Robustness Of Entanglement Research Articles

Robustness of Entanglement for Dicke-W and Greenberger-Horne-Zeilinger Mixed States.

Quantum entanglement is a fundamental characteristic of quantum mechanics, and understanding the robustness of entanglement across different mixed states is crucial for comprehending the entanglement properties of general quantum states. In this paper, the robustness of entanglement of Dicke-W and Greenberger-Horne-Zeilinger (GHZ) mixed states under different mixing ratios is calculated using the entanglement witness method. The robustnesses of entanglement of Dicke-W and GHZ mixed states are different when the probability ratio of Dicke to W is greater than 32 and less than 32. For the probability of Dicke and W states greater than or equal to 32, we study the robustness of entanglement of Dicke and GHZ mixed states and analyze and calculate their upper and lower bounds. For the probability of Dicke and W states less than 32, we take the equal probability ratio of Dicke and W states as an example and calculate and analyze the upper and lower bounds of their robustness of entanglement in detail.

Entanglement enhancement through magnon squeezing and optical parametric amplifier in cavity magnomechanics

We consider a cavity magnomechanical (CMM) system comprising magnon, cavity, and phonon modes. The coupling between the magnon and cavity, as well as between magnon and phonon, is mediated by the magnetic-dipole interaction and magnetostrictive interaction, respectively. By incorporating the optical parametric amplifier (OPA) and magnon squeezing mechanisms induced by the magnon self-Kerr nonlinearity, we observe a significant enhancement in entanglement between magnon-cavity, cavity-phonon, as well as tripartite entanglement, compared to the case where OPA and magnon squeezing are not introduced. We also explore the adverse effect of the thermal bath on the mechanical mode, specifically concerning the generation of magnon–phonon entanglement. Additionally, the presence of both magnon squeezing and OPA has been shown to play a crucial role in enhancing the robustness of entanglement against thermal effects compared to the cases when OPA is applied alone or when magnon squeezing is used alone. Here, the entanglement between the magnon and cavity persists up to a temperature of 284 mK, higher than previously observed values. The current CMM system shows promise for use in quantum tasks where it is necessary to enhance entanglement.

Open dynamics of entanglement in mesoscopic bosonic systems

A key issue in quantum information is finding an adequate description of mesoscopic systems that is simpler than full quantum formalism yet retains crucial information about non-classical phenomena like entanglement. In particular, the study of fully bosonic systems undergoing open evolution is of great importance for the advancement of photonic quantum computing and communication. In this paper, we propose a mesoscopic description of such systems based on boson number correlations. This description allows for tracking Markovian open evolution of entanglement of both non-Gaussian and Gaussian states and their sub-Poissonian statistics. It can be viewed as a generalization of the reduced state of the field formalism (Alicki 2019 Entropy 21 705), which by itself does not contain information about entanglement. As our approach adopts the structure of the description of two particles in terms of first quantization, it allows for broad intuitive usage of known tools. Using the proposed formalism, we show the robustness of entanglement against low-temperature damping for four-mode bright squeezed vacuum state and beam-splitted single photon. We also present a generalization of the Mandel Q parameter. Building upon this, we show that the entanglement of the state obtained by beam splitting of a single occupied mode is inherited from sub-Poissonian statistics of the input state.

Shor–Laflamme distributions of graph states and noise robustness of entanglement

The Shor–Laflamme distribution (SLD) of a quantum state is a collection of local unitary invariants that quantify k-body correlations. We show that the SLD of graph states can be derived by solving a graph-theoretical problem. In this way, the mean and variance of the SLD are obtained as simple functions of efficiently computable graph properties. Furthermore, this formulation enables us to derive closed expressions of SLDs for some graph state families. For cluster states, we observe that the SLD is very similar to a binomial distribution, and we argue that this property is typical for graph states in general. Finally, we derive an SLD-based entanglement criterion from the purity criterion and apply it to derive meaningful noise thresholds for entanglement. Our new entanglement criterion is easy to use and also applies to the case of higher-dimensional qudits. In the bigger picture, our results foster the understanding both of quantum error-correcting codes, where a closely related notion of SLDs plays an important role, and of the geometry of quantum states, where SLDs are known as sector length distributions.

Robustness of entanglement in Hawking radiation for optical systems immersed in thermal baths

Entanglement is the quantum signature of Hawking's particle pair-creation from causal horizons, for gravitational and analog systems alike. Ambient thermal fluctuations, ubiquitous in realistic situations, strongly affects the entanglement generated in the Hawking process, completely extinguishing it when the ambient temperature is comparable to the Hawking temperature. In this work, we show that optical analog systems have a built-in robustness to thermal fluctuations which are at rest in the laboratory. In such systems, horizons move relative to the laboratory frame at velocities close to the speed of light. We find that a subtle interplay between this relative velocity and dispersion protects the Hawking-generated entanglement -- allowing ambient temperatures several orders of magnitude larger than the Hawking temperature without significantly affecting entanglement.

Computable lower bounds on the entanglement cost of quantum channels

A class of lower bounds for the entanglement cost of any quantum state was recently introduced in Lami and Regula (2023 Nature Physics) in the form of entanglement monotones known as the tempered robustness and tempered negativity. Here we extend their definitions to point-to-point quantum channels, establishing a lower bound for the asymptotic entanglement cost of any channel, whether finite or infinite dimensional. This leads, in particular, to a bound that is computable as a semidefinite program and that can outperform previously known lower bounds, including ones based on quantum relative entropy. In the course of our proof we establish a useful link between the robustness of entanglement of quantum states and quantum channels, which requires several technical developments such as showing the lower semicontinuity of the robustness of entanglement of a channel in the weak*-operator topology on bounded linear maps between spaces of trace class operators.

Entanglement enhancement in cavity magnomechanics by an optical parametric amplifier

We propose a method to enhance bipartite and tripartite entanglement in cavity magnomechanics using an optical parametric amplifier (OPA). We analyze this system and identified parametric regimes where different types of entanglement are enhanced. We show that a proper choice of phase of the parametric amplifier leads to the enhancement of the bipartite entanglements. Moreover, the tripartite entanglement is also significantly enhanced in the presence of the OPA. The OPA not only enhances the strength of entanglement but also increases the domain of entanglement over a wider space of detunings as compared to the system when no OPA is present. Similarly, the robustness of entanglement against temperature is also enhanced. Another important consequence of the OPA is the fact that it relaxes the requirement of strong magnon-phonon coupling to generate cavity-magnon entanglement which is necessary for the case when the OPA is not present. We believe that the presented scheme is a step forward to realize robust quantum entanglement using current technology.

Evolution of two-mode quantum states under a dissipative environment: Comparison of the robustness of squeezing and entanglement resources

We explore the relative robustness of single-mode squeezing and entanglement (which are quantum resources interconvertible via passive optics) for two-mode Gaussian states under different dissipative environments. When the individual modes interact with identical local baths, entanglement and squeezing decay at the same rate. However, when only one of the modes interacts with a local bath, the comparative robustness of entanglement and squeezing depends on the initial squeezing of the state. Similarly, when the system interacts with a global bath, the robustness of entanglement and squeezing depends on the initial squeezing. Thus depending on the nature of dissipative environments and the initial squeezing of the state, one can select the more robust form of resource out of squeezing and entanglement to store quantumness. This can be used to effectively enhance the performance of various quantum information processing protocols based on continuous variable Gaussian states.

Blindly verifying partially unknown entanglement

SummaryQuantum entanglement has shown distinguished features beyond any classical state. Many methods have been presented to verify unknown entanglement with the complete information about the density matrices by quantum state tomography. In this work, we aim to identify unknown entanglement with only partial information of the state space. The witness consists of a generalized Greenberger-Horne-Zeilinger-like paradox expressed by Pauli observables, and a nonlinear entanglement witness expressed by density matrix elements. First, we verify unknown bipartite entanglement and study the robustness of entanglement witnesses against the white noise. Second, we generalize such verification to partially unknown multipartite entangled states, including the Greenberger-Horne-Zeilinger-type and W-type states. Third, we give a quantum-information application related to the quantum zero-knowledge proof. It further provides a useful method in blindly verifying universal quantum computation resources. These results may be interesting in entanglement theories, quantum communication, and quantum networks.

Automated machine learning can classify bound entangled states with tomograms

For quantum systems with a total dimension greater than six, the positive partial transposition (PPT) criterion is sufficient but not necessary to decide the non-separability of quantum states. Here, we present an Automated Machine Learning approach to classify random states of two qutrits as separable or entangled using enough data to perform a quantum state tomography, without any direct measurement of its entanglement. We could successfully apply our framework even when the Peres-Horodecki criterion fails. In addition, we could also estimate the Generalized Robustness of Entanglement with regression techniques and use it to validate our classifiers.

Preparation and verification of two-mode mechanical entanglement through pulsed optomechanical measurements

We propose a protocol how to generate and verify bipartite Gaussian entanglement between two mechanical modes coupled to a single optical cavity, by means of short optical pulses and measurement. Our protocol requires neither the resolved sideband regime, nor low thermal phonon occupancy, and allows the generation and verification of quantum entanglement in less than a mechanical period of motion. Entanglement is generated via effective two-mode mechanical squeezing through conditioning position measurements. We study the robustness of entanglement to experimental deviations in mechanical frequencies and optomechanical coupling rates.

Entanglement distance for arbitrary M -qudit hybrid systems

We propose a measure of entanglement that can be computed for any pure state of an $M$-qubit system. The entanglement measure has the form of a distance that we derive from an adapted application of the Fubini-Study metric. This measure is invariant under local unitary transformations and defined as trace of a suitable metric that we derive, the entanglement metric $\tilde{g}$. Furthermore, the analysis of the eigenvalues of $\tilde{g}$ gives information about the robustness of entanglement.

Robustness of entanglement as an indicator of topological phases in quantum walks

How to reveal topological phases and their boundaries is an intriguing issue in various systems. Entanglement, which plays a fundamental role in quantum information, has been found profoundly related to topological phases. However, experimentally exploring this relation is precluded by the limited ability to obtain entanglement in many-body systems. In this work, we propose and experimentally demonstrate that the robustness of entanglement, quantified by the von Neumann entropy, can be used to reveal the topological phase with winding number W = 1 and topological phase with W = 0 in quantum walks. With the different robustness of entanglement against perturbations of a parameter, the phase boundaries between the distinct topological phases can be further determined. As a result, our work not only offers a new perspective for quantum walks but also exhibits the deep connection between entanglement and topological physics.

Entanglement Sudden Death and Birth Effects in Two Qubits Maximally Entangled Mixed States Under Quantum Channels

In the present article, the robustness of entanglement in two qubits maximally entangled mixed states (MEME) have been studied under quantum decoherence channels. Here we consider bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels. To quantify the entanglement, the concurrence has been used as an entanglement measure. During this study interesting results have been found for sudden death and birth of entanglement under bit flip and bit-phase-flip channels. While amplitude damping channel produces entanglement sudden death and does not allow re-birth of entanglement. On the other hand, two qubits MEMS exhibit the robust character against the phase flip, phase damping and depolarization channels. The elegant behavior of all the quantum channels have been investigated with varying parameter of quantum state MEMS in different cases.

Enhanced Multiqubit Phase Estimation in Noisy Environments by Local Encoding.

The first generation of multiqubit quantum technologies will consist of noisy, intermediate-scale devices for which active error correction remains out of reach. To exploit such devices, it is thus imperative to use passive error protection that meets a careful trade-off between noise protection and resource overhead. Here, we experimentally demonstrate that single-qubit encoding can significantly enhance the robustness of entanglement and coherence of four-qubit graph states against local noise with a preferred direction. In particular, we explicitly show that local encoding provides a significant practical advantage for phase estimation in noisy environments. This demonstrates the efficacy of local unitary encoding under realistic conditions, with potential applications in multiqubit quantum technologies for metrology, multipartite secrecy, and error correction.

Boundary states for entanglement robustness under dephasing and bit flip channels**Project supported by the National Key Research and Development Program of China (Grant No. 2016YFE0200700) and the National Natural Science Foundation of China (Grant Nos. 61627820 and 61934003).

We investigate the robustness of entanglement for a multiqubit system under dephasing and bit flip channels. We exhibit the difference between the entanglement evolution of the two forms of special states, which are locally unitarily equivalent to each other and therefore possess precisely the same entanglement properties, and demonstrate that the difference increases with the number of qubits n. Moreover, those two forms of states are either the most robust genuine entangled states or the most fragile ones, which confirm that local unitary (LU) operations can greatly enhance the entanglement robustness of n-qubit states.

Robustness of qubit–qudit entanglement under decoherence

We investigate the robustness of entanglement for a qubit-qudit system under depolarizing and dephasing channels. For depolarizing channel, we obtain a simple analytical expression of entanglement evolution. It is shown that the larger dimension d a qudit subsystem has, the more robust a pure state becomes. For dephasing channel, we find the most robust entangled states and the most fragile ones. Moreover, the robustness of these states is independent of the qudit’s dimension d.

Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations

In a recent work [Phys. Rev. Lett. 116, 240401 (2016)], a framework known by the name of "assemblage moment matrices" (AMMs) has been introduced for the device-independent quantification of quantum steerability and measurement incompatibility. In other words, even with no assumption made on the preparation device nor the measurement devices, one can make use of this framework to certify, directly from the observed data, the aforementioned quantum features. Here, we further explore the framework of AMM and provide improved device-independent bounds on the generalized robustness of entanglement, the incompatibility robustness and the incompatibility weight. We compare the tightness of our device-independent bounds against those obtained from other approaches. Along the way, we also provide an analytic form for the generalized robustness of entanglement for an arbitrary two-qudit isotropic state. When considering a Bell-type experiment in a tri- or more-partite scenario, we further show that the framework of AMM provides a natural way to characterize a superset to the set of quantum correlations, namely, one which also allows post-quantum steering.

Comparing coherence and entanglement under resource non-generating unitary transformations

Quantum coherence is a fundamental property of quantum systems that can be studied within the framework of a quantum resource theory. From this resource-theoretic approach, many similarities emerge between coherence and quantum entanglement, the latter being another prominent quantum resource. In this paper, we study the relationship between coherence and entanglement from the perspective of resource loss/gain by unitary dynamics. Specifically we consider how much coherence can be either generated or destroyed on a bipartite system when the action is restricted to local unitary (LU) operations. For pure states, we find that the relative entropy of entanglement and the robustness of entanglement provide tight lower bounds on the amount of coherence that can be destroyed by LUs, as measured by the relative entropy and measures of coherence, respectively. This provides new operational interpretations of the entanglement entropy and robustness of entanglement in pure states as the minimal amount of coherence that persists when the system is subjected to LU transformations. We then study the amount of bipartite pure entanglement that can be either maximized or minimized when the action is restricted to a global incoherent operation. For two-qubit pure states, maximum and minimum are shown in terms of coefficients of given state with incoherent basis. Finally we consider a generalized version of the recently introduced CCP of a quantum channel.

Non-Markovianity quantifier of an arbitrary quantum process

Calculating the degree of non-Markovianity of a dissipative process is a difficult task, even for the dynamics of a single qubit, given the complex maximization problem. In this work, focusing on the entanglement-based quantifier of non-Markovianity, we present an analytical solution for such an optimization problem. We then propose a computable non-Markovianity measure based on generalized robustness of entanglement, an entanglement measure that can be readily calculated by a semidefinite programming method. We show that the non-Markovianity, in a given interval of time, can be witnessed by calculating the expectation value of an observable, making it attractive for experimental investigations.