Mixed Entangled States Research Articles

Entanglement manipulation through multicore fibres

Multicore fibres are recently gaining considerable attention in the context of quantum communication, where their capability to transmit multiple quantum states along different cores of the same channel makes them a promising candidate for the implementation of scalable quantum networks. Here, we show that multicore fibres can be effectively used not only for the scope of communication but also for the manipulation of entangled states. Exploiting the formalism of completely positive trace-preserving maps, we describe the action of a multicore fibre as a quantum channel and investigate the propagation of a transmitted state under the effect of decoherence and inter-core crosstalk. Then, we propose a novel protocol for the manipulation of the entanglement where, starting from a maximally entangled state of two qudits, we use a multicore fibre to create new families of mixed entangled states. Notably, the presence of crosstalk is fundamental for the generation of such states.

Using linear and nonlinear entanglement witnesses to generate and detect bound entangled states on an IBM quantum processor

Abstract We investigate bound entanglement in three-qubit mixed states which are diagonal in the Greenberger-Horne-Zeilinger (GHZ) basis. Entanglement in these states is detected using entanglement witnesses and the analysis focuses on states exhibiting positive partial transpose (PPT). We then compare the detection capabilities of optimal linear and nonlinear entanglement witnesses. In theory, both linear and nonlinear witnesses produce non-negative values for separable states and negative values for some entangled GHZ diagonal states with PPT, indicating the presence of entanglement. Our experimental results reveal that in cases where linear entanglement witnesses fail to detect entanglement, nonlinear witnesses are consistently able to identify its presence. Optimal linear and nonlinear witnesses were generated on an IBM quantum computer and their performance was evaluated using two bound entangled states (Kay and Kye states) from the literature, and randomly generated entangled states in the GHZ diagonal form. Additionally, we propose a general quantum circuit for generating a three-qubit GHZ diagonal mixed state using a six-qubit pure state on the IBM quantum processor. We experimentally implemented the circuit to obtain expectation values for three-qubit mixed states and compute the corresponding entanglement witnesses.

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.

Mixed-State Quantum Phases: Renormalization and Quantum Error Correction

Open system quantum dynamics can generate a variety of long-range entangled mixed states, yet it has been unclear in what sense they constitute phases of matter. To establish that two mixed states are in the same phase, as defined by their two-way connectivity via local quantum channels, we use the renormalization group (RG) and decoders of quantum error correcting codes. We introduce a real-space RG scheme for mixed states based on local channels which ideally preserve correlations with the complementary system, and we prove this is equivalent to the reversibility of the channel’s action. As an application, we demonstrate an exact RG flow of finite temperature toric code in two dimensions to infinite temperature, thus proving it is in the trivial phase. In contrast, for toric code subject to local dephasing, we establish a mixed-state toric code phase using local channels obtained by truncating an RG-type decoder and the minimum weight perfect matching decoder. We also discover a precise relation between mixed-state phase and decodability, by proving that local noise acting on toric code cannot destroy logical information without bringing the state out of the toric code phase. Published by the American Physical Society 2024

Many-Body Entropies and Entanglement from Polynomially Many Local Measurements

Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical postprocessing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix, which allow us to reconstruct entropies and PT moments from information on local subsystems. This identification yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements providing a practical and common measurement scheme, we prove that our protocol requires only polynomially many measurements and postprocessing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators and provide numerical evidence that they are satisfied in more general, physically interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today’s quantum platforms. Published by the American Physical Society 2024

Reflected entropy and timelike entanglement in TT¯ -deformed CFT2s

We develop a covariant formalism to investigate the mixed state entanglement between time-dependent boosted subsystems in TT¯-deformed CFT2s through the reflected entropy. To this end we utilize a conformal perturbation theory to obtain the Rényi reflected entropy through the partition function on the replica manifold. The correction to the reflected entropy to the first order in the deformation parameter μ is then obtained in the replica limit for finite temperature and finite-sized systems. We further perform an analytic continuation of our results to obtain the reflected entropy for timelike subsystems in such TT¯-deformed CFT2s. We verify our field theoretic computations for both spacelike and timelike subsystems by obtaining the dual EWCS in the corresponding bulk cutoff AdS3 geometries and find perfect agreement between the two. Published by the American Physical Society 2024

Performance of entanglement purification including maximally entangled mixed states

Entanglement between distant quantum systems is a critical resource for implementing quantum communication. This property is affected by external agents and can be restored by employing efficient entanglement purification protocols. In this work, we propose an entanglement purification protocol based on two entangling two-qubit operations that replace the usual controlled-NOT (CNOT) gate. These operations arise from a generalised quantum measurement and can be understood as measurement operators in a positive operator-valued measure. Furthermore, two variants of the core protocol are introduced and their performances are studied in terms of the overall success probability of reaching a Bell state and the number of purifiable states. Based on rank-two states, we can obtain analytical expressions for the success probability that we extend and refine using numerical calculations to the case of maximally entangled states. We also consider more general rank-three states to show that our procedure is in general more convenient compared to purification protocols based on Bell diagonal states. Finally, we test the protocols using initial random states. In all cases, we find a better performance and a larger amount of purifiable states using our schemes compared to the CNOT-based protocol.

Nonlocality activation using local filtering operations based on CGLMP inequality

Entanglement is necessary but not sufficient to demonstrate nonlocality as there exist local entangled states which do not violate any Bell inequality. In recent years, the activation of nonlocality (known as hidden nonlocality) by using local filtering operations has gained considerable interest. In the original proposal of Popescu [Phys. Rev. Lett. 74, 2619 (1995)] the hidden nonlocality was demonstrated for the Werner class of states in d ≥ 5. In this paper, we demonstrate the hidden nonlocality for a class of mixed entangled states (convex mixture of a pure state and color noise) in an arbitrary d-dimensional system using suitable local filtering operations. For our demonstration, we consider the quantum violation of Collins-Linden-Gisin-Masser-Popescu (CGLMP) inequality which has hitherto not been considered for this purpose. We show that when the pure state in the aforementioned mixed entangled state is a maximally entangled state, the range of the mixing parameter for revealing hidden nonlocality increases with increasing the dimension of the system. Importantly, we find that for d ≥ 8, hidden non-locality can be revealed for the whole range of mixing parameter. Further, by considering another pure state, the maximally CGLMP-violating state, we demonstrate the activation of nonlocality by using the same local filtering operation. We have also shown the activation of quantum fidelity for mixed entangled states using the same local filtering operator.

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.

Entanglement transition and heterogeneity in long-range quadratic Lindbladians

The generation of entanglement in mixed states is relevant to quantum systems coupled to an environment. The dissipative and mixing properties of the environment are unavoidable in physical platforms for quantum simulation and information processing, where entanglement can be a vital resource. In this work, we explore entanglement and heterogeneity in random Lindbladian dynamics describing open quantum systems. We propose a model of a one-dimensional chain of noninteracting, spinless fermions coupled to a local ensemble of baths. The jump operator mediating the interaction with the bath linked to each site has a power-law tail with an exponent p. We show that the system undergoes volume-to-area law entanglement phase transition in the mixed steady state by tuning p which remains stable in the presence of coherent hopping. Unlike the entanglement transition in the pure-state quantum trajectories of open systems, this transition is exhibited by the averaged steady-state density matrix of the Lindbladian. The steady state in the area-law phase is characterized by a spatial heterogeneity in local population imbalance, while the jump operators exhibit a constant participation ratio of the sites they affect. Our work provides a theoretical description of an entanglement transition realized in long-ranged open quantum systems and provides an avenue to stabilize quantum correlations in mixed states. Published by the American Physical Society 2024

Sequentially witnessing entanglement by independent observer pairs

This study delves into measurement strategies within a scenario where multiple pairs of Alices and Bobs independently and sequentially observe entangled states. The goal is to maximize the number of observer pairs (Ak,Bl) capable of witnessing entanglement. Previous research has shown that arbitrary pairs (Ak,Bk) (k≤n) can detect entanglement in all pure entangled states and a specific class of mixed entangled states [Pandit et al. (2022) [37]]. However, it's worth noting that other pairs (Ak,Bl) with (k≠l≤n) may not observe entanglement using the same method. Additionally, a novel strategy is introduced, allowing every pair of arbitrarily many Alices and Bobs to witness entanglement regardless of whether the initial state is a Bell state or a particular class of mixed entangled states. These findings contribute to our understanding of measurement strategies aimed at maximizing entanglement observation in various contexts.

Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences

Multipartite entangled states are an essential resource for sensing, quantum error correction, and cryptography. Color centers in solids are one of the leading platforms for quantum networking due to the availability of a nuclear spin memory that can be entangled with the optically active electronic spin through dynamical decoupling sequences. Creating electron-nuclear entangled states in these systems is a difficult task as the always-on hyperfine interactions prohibit complete isolation of the target dynamics from the unwanted spin bath. While this emergent cross-talk can be alleviated by prolonging the entanglement generation, the gate durations quickly exceed coherence times. Here we show how to prepare high-quality GHZM-like states with minimal cross-talk. We introduce the M-tangling power of an evolution operator, which allows us to verify genuine all-way correlations. Using experimentally measured hyperfine parameters of an NV center spin in diamond coupled to carbon-13 lattice spins, we show how to use sequential or single-shot entangling operations to prepare GHZM-like states of up to M=10 qubits within time constraints that saturate bounds on M-way correlations. We study the entanglement of mixed electron-nuclear states and develop a non-unitary M-tangling power which additionally captures correlations arising from all unwanted nuclear spins. We further derive a non-unitary M-tangling power which incorporates the impact of electronic dephasing errors on the M-way correlations. Finally, we inspect the performance of our protocols in the presence of experimentally reported pulse errors, finding that XY decoupling sequences can lead to high-fidelity GHZ state preparation.

The controlled SWAP test for entanglement of mixed quantum states

Quantum entanglement plays a key role in the field of quantum computing and quantum communication. The controlled SWAP test has been used to detect pure state entanglement (Foulds S. et al. Quantum Sci. Technol., 6 (2021) 035002; Beckey J. L. et al. Phys. Rev. Lett., 127 (2021) 140501). In this paper, we investigate that quantum circuits for controlled SWAP test can be used to detect the entanglement of multipartite mixed state. Based on the measured probability, we propose entanglement criteria for detecting multipartite entanglement and genuine entanglement of pure states. In addition, we give representation of the entanglement measures based on the measured probability of the controlled SWAP tests. Numerical examples are used to illustrate the efficiency of the entanglement criteria.

Benchmarking highly entangled states on a 60-atom analogue quantum simulator

Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states1,2. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices2–5, and it remains unsolved how to estimate the actual entanglement content of experiments6. Here, we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analogue Rydberg quantum simulator, reaching a high-entanglement entropy regime in which exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement6, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution2–5. Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we use. Our results enable a new model for evaluating the ability of both analogue and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

Mixed-state entanglement and transport in Einstein–Maxwell–Axion–Horndeski theory

We present a comprehensive study exploring the relationship between transport properties and measures of quantum entanglement in the Einstein–Maxwell–Axion–Horndeski theory. By using holographic duality, we study the entanglement measures, holographic entanglement entropy (HEE) and entanglement wedge cross-section (EWCS), and transport coefficients, for this model and analyze their dependence on free parameters which we classify into action parameters, observable parameters and axion factor. We find contrasting behaviors between HEE and EWCS with respect to observable parameters (charge and temperature), and the axion factor, indicating that they capture different types of quantum correlations. We also find that HEE exhibits positive correlation with both charge and thermal excitations, whereas EWCS exhibits a negative correlation with charge-related conductivities and thermal fluctuations. Furthermore, we find that the Horndeski coupling term, as the modification to standard gravity theory, does not change the qualitative behaviors of the conductivities and the entanglement measures.

Universal Highly Effective Entanglement Purification with Single‐Copy Hyperentangled State

AbstractEntanglement purification is a powerful way to protect the quality of entangled system from channel noise and environment noise. A universal highly effective entanglement purification protocol with single‐copy hyperentangled state (H‐UHEPP) is proposed for distillable mixed entangled states with bilateral controlled‐not gate operations, bilateral asymmetrical rotation operations and single photon Bell‐state measurements, where all of these operations and measurements are easy to implement in polarization, spatial and time‐bin degrees of freedom (DOFs) of photon system. This H‐UHEPP, which requires only one pair of hyperentangled photons and simple unitary operations on three DOFs of a photon, can significantly enhance the fidelity of the purified state compared with the previous works. As a consequence, H‐UHEPP can speed up the entanglement purification process and reduce the resource consumption, which makes it useful in future quantum information processing.

Mixed state entanglement measures for the dipole deformed supersymmetric Yang–Mills theory

Two different entanglement measures for mixed states, namely, the entanglement of purification and entanglement negativity has been holographically computed for the dipole deformed supersymmetric Yang–Mills (SYM) theory by considering its gravity dual. The dipole deformation induces non-locality in the SYM theory which is characterized by a length-scale a=λ12L̃. Considering a strip like subsystem of length la (in dimensionless form), we first analytically calculate the holographic entanglement entropy for and compare the obtained results with that of obtained numerically. The analytical calculations have been carried out by considering aut≤1, 1≤aut<aub and aut∼aub, where aub is the UV cut-off. The choice of these regions enable us to identify the expansion parameters needed to carry out binomial expansions. The entanglement measures expectedly displays a smooth behaviour with respect to the subsystem size as the geometry has a smooth transition between the mentioned regions. Using these results, the holographic mutual information is then computed for two disjoint subsystems A and B. Based upon the EP=EW duality, the entanglement of purification (EP) is then computed and the effects of dipole deformation in this context have been studied. Finally, we proceed to compute entanglement negativity for this theory and compare the obtained result with that of the standard SYM theory in order to get a better understanding about the effects of the non-locality.

Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory

A standard approach to quantifying resources is to determine which operations on the resources are freely available, and to deduce the partial order over resources that is induced by the relation of convertibility under the free operations. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, i.e., entanglement, then the common assumption is that the appropriate choice of free operations is Local Operations and Classical Communication (LOCC). We here advocate for the study of a different choice of free operations, namely, Local Operations and Shared Randomness (LOSR), and demonstrate its utility in understanding the interplay between the entanglement of states and the nonlocality of the correlations in Bell experiments. Specifically, we show that the LOSR paradigm (i) provides a resolution of the anomalies of nonlocality, wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails new notions of genuine multipartite entanglement and nonlocality that are free of the pathological features of the conventional notions, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which generalizes and simplifies prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. The resource-theoretic perspective also clarifies why it is neither surprising nor problematic that there are mixed entangled states which do not violate any Bell inequality. Our results motivate the study of LOSR-entanglement as a new branch of entanglement theory.

Maximum entanglement of mixed symmetric states under unitary transformations

We study the maximum entanglement that can be produced by a global unitary transformation for systems of two and three qubits constrained to the fully symmetric states. This restriction to the symmetric subspace appears naturally in the context of bosonic or collective spin systems. We also study the symmetric states that remain separable after any global unitary transformation, called symmetric absolutely separable (SAS) states, or absolutely classical for spin states. The results for the two-qubit system are deduced analytically. In particular, we determine the maximal radius of a ball of SAS states around the maximally mixed state in the symmetric sector, and the minimal radius of a ball that contains the set of SAS states. As an application of our results, we also analyse the temperature dependence of the maximum entanglement that can be obtained from the thermal state of a spin-1 system with a spin-squeezing Hamiltonian. For the symmetric three-qubit case, our results are mostly numerical, and we conjecture a 3-parameter family of states that achieves the maximum negativity in the unitary orbit of any mixed state. In addition, we derive upper bounds, apparently tight, on the radii of balls containing only/all SAS states.

Mixed-state entanglement for AdS Born-Infeld theory

We study the mixed-state entanglement for AdS Born-Infeld (BI) theory. We calculate the mixed-state entanglement and investigate the relationship between it and the system parameters. We find that the holographic entanglement entropy (HEE) and mutual information (MI) exhibit monotonically increasing and decreasing behavior with BI factor b. However, the entanglement wedge cross-section (EWCS) exhibits a very rich set of phenomena about system parameters. EWCS always increases with b when b is small and then monotonically decreases with b. These behaviors suggest that increasing the BI factor, which is essentially enhancing the coupling between the background geometry and the transport properties can always enhance the EWCS. The coupling between the entanglement and the transport behaviors has also been studied in condensed matter theories and is important to construct a stable quantum circuit. We also provide analytical understanding of the above phenomenon. Furthermore, we have tested two additional BI-like models and find the universality of these results, suggesting the crucial role of the BI term in governing the interplay between nonlinear electromagnetic effects and entanglement.