Initial Entangled State Research Articles

Efficient entanglement enhancement of partially entangled pairs

We present a comprehensive approach to transform a partially entangled pure state into a maximally entangled state, utilizing only local operations and a single copy of the entangled state. Our approach eliminates the need for multiple copies of entangled states, bilateral operations, and the time-consuming partial-collapse weak measurements. Integrating ancilla qubits, rotation gates, and CNOT gates, we simplify the process of enhancing entanglement, achieving significant efficiency using only a single partially entangled state. Assuming perfect local operations, we showcase the efficacy of our method through both mathematical analysis and the practical implementation of the corresponding circuit in Qiskit. Furthermore, we explore the impact of imperfect local operations, specifically focusing on the CNOT gate and measurement, for a comprehensive analysis. Additionally, we address the case of unknown parameters in the partially entangled pure state and introduce a robust method to effectively handle this uncertainty, ensuring reliable entanglement fidelity optimization in practical situations. We extend our investigation to the application of our method to mixed initial entangled states. Our results demonstrate the reliability of our method in increasing entanglement even in the presence of phase damping and amplitude damping. Additionally, we illustrate its effectiveness in transforming specific mixed initial states in the presence of depolarization into states with enhanced entanglement.

Nonlocality activation in a photonic quantum network

Bell nonlocality refers to correlations between two distant, entangled particles that challenge classical notions of local causality. Beyond its foundational significance, nonlocality is crucial for device-independent technologies like quantum key distribution and randomness generation. Nonlocality quickly deteriorates in the presence of noise, and restoring nonlocal correlations requires additional resources. These often come in the form of many instances of the input state and joint measurements, incurring a significant resource overhead. Here, we experimentally demonstrate that single copies of Bell-local states, incapable of violating any standard Bell inequality, can give rise to nonlocality after being embedded into a quantum network of multiple parties. We subject the initial entangled state to a quantum channel that broadcasts part of the state to two independent receivers and certify the nonlocality in the resulting network by violating a tailored Bell-like inequality. We obtain these results without making any assumptions about the prepared states, the quantum channel, or the validity of quantum theory. Our findings have fundamental implications for nonlocality and enable the practical use of nonlocal correlations in real-world applications, even in scenarios dominated by noise.

A Study of Quantum Game for Low-Carbon Transportation with Government Subsidies and Penalties

Traditional classical game theory struggles to effectively address the inefficiencies in subsidizing and penalizing the R&D and production of low-carbon transportation vehicles. To avoid the shortcomings of classic game theory, this research integrates quantum game theory with Nash games to explore the characteristics of automakers’ behavior for low-carbon transportation with government subsidies and penalties. We first constructed a low-carbon transportation game model between the government and automakers. Then, the optimal profit strategies for both parties in a quantum entangled state were analyzed. Finally, the impact of quantum superposition states and the initial entangled state on the profit strategies of both parties was simulated and analyzed using Monte Carlo simulations. We find that under the joint effects of government subsidies and penalties, quantum game states and the initial quantum entangled state have a crucial influence on the game’s outcomes. They can encourage the realization of Nash equilibrium and perfect coordination in the quantum game, significantly increasing the profits for both parties. This in turn effectively stimulates automakers to research and produce low-carbon transportation solutions, promoting the rapid development of low-carbon transportation technology. In theory, this research can enrich the Quantum game for improvements in the Nash equilibrium solution for the government to subsidize and penalize the low-carbon transportation problem. Meanwhile, in practice, it can provide guidance and reference in optimal strategy selection conditions for government policymakers and automakers for low-carbon transportation.

Production and protection of entanglement via vacuum induced coherences

The entanglement dynamics of a pair of three-level V-type atoms decaying spontaneously in a common vacuum reservoir is investigated. Under the condition that the decaying transitions in the atoms have parallel dipole moments, the effect of coherences induced by spontaneous emission is considered in the atomic dynamics. We show that vacuum-induced coherence (VIC) and collective effects in atomic decay play a significant role in the creation of entanglement. By using negativity as a measure of entanglement, we study the time evolution of entanglement for initial separable and generalized Dicke states as well as maximally entangled qutrit states. We show that the effects of VIC enhance the production of entanglement from initial separable states of the atoms. We also show that the entanglement can be protected in steady-state for atoms evolving from initial entangled states. The amount of entanglement that can be preserved is more in the presence of VIC than in its absence.

Entanglemnt in nonlinear three-qubits Jaynes — Cummings

In this paper, we investigated the dynamics of entanglement of pairs of qubits in a system of three identical qubits that interact non-resonantly with the selected mode of a microwave resonator without loss with the Kerr medium by means of single-photon transitions. We have found solutions to the quantum time Schrodinger equation for the total wave function of the system for the initial separable, biseparable and true entangled states of qubits and the Fock initial state of the resonator field. Based on these solutions, the criterion of entanglement of qubit pairs — negativity is calculated. The results of numerical simulation of the negativity of qubit pairs have shown that the presence of disorder and Kerr nonlinearity in the case of an initial non-entangled state of a pair of qubits can lead to a significant increase in the degree of their entanglement. In the case of an initial entangled state of a pair of qubits, the disorder and the Kerr medium can lead to a significant stabilization of the initial entanglement.

Initial Correlations and Complete Positivity of Dynamical Maps

It is now increasingly realized in the study of open system dynamics that initial correlations do not pose a conceptual difficulty as traditionally believed. A similar methodology as used to describe initial product states can be adopted, with the only difference being that the reduced dynamics is possibly not completely positive, entailing that only a restricted set of initial reduced states lead to a physically valid dynamics. Here we study the interplay between the initial correlations, especially in the form of highly entangled states, and the system–environment unitary. In particular, for almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. Restricting to the case of initial, pure entangled states, we obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.

Theory of singlet fission in carotenoid dimers.

We develop a theory of singlet fission in carotenoid dimers. Following photoexcitation of the "bright" state (i.e., a singlet electron-hole pair) in a single carotenoid, the first step in the singlet fission process is ultrafast intramolecular conversion into the highly correlated "dark" (or 2Ag) state. This state has both entangled singlet triplet-pair and charge-transfer character. Our theory is predicated on the assumption that it is the singlet triplet-pair component of the "dark" state that undergoes bimolecular singlet fission. We use valence bond theory to develop a minimal two-chain model of the triplet-pair states. The single and double chain triplet-pair spectra are described, as this helps explain the dynamics and the equilibrated populations. We simulate the dynamics of the initial entangled pair state using the quantum Liouville equation, including both spin-conserving and spin-nonconserving dephasing processes. By computing the intrachain and interchain singlet, triplet, and quintet triplet-pair populations, we show that singlet fission critically depends on the interchain coupling and the driving potential (that determines endothermic vs exothermic fission).

Exact dynamics of multimode periodic input states in coupled waveguide arrays

In this work, we investigate the quantum state reconstruction of the periodic input state in a 1-D waveguide array. In particular, we consider a single-photon multimode entangled W-state with different periodicities as an input to the array and study the effect of periodicity in the output. For comparison, we also study separable single photon periodic input states. We study the evolution of average photon number and the fidelity of the periodic input state and give the exact solution to investigate the revival of single photon multimode periodic input. Our solution is valid for any number of waveguides in the array. Our findings show the revival of the average photon number and almost complete quantum state reconstruction of the initial multimode entangled state for certain periodicities. The results reported here are significant because multimode-entangled states are essential resources for various applications in the physical implementation of photonic quantum technologies.

Dynamic entanglement for continuous variables in an electric field background

Quantum entanglement is a typical nonclassical correlation. Here, we use this concept to analyze quantum entanglement for continuous variables generated by the Schwinger pair production for constant and pulsed electric fields. An initial two-mode entangled state evolves into a three-mode entangled state through a Gaussian channel of the Schwinger effect, which encodes the information about the Schwinger effect. By detecting the entanglement of the output three-mode state, we obtain the optimal parameters for easier to generate particle–antiparticle pairs. We find that the generated 1 → 2 entanglement is more sensitive to the parameters than the generated 1 → 1 entanglement. Therefore, we should choose the generated 1 → 2 entanglement to extract information. We argue that extracting the optimal parameters from quantum entanglement may guide future experiments.

Entanglement Swapping and Swapped Entanglement

Entanglement swapping is gaining widespread attention due to its application in entanglement distribution among different parts of quantum appliances. We investigate the entanglement swapping for pure and noisy systems, and argue different entanglement quantifiers for quantum states. We explore the relationship between the entanglement of initial states and the average entanglement of final states in terms of concurrence and negativity. We find that if initial quantum states are maximally entangled and we make measurements in the Bell basis, then average concurrence and average negativity of final states give similar results. In this case, we simply obtain the average concurrence (average negativity) of the final states by taking the product of concurrences (negativities) of the initial states. However, the measurement in non-maximally entangled basis during entanglement swapping degrades the average swapped entanglement. Further, the product of the entanglement of the initial mixed states provides an upper bound to the average swapped entanglement of final states obtained after entanglement swapping. The negativity work well for weak entangled noisy states but concurrence gives better results for relatively strong entanglement regimes. We also discuss how successfully the output state can be used as a channel for the teleportation of an unknown qubit.

Effects of Polymerization Medium on Nascent UHMWPE Properties and Sintered Material Performance

High-performance and easy-processing UHMWPE products with less entanglement and small particle size are difficult to synthesize efficiently in the polymerization process. In this study, a mixture of heptane and light paraffin is proposed as the polymerization medium to control the concentration of ethylene in the slurry during polymerization. Influences of the mixture composition on the polymerization behavior of ethylene, the particle size and its distribution of nascent UHMWPE, and the initial entangled state of UHMWPE were explored. Experimental results showed that as the volume fraction of heptane decreased, the viscosity of the solvent mixture increased exponentially, and ethylene solubility as well as mass transfer coefficient of ethylene in solvent decreased, which greatly affected the ethylene polymerization rate. By adjusting the volume fraction of heptane in the polymerization medium, the particle size, initial entanglement state density, and molecular weight of nascent UHMWPE will be coordinately controlled. UHMWPE with smaller particle size, lower entanglement density, and higher molecular weight can be prepared using the conventional Ziegler–Natta catalyst and polymerization medium with a lower heptane content, and its sintered UHMWPE material shows good mechanical properties.

Is entanglement a unique resource in quantum illumination?

It is well known that quantum illumination with a two-mode squeezed vacuum state as an initial entangled bipartite state achieves 6 dB quantum advantage in the error probability compared to classical coherent-state illumination. Is entanglement the only resource responsible for the quantum advantage? We explore this issue by applying the various squeezing operators to the two-mode squeezed vacuum state. Even though the operations do not decrease the bipartite entanglement, it is shown that the quantum advantage drastically decreases with increasing the squeezing parameters. Based on the fact, we conclude that entanglement is not unique resource responsible for the quantum advantage.

Superior Resilience of Non-Gaussian Entanglement against Local Gaussian Noises.

Entanglement distribution task encounters a problem of how the initial entangled state should be prepared in order to remain entangled the longest possible time when subjected to local noises. In the realm of continuous-variable states and local Gaussian channels it is tempting to assume that the optimal initial state with the most robust entanglement is Gaussian too; however, this is not the case. Here we prove that specific non-Gaussian two-mode states remain entangled under the effect of deterministic local attenuation or amplification (Gaussian channels with the attenuation factor/power gain κi and the noise parameter μi for modes i=1,2) whenever κ1μ22+κ2μ12<14(κ1+κ2)(1+κ1κ2), which is a strictly larger area of parameters as compared to where Gaussian entanglement is able to tolerate noise. These results shift the “Gaussian world” paradigm in quantum information science (within which solutions to optimization problems involving Gaussian channels are supposed to be attained at Gaussian states).

DYNAMICS OF THE THREE-QUBITS TAVIS — CUMMINGS MODEL

In this article, we have studied the entanglement dynamics of three identical qubits (natural or artificial two-level atoms) resonantly interacting with the one mode of the thermal field of a microwave lossless resonator via one-photon transitions. An exact solution of the quantum time Schrodinger equation is found for the total wave function of the system for the initial separable and entangled states of qubits and the Fock initial state of the resonator. On the basis of this solution, an exact solution of the quantum Liouville equation for the total time-dependent density matrix of the system in the case of a thermal field of the resonator is constructed. The exact solution for the full density matrix is used to calculate the criterion of entanglement of pairs of qubits negativity. The resultsof numerical simulation of the time dependence of the negativity of pairs of qubits showed that with an increase in the intensity of the thermal resonator field, the degree of entanglement of pairs of qubits decreases. It is also shown that In the model under consideration, for any initial states of qubits and intensities of the thermal field of the resonator, the effect of sudden death of entanglement takes place. This behavior of the entanglement parameter in the model under consideration differs from that in the two-qubit model. For two-qubit model, the effect of the sudden death of entanglement takes place only for the initial entangled states of qubits and intense thermal fields of the resonator.

Quantum discord and entropic measures of two relativistic fermions

In the present work, we study the interplay between relativistic effects and quantumness in the system of two relativistic fermions. In particular, we explore entropic measures of quantum correlations and quantum discord before and after application of a boost and subsequent Wigner rotation. We also study the positive operator-valued measurements (POVMs) invasiveness before and after the boosts. While the relativistic principle is universal and requires Lorentz invariance of quantum correlations in the entire system, we have found specific partitions where quantum correlations stored in particular subsystems are not invariant. We calculate quantum discords corresponding of the states before and after applying a boost, and observe that the state gains extra discord after the boost. When analyzing the invasiveness of the POVMs, we have found that the POVM applied to the initial entangled state reduces the discord to zero. However, discord of the boosted state survives after the same POVM. Thus we conclude that the quantum discord generated by Lorentz boost is robust concerning the protective POVM, while the measurement exerts an invasive effect on the discord of the initial state. Finally, we discuss potential implementation of the ideas of this work using top quarks as a benchmark scenario.

Frequency estimation under non-Markovian spatially correlated quantum noise

We study the estimation precision attainable by entanglement-enhanced Ramsey interferometry in the presence of spatiotemporally correlated non-classical noise. Our analysis relies on an exact expression of the reduced density matrix of the qubit probes under general zero-mean Gaussian stationary dephasing, which is established through cumulant-expansion techniques and may be of independent interest in the context of non-Markovian open dynamics. By continuing and expanding our previous work (Beaudoin et al 2018 Phys. Rev. A 98 020102(R)), we analyze the effects of a non-collective coupling regime between the qubit probes and their environment, focusing on two limiting scenarios where the couplings may take only two or a continuum of possible values. In the paradigmatic case of spin–boson dephasing noise from a thermal environment, we find that it is in principle possible to suppress, on average, the effect of spatial correlations by randomizing the location of the probes, as long as enough configurations are sampled where noise correlations are negative. As a result, superclassical precision scaling is asymptotically restored for initial entangled states, including experimentally accessible one-axis spin-squeezed states.

Deterministic linear-optical quantum control gates utilizing path and polarization degrees of freedom

We present a general scheme for a family of linear-optical quantum control gates, including controlled-not and controlled-swap gates for two or three qubits. Our approach utilizes polarization-path-entangled pairs of photons and encodes qubits in mixed degrees of freedom with the control qubit specifically occupying the polarization degree of freedom. By exploiting multiple degrees of freedom and initial state entanglement of the two photons, the proposed control gates do not require any ancilla photons or measurement-induced nonlinearities. Since our gates are purely linear and we implicitly use nonlinearities in a standard manner to create entanglement via parametric nonlinear process, our work demonstrates that a need to have nonlinearities in the photonic gates can be shifted to the state preparation stage; the cost of such shift is that the construction of a certain class of single-qubit operations, such as Hadamard, needs to be probabilistic. In particular, we focus on a deterministic linear-optical quantum Fredkin (controlled-swap) gate and perform a full characterization of the gate performance with a high fidelity typically well above $99%$ under realistic conditions. The proposed control gates rely on simple linear-optical elements and polarization-entangled photon pairs readily generated from ubiquitous sources, making the gates experimentally feasible with current technologies.

Enhancing entanglement and total correlation dynamics via local unitaries

The interaction with the environment is one of the main obstacles to be circumvented in practical implementations of quantum information tasks. The use of local unitaries, while not changing the initial entanglement present in a given state, can enormously change its dynamics through a noisy channel, and consequently its ability to be used as a resource. In this way, local unitaries provide an easy and accessible way to enhance quantum correlations in a variety of different experimental platforms. Given an initial entangled state and a certain noisy channel, what are the local unitaries providing the most robust dynamics? In this paper we solve this question considering two-qubit states, together with paradigmatic and relevant noisy channels, showing its consequences for teleportation protocols and identifying cases where the most robust states are not necessarily the ones imprinting the least information about themselves into the environment. We also derive a general multipartite law relating the interplay between the total correlations in the system and environment with their mutual information built up over the noisy dynamics. Finally, we employ the IBM Quantum Experience to provide a proof-of-principle experimental implementation of our results.

Quantum speedup dynamics process in Schwarzschild space–time

Quantum speed limit time (QSLT) can be used to characterize the intrinsic minimal time interval for a quantum system evolving from an initial state to a target state. We investigate the QSLT of the open system in Schwarzschild space–time. We show that, in some typical noisy channels, the Hawking effect can accelerate the evolution of the system. For an initial entangled state, the evolution speed of the system can be enhanced in the depolarizing, bit flip, and bit-phase flip channels as the Hawking temperature increases, which are in sharp contrast to the phase flip channel. Moreover, the optimal initial entanglement exists in other noise channels except the phase flip channel, which minimizes the QSLT of the system and thus leads to the maximum evolution speed of the system.

Amplification of entangled beam based on four-wave mixing process

Two-mode entangled state is an important quantum resource for quantum information. In this paper, the amplification of a single mode of two-mode entangled state (single-mode amplification scheme) and two modes of two-mode entangled state (two-mode amplification scheme) are theoretically proposed. Here, the optical beam splitter model is used to simulate the vacuum noise introduced by the loss in the optical transmission process. By utilizing the positivity under partial transpose criterion, we analyze the effect of the gain of the four-wave mixing process on the entanglement degree of the initial two-mode entangled state in two different amplification schemes. In these two schemes, we set the gain of the initial two-mode entangled state generation process to be 1.5, 2.5 and 50.0 respectively, and then change the gain of the amplification process in a certain range. We also set the transmission efficiency of the amplified beams for each of the two schemes to be a definite value. The results show that the entanglement of the initial two-mode entangled state decreases with the gain increasing under the condition of specific transmission loss in two schemes. When the gain does not exceed a certain value, the entanglement of the initial two-mode entangled state can be maintained. Then, with the increase of the gain, the entanglement of the initial two-mode entangled state will disappear. Moreover, the entanglement of the initial two-mode entangled state of the two-mode amplification scheme disappears faster than that of the single-mode amplification scheme. Our theoretical results pave the way for the experimental realization of the amplification of two-mode entangled state based on four-wave mixing process.