation in the tracial ultraproduct of matrix algebras.