Stability investigation on quantum correlations of coupled qubits in non-Markovian process

Utilizing the concurrence and the quantum discord as the measure method, in this paper we compare and investigate the dynamic evolution features of quantum correlations of coupled qubits in non-Markovian process. We focus attention on decoherence effect influences the stability of quantum correlations. The investigation results show that because of the decoherence influence between the system and environment, the concurrence always evolves with time in oscillation form in the way of deaths and survivals, however, the quantum discord time evolution does not appear the deaths and survivals. The quantum discord survives obviously longer than concurrence, which indicates that quantum discord has a stronger ability to resist decoherence than entanglement. Through regulating and controlling the purity and entanglement of the initial quantum state, we can effectively suppress the decay of the quantum correlations, which is advantaged to complete the quantum information processing.     

Concurrence of arbitrary dimensional bipartite quantum states

We derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension. A functional relation is established relating concurrence, the Peres-Horodecki criterion, and the realignment criterion. We demonstrate that our bound is exact for some mixed quantum states. The significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states, some of which fail to be identified by the usual concurrence estimation method.     

Demonstration of essentiality of entanglement in a Deutsch-like quantum algorithm

Quantum algorithms can be used to efficiently solve certain classically intractable problems by exploiting quantum parallelism. However, the effectiveness of quantum entanglement in quantum computing remains a question of debate. This study presents a new quantum algorithm that shows entanglement could provide advantages over both classical algorithms and quantum algo- rithms without entanglement. Experiments are implemented to demonstrate the proposed algorithm using superconducting qubits. Results show the viability of the algorithm and suggest that entanglement is essential in obtaining quantum speedup for certain problems in quantum computing. The study provides reliable and clear guidance for developing useful quantum algorithms.     

Thermal Entanglement and Correlated Coherence in Two Coupled Double Quantum Dots Systems

In this work, the thermal quantum correlations in two coupled double semiconductor charge qubits are investigated. This is carried out by deriving analytical expressions for both the thermal concurrence and the correlated coherence. The effects of the tunneling parameters, the Coulomb interaction, and the temperature on the thermal entanglement and on the correlated coherence are studied in detail. It is found that the Coulomb potential plays an important role in the thermal entanglement and in the correlated coherence of the system. The results also indicate that the Coulomb potential can be used for significant enhancement of the thermal entanglement and quantum coherence. One interesting aspect is that the correlated coherence capture all the thermal entanglement at low temperatures, that is, the local coherences are totally transferred to the thermal entanglement. Finally, the role played by thermal entanglement and the correlated coherence responsible for quantum correlations are focused on. It is shown that in all cases, the correlated coherence is more robust than the thermal entanglement so that quantum algorithms based only on correlated coherence may be more robust than those based on entanglement.     

Entanglement in four qubit states: Polynomial invariant of degree 2, genuine multipartite concurrence and one-tangle

Characterization of the multipartite mixed state entanglement is still a challenging problem. This is due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement measure of a mixed state ρ of a quantum system can be defined as the minimum average entanglement of an ensemble of pure states. In this paper, we show that polynomial entanglement measures of degree 2 of even-N qubits X states is in the full agreement with the genuine multipartite (GM) concurrence. Then, we plot the hierarchy of entanglement classification for four qubit pure states and then using new invariants, we classify the four qubit pure states. We focus on the convex combination of the classes whose at most the one of the invariants is non-zero and find the relationship between entanglement measures consist of non-zero-invariant, GM concurrence and one-tangle. We show that in many entanglement classes of four qubit states, GM concurrence is equal to the square root of one-tangle.     

Coherence and Entanglement Dynamics in Training Variational Quantum Perceptron

In quantum computation, what contributes supremacy of quantum computation? One of the candidates is known to be a quantum coherence because it is a resource used in the various quantum algorithms. We reveal that quantum coherence contributes to the training of variational quantum perceptron proposed by Y. Du et al., arXiv:1809.06056 (2018). In detail, we show that in the first part of the training of the variational quantum perceptron, the quantum coherence of the total system is concentrated in the index register and in the second part, the Grover algorithm consumes the quantum coherence in the index register. This implies that the quantum coherence distribution and the quantum coherence depletion are required in the training of variational quantum perceptron. In addition, we investigate the behavior of entanglement during the training of variational quantum perceptron. We show that the bipartite concurrence between feature and index register decreases since Grover operation is only performed on the index register. Also, we reveal that the concurrence between the two qubits of index register increases as the variational quantum perceptron is trained.     

Quantitative complementarity relations in bipartite systems: Entanglement as a physical reality

We introduce a complete set of complementary quantities in bipartite, two-dimensional systems. Complementarity then relates the quantitative entanglement measure concurrence which is a bipartite property to the single-particle quantum properties predictability and visibility, for the most general quantum state of two qubits. Consequently, from an interferometric point of view, the usual wave-particle duality relation must be extended to a “triality” relation containing, in addition, the quantitative entanglement measure concurrence, which has no classical counterpart and manifests a genuine quantum aspect of bipartite systems. A generalized duality relation, that also governs possible violations of the Bell’s inequality, arises between single- and bipartite properties.     

Complementarity Relations for Multi-Qubit Systems

No Heading We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the degree to which single particle properties are possessed by an individual member of the system is limited by the bipartite entanglement that exists between that qubit and the remainder of the system. This result implies that the phenomenon of entanglement sharing is one specific consequence of complementarity. The second expression, which holds for an arbitrary state of two qubits, pure or mixed, quantifies a tradeoff between the amounts of entanglement, separable uncertainty, and single particle properties that are encoded in the quantum state. The separable uncertainty is a natural measure of our ignorance about the properties possessed by individual subsystems, and may be used to completely characterize the relationship between entanglement and mixedness in two-qubit systems. The two-qubit complementarity relation yields a useful geometric picture in which the root mean square values of local subsystem properties act like coordinates in the space of density matrices, and suggests possible insights into the problem of interpreting quantum mechanics.     

Concurrence and Wigner-Yanase Skew Information

A measure of entanglement on n qubits is defined in terms of Wigner-Yanase skew information. It is shown that the measure coincides essentially with the concurrence on two qubits. This uncovers the information-theoretic meaning of the concurrence of entangled states.     

Robustness investigations on quantum entanglement and quantum discord of coupled qubits in squeezed vacuum reservoir

We investigate the quantum discord of coupled qubits in squeezed vacuum reservoir and compare it with the quantum entanglement of system. We find that the quantum discord and entanglement perform completely oppositely with the change of squeezed parameters. Quantum discord survives longer with the increase of squeezed amplitude parameter and entanglement death faster on the contrary. Under high squeezed amplitude parameter, the quantum discord can keep nonzero which indicate that the quantum discord is more robust than entanglement. We also find that the purity reduction of the initial quantum state will lead to the decay of concurrence or quantum discord. However, the quantum discord damps remarkably more slowly and survives longer than concurrence.     

Modulation of entanglement and quantum discord for circuit cavity QED states

The paper investigates the dynamic evolution behaviors of entanglement and quantum discord of coupled superconducting qubits in circuit QED system. We put emphasis on the effects of cavity field quantum state on quantum entanglement and quantum correlations dynamic behaviors of coupling superconducting qubits. The results show that, (1) generally speaking, the entanglement will appear the death and new birth because of the interaction between qubits and cavity field, on the contrary, this phenomenon will not appear in quantum discord. (2) When the cavity field is in coherent state, the entanglement survival time is controlled by the average photon number. The more the average photon number is, the longer survival time of entanglement is prolonged. Thus it has the benefit of keeping quantum correlations. (3) When the cavity field is in squeezed state, the squeezed amplitude parameters have controlling effects on quantum correlations including entanglement and quantum discord. On the one hand, the increase of squeezed amplitude parameters can prolong the survival time of entanglement, on the other hand, with the increase of squeezed amplitude parameters, the robustness of quantum discord is more and more superior to concurrence and is more advantage to keep the system quantum correlations. The further study results show that the increase of the initial relative phase of coupling superconducting qubits can also keep the quantum correlations.     

Relative phase based manipulation of quantum entanglement and measurement of supercurrent

We investigate the quantum entanglement and supercurrent of coupling superconducting qubits in circuit QED system. We compare the effect of the relative phase of the coupling qubits on the concurrence and supercurrent when the microwave field is initially in coherent state, even coherent state and odd coherent state. The results show that entanglement death can be avoided via manipulating the relative phase only in the coherent state since the improvement for entanglement death is unsatisfactory in the even coherent state and odd coherent state.     

Exact Entanglement Dynamics in Three Interacting Qubits

Motivated by recent experimental studies on coherent dynamics transfer in three interacting atoms or electron spins [Phys. Rev. Lett 114(2015) 113002, Phys. Rev. Lett 120(2018) 243604], here we study entanglement entropy transfer in three interacting qubits. We analytically calculate time evolutions of wave function, density matrix and entanglement of the system. We find that initially entangled two qubits may alternatively transfer their entanglement entropy to other two qubit pairs. Thus dynamical evolution of three interacting qubits may produce a genuine three-partite entangled state through entanglement entropy transfers. In particular, different pairwise interactions of the three qubits endow symmetric and asymmetric evolutions of the entanglement transfer,characterized by the quantum mutual information and concurrence. Finally, we discuss an experimental proposal of three Rydberg atoms for testing the entanglement dynamics transfer of this kind.     

Entanglement generation through the interplay of harmonic driving and interaction in coupled superconducting qubits

We study the manipulation of quantum entanglement by periodic external fields. As an entanglement measure we compute numerically the concurrence of two coupled superconducting qubits both driven by a dc + ac external control parameter. We show that when the driving term of the Hamiltonian commutes with the qubit–qubit interaction term, it is possible to create or destroy entanglement in a controlled way by tuning the system at or near multiphoton resonances. On the other hand, when the driving does not commute with the qubit–qubit interaction, the control and generation of entanglement induced by the driving field is more robust and extended in parameter space, beyond the multiphoton resonances.     

Investigations on quantum correlation of coupled qubits in squeezed vacuum reservoir

In this paper, we investigate the quantum correlation of coupled qubits which are initially in maximally entangled mixed states in squeezed vacuum reservoir. We compare and analyse the effects of squeezed parameters on quantum discord and quantum concurrence. The results show that in squeezed vacuum reservoir, the quantum discord and quantum concurrence perform completely opposite behaviors to the change of squeezed parameters. Quantum discord survives longer with the increase of squeezed amplitude parameter, but entanglement death turns faster on the contrary. The results also indicate that the classical correlation of the system is smaller than quantum discord in vacuum reservoir, while it is bigger than quantum discord in squeezed vacuum reservoir. The quantum discord and classical correlation are more robust than quantum concurrence in the two reservoir environments, which indicates that the entanglement actually is easily affected by decoherence and quantum discord has stronger ability to avoid decoherence in squeezed vacuum reservoir.     

Influence of Interaction Between Qubits on Entanglement Sudden Death and Birth

Dynamic evolution of entanglement is studied for coupling two-qubit system in non-Markov environment in terms of concurrence. We find that the degree of entanglement depends on the initial quantum state of the system and the interaction between the two-qubit system and the environment. When the interaction between the qubits and the environment is completely symmetric, especially, the environment has no effect on the entanglement, where the decoherence is entirely resulted from the interaction between qubits. By controlling the coupling way of the interaction, thus, one may avoid the entanglement sudden death (ESD).     

Binegativity of two qubits under noise

Recently, it was argued that the binegativity might be a good quantifier of entanglement for two-qubit states. Like the concurrence and the negativity, the binegativity is also analytically computable quantifier for all two qubits. Based on numerical evidence, it was conjectured that it is a PPT (positive partial transposition) monotone and thus fulfills the criterion to be a good measure of entanglement. In this work, we investigate its behavior under noisy channels which indicate that the binegativity is decreasing monotonically with respect to increasing noise. We also find that the binegativity is closely connected to the negativity and has closed analytical form for arbitrary two qubits. Our study supports the conjecture that the binegativity is a monotone.     

Atomic Evolution and Entanglement of Two Qubits in Photon Superfluid

By using reservoir theory, we investigate the evolution of an atom placed in photon superfluid and study the entanglement properties of two qubits interacting with photon superfluid. It is found that the atomic decay rate in photon superfluid changes periodically with position of the atom and the decay rate can be inhibited compared to that in usual electromagnetic environment without photon superfluid. It is also found that when two atoms are separately immersed in their own local photon-superfluid reservoir, the entanglement sudden death or birth occurs or not only depends on the initial state of the qubits. What is more, we find a possible case that the concurrence between two qubits can remain a constant value by choosing proper values of parameters of the system, which may provide a new way to preserve quantum entanglement.     

Dynamics of entanglement protection of two qubits using a driven laser field and detunings:Independent and common,Markovian and/or non-Markovian regimes

Preventing quantum entanglement from decoherence effect is of theoretical and practical importance in the quantum information processing technologies.In this regard,we consider the entanglement dynamics of two identical qubits where the qubits which are coupled to two independent(Markovian and/or non-Markovian) as well as a common reservoir at zero temperature are further interacted with a classical driving laser field.Then,we study the preservation of generated two-qubit entanglement in various situations using the concurrence measure.It is shown that by applying the classical driving field and so the possibility of controlling the Rabi frequency,the amount of entanglement of the two-qubit system is improved in the off-resonance condition between the qubit and the central cavity frequencies(central detuning) in both non-Markovian and Markovian reservoirs.While the central detuning has a constructive role,the detuning between the qubit and the classical field(laser detuning) affects negatively on the entanglement protection.The obtained results show that long-living entanglement in the non-Markovian reservoir is more accessible than in the Markovian reservoir.We demonstrate that,in a common reservoir non-zero stationary entanglement is achievable whenever the two-qubit system is coupled to the reservoir with appropriate values of relative coupling strengths.     

Quantum entanglement and control in a capacitively coupled charge qubit circuit

The macroscopic quantum entanglement in capacitively coupled SQUID (superconducting quantum interference device)-based charge qubits is investigated theoretically. The entanglement characteristic is discussed by employing the quantum Rabi oscillations and the concurrence. An interesting conclusion is obtained, i.e., the magnetic fluxes Ф_x1 and Ф_x2 through the superconducting loops can adjust the entanglement degree between the qubits.