Entanglement Complexity Research Articles

Postgenocide and decolonizing approaches to peace education in the Anthropocene

ABSTRACT This article addresses the intersection of genocide studies, climate change, and peace education. It does so by examining the state of these connections, and proposes a fresh concept for considering the entanglements of contemporary violence in the Anthropocene. A notion of postgenocide sees the elements of geopolitical order, warlordism, climate change and resource exploitation. Postgenocide is an approach to mass violence occurring beyond the usual framing of state violence and intent. It aims to enrich the ongoing decolonization of peace education, as well as empower peace educators in conveying these often-complex relations in a violence-prone and climate changing world. Thinking outside of legal constraints of genocide or emotive fuzziness of climate change, educators can broaden their appeals and promote decolonized thinking of how violence works, its agents, and who it impacts in the Anthropocene. Postgenocide offers a transformative research and praxis link frame beyond globalizing Holocaust education as a stand-in for human rights education. Peace educators can leverage global concepts like postgenocide to cut through and examine the complexity of such entanglements.

Information theoretic measures for Lifshitz system

In this work, we have studied various mixed state information theoretic quantities for an excited state of Lifshitz spacetime in 3 + 1-dimensions. This geometry is the gravity dual to a class of 2 + 1-dimensional quantum field theories having Lifshitz symmetry. We have holographically calculated mutual information, entanglement wedge cross section, entanglement negativity and mutual complexity for strip like subsystems at the boundary. For this we have used the results of holographic entanglement entropy and complexity present in the literature. We first calculate all of these mentioned quantities for the pure state of Lifshitz spacetime. Then we have moved on to calculate all these quantities for excited state of the Lifshitz spacetime. The gravity dual of excited state of Lifshitz systems in field theory can be obtained by applying constant perturbations along the boundary direction. Further, we would like to mention that for the simplicity of calculation we are only considering results up to the first order in perturbation. The change in the obtained holographic information theoretic quantities are then related to entanglement entropy, entanglement pressure, entanglement chemical potential and charge using the stress tensor complex. These relations are analogous to the first law of entanglement thermodynamics given earlier in the literature. All the calculations are carried out for both values of dynamical scaling exponent (z) present in the Lifshitz field theory.

Mishima: Writer of body, life and death

On the basis of a longitudinal study, the aim of this paper is to examine the life and work of Yukio Mishima (1925–1970) in an attempt to understand the creative genius of this renowned Japanese author who took his own life by committing seppuku. Does the key to understanding Mishima lie in his work, in his life, or in his suicide? Was he a manic-depressive? An exhibitionist obsessed with beauty, death and glory? A terrorist? A megalomaniac? Attempts have been made to pigeonhole him into different categories, but he remains an enigma. How can clinical psychologists understand the entangled complexity of all this? What can be deduced from the kaleidoscope of possible diagnoses?

Phosphorescent metallaknots of Au(I)-bis(acetylide) strands directed by Cu(I) π-coordination

Knots containing metal atoms as part of their continuous strand backbone are termed as metallaknots. While several metallaknots have been synthesized through one-pot self-assembly, the designed synthesis of metallaknots by controlling the arrangement of entanglements and strands connectivity remains unexplored. Here, we report the synthesis of metallaknots composed with Au(I)-bis(acetylide) linkages and templated by Cu(I) ions. Varying the ratio of the building blocks results in the switchable formation of two trefoil knots with different stoichiometries and symmetries (C2 or D3) and an entangled metalla-complex. While the entangled complex formed serendipitously, the strand ends can be subsequently linked through coordinative closure to generate a 41 metallaknot in a highly designable fashion. The comparable structural characteristics of resulting metalla-complexes allow us to probe the correlations between their topologies and photophysical properties, showing the backbone rigidity of knots endows complexes with excellent phosphorescent properties. This strategy, in conjunction with the coordinative closure approach, provides a straightforward route for the formation of highly phosphorescent metallaknots that were previously challenging to access.

Schrödinger as a Quantum Programmer: Estimating Entanglement via Steering

Quantifying entanglement is an important task by which the resourcefulness of a quantum state can be measured. Here, we develop a quantum algorithm that tests for and quantifies the separability of a general bipartite state by using the quantum steering effect, the latter initially discovered by Schrödinger. Our separability test consists of a distributed quantum computation involving two parties: a computationally limited client, who prepares a purification of the state of interest, and a computationally unbounded server, who tries to steer the reduced systems to a probabilistic ensemble of pure product states. To design a practical algorithm, we replace the role of the server with a combination of parameterized unitary circuits and classical optimization techniques to perform the necessary computation. The result is a variational quantum steering algorithm (VQSA), a modified separability test that is implementable on quantum computers that are available today. We then simulate our VQSA on noisy quantum simulators and find favorable convergence properties on the examples tested. We also develop semidefinite programs, executable on classical computers, that benchmark the results obtained from our VQSA. Thus, our findings provide a meaningful connection between steering, entanglement, quantum algorithms, and quantum computational complexity theory. They also demonstrate the value of a parameterized mid-circuit measurement in a VQSA.

A Two‐Step Entanglement Concentration for the Less‐Entangled Four‐Photon Cluster States

AbstractEntanglement concentration serves as an essential tool to obtain the maximally entangled states from the less‐entangled states in quantum information processing tasks. An efficient two‐step entanglement concentration protocol (ECP) is proposed to concentrate the less‐entangled four‐photon cluster states with four unknown coefficients into the maximally entangled states in this paper. The protocol utilizes parity‐check gate and photon‐polarized controlled‐Z gate, constructed with a single semiconductor quantum dot in a single optical microcavity (quantum dot‐cavity coupled system) and several linear optical elements. The discarded quantum states can be recycled in the next round concentration to achieve a higher success probability. Under conditions of strong coupling and weak side leakage rate, the ECP can tend toward ideal fidelity and efficiency. Compared to the previously proposed ECPs that utilize various auxiliary tools such as additional entangled states and complex quantum logic gates, the ECP significantly simplifies the analysis process and enables efficient implementation. Thus, the ECP is more economical and feasible in future optical systems.

Enacting Musical Aesthetics: The Embodied Experience of Live Music

The vitality and affective potential of the live concert experience is a result of rich, cross-sensory interactions and varied participatory practices. The complexity of such entanglements has recently led philosophers to argue for an enactive, affordance-based approach that interrogates a variety of perceptual and sensory possibilities inherent in aesthetic experiences. Further, Shaun Gallagher's recent addition of the 4As (Affect, Agency, Affordance, Autonomy) to the 4Es (Embodied, Embedded, Enacted, Extended) for clarifying mind–world relations seem to have potent explanatory power for these kinds of encounters. Building on such current philosophical approaches while examining specific (and actual) live musical engagement, this article offers an interpretation of selected audience data from the MusicLab Copenhagen with the Danish String Quartet research concert to discuss particular responses from the audience physically present at the venue. Responding to neuroaesthetic approaches, we clarify the audience members’ individual and collective aesthetic experience through an enactive, affordance-based approach. We suggest that what is at play in the live concert environment is a mode of attentive dynamic listening. Rather than seeking to characterize the audience as passively responding to music, a 4Es/4As approach to aesthetic experience seeks to clarify embodied-enactive audience engagement for which anticipation is a dynamic factor that enables further musical action and resonance, also for the musicians on stage.

The effects of stem bromelain on the gelation behavior of kappa carrageenan under linear and nonlinear rheological regimes

Carrageenans have shown a versatile and wide range of applications in the food and biomedical fields. To tune the rheological properties and improve the biological functions of carrageenan gels, the effect of stem bromelain (SBr) on the intermolecular interaction and rheological property of κ-carrageenan (κC) was investigated. The viscoelastic properties and gel network structure of pure SBr, κC, and SBr/κC mixtures were studied using dynamic rheology in the linear and nonlinear viscoelastic regimes. Different SBr/κC mixtures were prepared with varying final pH levels (pH 6.06, 6.95, and 8.08). The time series and frequency dependence of SBr/κC mixtures in the linear viscoelastic regime showed that the elastic modulus is (3–10 times) greater than the viscous modulus, indicating network structure formation. The temperature dependence of the viscoelastic moduli SBr/κC mixtures exhibited a significantly improved physical property than the pure SBr and κC, demonstrating synergistic relation between SBr and κC via enhanced electrostatic interaction. By increasing the pH level of the mixtures, a decrease in the shear moduli was observed attributed to the increasing repulsive interaction between SBr and κC. The observed nonlinear rheological responses suggest a transiently crosslinked network. Accordingly, with the gentle imposition of increasing stress levels, the nonlinear responses suggest that SBr/κC is a stress-mediated, highly entangled complex network with a pH-controlled dynamic viscoelastic property. Therefore, our results provide structural insights into the microscopic origins of the rheological behavior of SBr/κC mixtures as a basis for precise material design.

Rethinking plastic realities in Ghana: A call for a well-being approach to understanding human-plastics entanglements for more equitable plastics governance

Plastics and plastic waste have emerged as one of the major challenges of the Anthropence, a so-called “wicked problem” complicated by a myriad of political, economic, cultural, and historical factors. The ubiquity of plastic waste has garnered increased attention from governments, non-profit organizations and the media, in turn expanding mitigative efforts. Yet much of this action has been ineffective, or in some cases, even harmful. Governance and management actions often neglect to understand the lived realities of those most burdened by plastic waste and thus solutions are not designed to address the complexity of human plastics entanglements. The human dimensions of plastic pollution are often narrowly focused on livelihood and physical human health, however, assessing human-plastics entanglements for equitable evaluation and decision-making requires a multidisciplinary One Health well-being approach that considers factors such as connections to natural systems, culture, social relationships, freedom, health, security, and livelihood. In this article, we highlight the value of adopting such an approach in understanding the local complexities of human-plastics entanglements. Drawing on the results from semi-structured surveys and focus group interviews implemented in two coastal communities in Ghana, we demonstrate the multitude of ways that local people are impacted by plastic waste. The survey used in this case study employed a framework to assess well-being and plastic waste via a grounded approach where well-being is defined by respondents based on their lived experience. Across these communities, respondents illustrated how plastic waste has influenced individual well-being including their livelihoods, environmental quality, cultural practices, physical and mental health. Overall, we argue that more holistic approaches of assessment are necessary for understanding the complex burdens of plastic waste and for informing more equitable governance solutions.

Random unitaries, Robustness, and Complexity of Entanglement

It is widely accepted that the dynamic of entanglement in presence of a generic circuit can be predicted by the knowledge of the statistical properties of the entanglement spectrum. We tested this assumption by applying a Metropolis-like entanglement cooling algorithm generated by different sets of local gates, on states sharing the same statistic. We employ the ground states of a unique model, namely the one-dimensional Ising chain with a transverse field, but belonging to different macroscopic phases such as the paramagnetic, the magnetically ordered, and the topological frustrated ones. Quite surprisingly, we observe that the entanglement dynamics are strongly dependent not just on the different sets of gates but also on the phase, indicating that different phases can possess different types of entanglement (which we characterize as purely local, GHZ-like, and W-state-like) with different degree of resilience against the cooling process. Our work highlights the fact that the knowledge of the entanglement spectrum alone is not sufficient to determine its dynamics, thereby demonstrating its incompleteness as a characterization tool. Moreover, it shows a subtle interplay between locality and non-local constraints.

Page curves and typical entanglement in linear optics

Bosonic Gaussian states are a special class of quantum states in an infinite dimensional Hilbert space that are relevant to universal continuous-variable quantum computation as well as to near-term quantum sampling tasks such as Gaussian Boson Sampling. In this work, we study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We first derive formulas that are asymptotically exact in the number of modes for the Rényi-2 Page curve (the average Rényi-2 entropy of a subsystem of a pure bosonic Gaussian state) and the corresponding Page correction (the average information of the subsystem) in certain squeezing regimes. We then prove various results on the typicality of entanglement as measured by the Rényi-2 entropy by studying its variance. Using the aforementioned results for the Rényi-2 entropy, we upper and lower bound the von Neumann entropy Page curve and prove certain regimes of entanglement typicality as measured by the von Neumann entropy. Our main proofs make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries. In this light, we propose future research directions where this symmetry might also be exploited. We conclude by discussing potential applications of our results and their generalizations to Gaussian Boson Sampling and to illuminating the relationship between entanglement and computational complexity.

Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions

Entanglement comes in different forms, some more complex than others. In this paper we study the transitions of entanglement complexity in an exemplary family of states---the Rokhsar-Kivelson-sign wavefunctions---whose degree of entanglement is controlled by a single parameter. This family of states is known to feature a transition between a phase exhibiting volume-law scaling of entanglement entropy and a phase with subextensive scaling of entanglement, reminiscent of the many-body-localization transition of disordered quantum Hamiltonians. We study the singularities of the Rokhsar-Kivelson-sign wavefunctions and their entanglement complexity across the transition using several tools from quantum information theory: fidelity metric, entanglement spectrum statistics, entanglement entropy fluctuations, stabilizer R\'enyi entropy, and the performance of a disentangling algorithm. Across the whole volume-law phase the states feature universal entanglement spectrum statistics. Yet a ``superuniversal'' regime appears for small values of the control parameter in which all metrics become independent of the parameter itself, the entanglement entropy as well as the stabilizer R\'enyi entropy appear to approach their theoretical maximum, the entanglement fluctuations scale to zero as in output states of random universal circuits, and the disentangling algorithm has essentially null efficiency. All these indicators consistently reveal a complex pattern of entanglement. In the sub-volume-law phase, on the other hand, the entanglement spectrum statistics is no longer universal, entanglement fluctuations are larger and exhibiting a nonuniversal scaling, and the efficiency of the disentangling algorithm becomes finite. Our results, based on model wavefunctions, suggest that a similar combination of entanglement scaling properties and of entanglement complexity features may be found in high-energy Hamiltonian eigenstates---a very strong candidate being offered by the many-body localization transition of disordered lattice-spin models.

Primordial Gravitational Wave Circuit Complexity

In this article, we investigate the various physical implications of quantum circuit complexity using the squeezed state formalism of Primordial Gravitational Waves (PGW). Recently, quantum information-theoretic concepts, such as entanglement entropy and complexity, have played a pivotal role in understanding the dynamics of quantum systems, even in diverse fields such as high-energy physics and cosmology. This paper is devoted to studying the quantum circuit complexity of PGW for various cosmological models, such as de Sitter, inflation, radiation, reheating, matter, bouncing, cyclic and black hole gas models, etc. We compute complexity measures using both Covariance and Nielsen’s wave function method for three different choices of quantum initial vacua: Motta-Allen, α and Bunch–Davies. Besides computing circuit complexity, we also compute the Von Neumann entanglement entropy. By making the comparison between complexity and entanglement entropy, we are able to probe various features regarding the dynamics of evolution for different cosmological models. Because entanglement entropy is independent of the squeezing angle, we are able to understand more details of the system using Nielsen’s measure of complexity, which is dependent on both squeezing parameter and angle. This implies that quantum complexity could indeed be a useful probe to study quantum features on a cosmological scale. Quantum complexity is also becoming a powerful technique to understand the chaotic behaviour and random fluctuations of quantum fields. Using the growth of complexity, we are able to compute the quantum Lyapunov exponent for various cosmological models and comment on its chaotic nature.

People-Tree Entanglements: Pine in Aotearoa New Zealand

ABSTRACT: Reflecting from the perspectives of a plant scientist, an Indigenous Māori scholar, a Māori tōhunga (spiritual leader), and an arts researcher, we engage with the concept of the "plantationocene" (Mitman 5). Our focus is to reclaim and communicate our different cultural narratives of people and trees, particularly focusing on Pinus radiata D. Don , introduced for commercial forestry in Aotearoa New Zealand. Like many large trees in the era of the plantationocene, pine plays a role in local and global carbon and water cycles, as well as in multiple and diverse cultural narratives. Drawing on Karen Barad's concept of entanglement, we seek to reveal our people-pine entanglements. In this paper, we utilize the methodologies of interviewing, observation, and the tools of narrative inquiry, as well as quantitative scientific techniques, to write back and forwards between personal experiences and the understandings of our wider social-cultural context in Aotearoa New Zealand. This writing back and forth mirrors the movement back and forth between our local experience at home in the Global South and the global theorizing of the plantationocene. We identify the complexity of people-tree entanglements, problematizing a simplistic application of the plantationocene in the context of Aotearoa New Zealand.

People-Tree Entanglements: Pine in Aotearoa New Zealand

ABSTRACT: Reflecting from the perspectives of a plant scientist, an Indigenous Māori scholar, a Māori tōhunga (spiritual leader), and an arts researcher, we engage with the concept of the "plantationocene" (Mitman 5). Our focus is to reclaim and communicate our different cultural narratives of people and trees, particularly focusing on Pinus radiata D. Don , introduced for commercial forestry in Aotearoa New Zealand. Like many large trees in the era of the plantationocene, pine plays a role in local and global carbon and water cycles, as well as in multiple and diverse cultural narratives. Drawing on Karen Barad's concept of entanglement, we seek to reveal our people-pine entanglements. In this paper, we utilize the methodologies of interviewing, observation, and the tools of narrative inquiry, as well as quantitative scientific techniques, to write back and forwards between personal experiences and the understandings of our wider social-cultural context in Aotearoa New Zealand. This writing back and forth mirrors the movement back and forth between our local experience at home in the Global South and the global theorizing of the plantationocene. We identify the complexity of people-tree entanglements, problematizing a simplistic application of the plantationocene in the context of Aotearoa New Zealand.

Entanglement-complexity geometric measure

We propose a class of geometric measures of entanglement for pure states by exploiting the matrix product state formalism. These measures are completely divested from the notion of separability and can be freely tuned as a function of the bond dimension to target states which vary in entanglement complexity. We first demonstrate its value in a toy spin-1 model where, unlike the conventional geometric entanglement, it successfully identifies the AKLT ground state. We then investigate the phase diagram of a Haldane chain with uniaxial and rhombic anisotropies, revealing that our measure can successfully detect all its phases; all of which are invisible to the conventional geometric entanglement. Finally we investigate the disordered spin-$1/2$ Heisenberg model, where we find that differences in our measure can be used as lucrative signatures of the ergodic-localized entanglement transition.

A computational package for measuring Topological Entanglement in Polymers, Proteins and Periodic systems (TEPPP)

Many materials, like polymer melts, solutions, biopolymers and textiles, are composed of entangled filaments. The entanglement in these systems significantly affects their mechanical properties and their function. We introduce the Topological Entanglement in Polymers, Proteins and Periodic systems (TEPPP) software, that enables to measure the topological and geometrical complexity in such systems. In particular, this software enables the computation of the Writhe, the Gauss linking integral and the Jones polynomial of each filament or pair of filaments in the system, whether they are open or closed. In particular, for systems employing Periodic Boundary Conditions (PBC), the software also allows to compute the total pairwise entanglement in PBC, using the Periodic linking number and the Periodic Writhe. For linear (open) chains, TEPPP can calculate all these topological parameters (including the Jones polynomial) without any closure scheme. In addition, TEPPP also enables measuring self and pairwise entanglement at different length-scales along a chain or a pair of chains. With appropriate preprocessing of input files, the code can also be used for star or branched architectures. We provide examples of how the code is used and we present results on the entanglement effect in polymers obtained using this package. We show how TEPPP can be used to measure the topological entanglement of linear polymer chains in a melt, revealing subtle entanglement transitions never seen before. We also used TEPPP to analyze the effect of knotting and its location in diblock copolymer melts, which reveals that knotting localization transition coincides with lamellar-disorder transition in these systems. Finally, we use TEPPP to reveal some of the topological structure of the SARS-CoV-2 Spike protein, which points to interesting structure in a region that contains the S1/S2 cleavage site. Program summaryProgram Title: Topological Entanglement in Polymers, Proteins and Periodic systems (TEPPP) softwareCPC Library link to program files:https://doi.org/10.17632/ygdbpnhpzw.1Developer's repository link:https://github.com/TEPPP-softwareLicensing provisions: BSD 3-clauseProgramming language: C++Supplementary material:Nature of problem: Measuring single and pairwise entanglement and knotting in systems of linear or ring filaments (open or closed curves) in 3-space or in systems employing Periodic Boundary Conditions (PBC) at different length scales.Solution method: TEPPP can be used to measure topological entanglement complexity in single or multi-chain filament systems in 3-space or in systems employing PBC. Given as input the coordinates of the curves, TEPPP can compute the Gauss linking integral, the Writhe, the Jones polynomial, the Periodic Linking Number and the Periodic Writhe. Also, TEPPP can measure effects of local linking and knotting using scanning methods along the chains.

The randomized measurement toolbox

Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large quantum systems is the source of their power, but also makes them difficult to control precisely or characterize accurately using measured classical data. We review recently developed protocols for probing the properties of complex many-qubit systems using measurement schemes that are practical using today's quantum platforms. In all these protocols, a quantum state is repeatedly prepared and measured in a randomly chosen basis; then a classical computer processes the measurement outcomes to estimate the desired property. The randomization of the measurement procedure has distinct advantages; for example, a single data set can be employed multiple times to pursue a variety of applications, and imperfections in the measurements are mapped to a simplified noise model that can more easily be mitigated. We discuss a range of use cases that have already been realized in quantum devices, including Hamiltonian simulation tasks, probes of quantum chaos, measurements of nonlocal order parameters, and comparison of quantum states produced in distantly separated laboratories. By providing a workable method for translating a complex quantum state into a succinct classical representation that preserves a rich variety of relevant physical properties, the randomized measurement toolbox strengthens our ability to grasp and control the quantum world.

The Jones polynomial of collections of open curves in 3-space

Measuring the entanglement complexity of collections of open curves in 3-space has been an intractable, yet pressing mathematical problem, relevant to a plethora of physical systems, such as in polymers and biopolymers. In this manuscript, we give a novel definition of the Jones polynomial that generalizes the classic Jones polynomial to collections of open curves in 3-space. More precisely, first we provide a novel definition of the Jones polynomial of linkoids (open link diagrams) and show that this is a well-defined single variable polynomial that is a topological invariant, which, for link-type linkoids, coincides with that of the corresponding link. Using the framework introduced in (Panagiotou E, Kauffman L. 2020Proc. R. Soc. A476, 20200124. ((doi:10.1098/rspa.2020.0124)), this enables us to define the Jones polynomial of collections of open and closed curves in 3-space. For collections of open curves in 3-space, the Jones polynomial has real coefficients and it is a continuous function of the curves’ coordinates. As the endpoints of the curves tend to coincide, the Jones polynomial tends to that of the resultant link. We demonstrate with numerical examples that the novel Jones polynomial enables us to characterize the topological/geometrical complexity of collections of open curves in 3-space for the first time.

Transitions in Entanglement Complexity in Random Circuits

Entanglement is the defining characteristic of quantum mechanics. Bipartite entanglement is characterized by the von Neumann entropy. Entanglement is not just described by a number, however; it is also characterized by its level of complexity. The complexity of entanglement is at the root of the onset of quantum chaos, universal distribution of entanglement spectrum statistics, hardness of a disentangling algorithm and of the quantum machine learning of an unknown random circuit, and universal temporal entanglement fluctuations. In this paper, we numerically show how a crossover from a simple pattern of entanglement to a universal, complex pattern can be driven by doping a random Clifford circuit with T gates. This work shows that quantum complexity and complex entanglement stem from the conjunction of entanglement and non-stabilizer resources, also known as magic.