Entanglement Concentration Research Articles

Exploring Nonlocal Correlations in Arbitrarily High-Dimensional Systems

Abstract The utilization of higher-dimensional systems holds promise for unveiling novel phenomena and enhancing the efficacy of practical tasks, such as entanglement-based quantum cryptography. However, detecting quantum correlations within qudit systems poses a formidable challenge. In this study, we delve into the intricacies of Bell’s nonlocality within higher-dimensional systems. We introduce a novel correlation function and leverage it to construct a family of Bell inequalities adapted for quantum systems of arbitrary dimensionality. By gauging the probability of local realism violation under random measurements as our primary metric, we explore the relation between pure state entanglement and nonlocality. Our findings align closely with predictions derived from the comprehensive polytope analysis via linear programming methods. While our focus predominantly centers on the two-qudit scenario, our methodology readily extends to the N -partite case, accommodating an arbitrary number of measurements per party.

Robustness of quantum correlation in quantum energy teleportation

In this article, we explore a feedback-control protocol in different quantum field theories (QFTs) to study the quantum correlation in nonunitary evolution of quantum systems. Traditional studies on QFTs focus on quantum entanglement of pure states under the unitary evolution, however, we examine quantum correlation in mixed states using quantum energy teleportation (QET), which is an energy transfer protocol by utilizing ground state entanglement, and introduce quantum discord as a measure. QET involves a midcircuit measurement, which disrupts pure state entanglement. Despite this, our analysis demonstrates that quantum discord maintains the correlation throughout the QET process. We conducted numerical analyses with benchmark models including the Nambu-Jona-Lasinio (NJL) model, revealing that quantum discord consistently acts as an order parameter for phase transitions. The model is extended in a way that it has both the chiral chemical potential and the chemical potential, which are useful to study the phase structures mimicking the chiral imbalance between left- and right- quarks coupled to the chirality density operator. In all cases we studied, the quantum discord behaved as an order parameter of the phase transition. Published by the American Physical Society 2024

Decoupling by Local Random Unitaries without Simultaneous Smoothing, and Applications to Multi-user Quantum Information Tasks

We show that a simple telescoping sum trick, together with the triangle inequality and a tensorisation property of expected-contractive coefficients of random channels, allow us to achieve general simultaneous decoupling for multiple users via local actions. Employing both old (Dupuis et al. in Commun Math Phys 328:251–284, 2014) and new methods (Dupuis in IEEE Trans Inf Theory 69:7784–7792, 2023), we obtain bounds on the expected deviation from ideal decoupling either in the one-shot setting in terms of smooth min-entropies, or the finite block length setting in terms of Rényi entropies. These bounds are essentially optimal without the need to address the simultaneous smoothing conjecture, which remains unresolved. This leads to one-shot, finite block length, and asymptotic achievability results for several tasks in quantum Shannon theory, including local randomness extraction of multiple parties, multi-party assisted entanglement concentration, multi-party quantum state merging, and quantum coding for the quantum multiple access channel. Because of the one-shot nature of our protocols, we obtain achievability results without the need for time-sharing, which at the same time leads to easy proofs of the asymptotic coding theorems. We show that our one-shot decoupling bounds furthermore yield achievable rates (so far only conjectured) for all four tasks in compound settings, which are additionally optimal for entanglement of assistance and state merging.

An architecture for two-qubit encoding in neutral ytterbium-171 atoms

We present an architecture for encoding two qubits within the optical “clock” transition and nuclear spin-1/2 degree of freedom of neutral ytterbium-171 atoms. Inspired by recent high-fidelity control of all pairs of states within this four-dimensional quotes space, we present a toolbox for intra-ququart (single-atom) one- and two-qubit gates, inter-ququart (two-atom) Rydberg-based two- and four-qubit gates, and quantum nondemolition (QND) readout. We then use this toolbox to demonstrate the advantages of the ququart encoding for entanglement distillation and quantum error correction which exhibit superior hardware efficiency and better performance in some cases since fewer two-atom operations are required. Finally, leveraging single-state QND readout in our ququart encoding, we present a unique approach to studying interactive circuits and to realizing a symmetry protected topological phase of a spin-1 chain with a shallow, constant-depth circuit.

Universal Time-Entanglement Trade-Off in Open Quantum Systems

We demonstrate a surprising connection between pure steady-state entanglement and relaxation time scales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems, A and B, interact locally with a common dissipative environment. This setup also encompasses a broad class of adaptive quantum dynamics based on continuous measurement and feedback. As steady-state entanglement increases, there is generically an emergent strong symmetry that leads to a dynamical slow-down. Using this, we can prove rigorous bounds on relaxation times set by steady-state entanglement. We also find that this time must necessarily diverge for maximal entanglement. To test our bound, we consider the dynamics of a random ensemble of local Lindbladians that support pure steady states, finding that the bound does an excellent job of predicting how the dissipative gap varies with the amount of entanglement. Our work provides general insights into how dynamics and entanglement are connected in open systems and has specific relevance to quantum reservoir engineering. Published by the American Physical Society 2024

Error-rejecting entanglement purification and concentration for one-dimensional waveguide-emitter system

Error-rejecting entanglement purification and concentration for one-dimensional waveguide-emitter system

Effect of concentration and electrical charge of maltodextrin, and packing factor on electrospinning processing

The power law ηrel ∼ Ca of maltodextrins with higher entanglement concentrations (Ce) of dextrose equivalent (DE) 4, 10, and 18 exhibits an unusually high exponent a, ranging from 10.34 to 14.38 in congested solutions where particles occupy significant space. This contrasts with the dilute exponents (a ∼2) typically observed in polymer–solvent systems. To address this issue, several viscosity factors were evaluated using the Einstein–Roscoe and Mooney equations, which demonstrated viscosity dependence due to volume fraction (ϕ) > 0.35, shape, crowding factor (k) packing factor (1/k∼0.5) and centered cubic cell (CC), particularly for larger chain sizes (>20 glucoses) in DE-4. Chain electrical charges significantly stiffen the chain and increase its length beyond the theoretically predicted Kuhn persistent length (Lp), which seems to be responsible for the exponential increase in viscosity. Normalizing the viscosity/charge data revealed a log–log plot consistent with the exponent a of the general power law theory. In addition to concentration, electrospinning processing is influenced by strong particle–particle charge interactions, (ϕ), packing factor (1/k), CC, and chain sizes. The Maxwell model demonstrated poor interaction for DE-4 (modulus ∼286 Pa at maximum ϕ due to loose packing of CC, in contrast to DE-18, which exhibited a modulus of 994 Pa for a solution with maximum ϕ> 0.5 and a congested solution of 52% w/v, packing factor of 0.68, and high particle–particle interaction of the body-centered cubic (BCC) cell, favoring electrospun fiber formation. The packing factor, ϕ, and cell type, are highly sensitive and have potential applications in food systems, 3D bioprinting, among many other scientific domains.

ARQUIN: Architectures for Multinode Superconducting Quantum Computers

Many proposals to scale quantum technology rely on modular or distributed designs wherein individual quantum processors, called nodes, are linked together to form one large multinode quantum computer (MNQC). One scalable method to construct an MNQC is using superconducting quantum systems with optical interconnects. However, internode gates in these systems may be two to three orders of magnitude noisier and slower than local operations. Surmounting the limitations of internode gates will require improvements in entanglement generation, use of entanglement distillation, and optimized software and compilers. Still, it remains unclear what performance is possible with current hardware and what performance algorithms require. In this article, we employ a systems analysis approach to quantify overall MNQC performance in terms of hardware models of internode links, entanglement distillation, and local architecture. We show how to navigate tradeoffs in entanglement generation and distillation in the context of algorithm performance, lay out how compilers and software should balance between local and internode gates, and discuss when noisy quantum internode links have an advantage over purely classical links. We find that a factor of 10–100× better link performance is required and introduce a research roadmap for the co-design of hardware and software towards the realization of early MNQCs. While we focus on superconducting devices with optical interconnects, our approach is general across MNQC implementations.

Efficient entanglement purification based on noise guessing decoding

In this paper, we propose a novel bipartite entanglement purification protocol built upon hashing and upon the guessing random additive noise decoding (GRAND) approach recently devised for classical error correction codes. Our protocol offers substantial advantages over existing hashing protocols, requiring fewer qubits for purification, achieving higher fidelities, and delivering better yields with reduced computational costs. We provide numerical and semi-analytical results to corroborate our findings and provide a detailed comparison with the hashing protocol of Bennet et al. Although that pioneering work devised performance bounds, it did not offer an explicit construction for implementation. The present work fills that gap, offering both an explicit and more efficient purification method. We demonstrate that our protocol is capable of purifying states with noise on the order of 10% per Bell pair even with a small ensemble of 16 pairs. The work explores a measurement-based implementation of the protocol to address practical setups with noise. This work opens the path to practical and efficient entanglement purification using hashing-based methods with feasible computational costs. Compared to the original hashing protocol, the proposed method can achieve some desired fidelity with a number of initial resources up to one hundred times smaller. Therefore, the proposed method seems well-fit for future quantum networks with a limited number of resources and entails a relatively low computational overhead.

Entanglement buffering with two quantum memories

Quantum networks crucially rely on the availability of high-quality entangled pairs of qubits, known as entangled links, distributed across distant nodes. Maintaining the quality of these links is a challenging task due to the presence of time-dependent noise, also known as decoherence. Entanglement purification protocols offer a solution by converting multiple low-quality entangled states into a smaller number of higher-quality ones. In this work, we introduce a framework to analyse the performance of entanglement buffering setups that combine entanglement consumption, decoherence, and entanglement purification. We propose two key metrics: the availability, which is the steady-state probability that an entangled link is present, and the average consumed fidelity, which quantifies the steady-state quality of consumed links. We then investigate a two-node system, where each node possesses two quantum memories: one for long-term entanglement storage, and another for entanglement generation. We model this setup as a continuous-time stochastic process and derive analytical expressions for the performance metrics. Our findings unveil a trade-off between the availability and the average consumed fidelity. We also bound these performance metrics for a buffering system that employs the well-known bilocal Clifford purification protocols. Importantly, our analysis demonstrates that, in the presence of noise, consistently purifying the buffered entanglement increases the average consumed fidelity, even when some buffered entanglement is discarded due to purification failures.

Heralded high-efficiency entanglement concentration of cluster states for photon systems with linear optics via time-delay effect

Entanglement concentration stands as a pivotal technique to safeguard against degraded fidelity in long-distance quantum communication. In this manuscript, propose ultra-efficient entanglement concentration protocols (ECPs) tailored for less-entangled two-photon cluster states and four-photon cluster states with two unknown parameters, leveraging simple linear optical elements and acute single-photon detectors. Additionally, ancillary photons, post-selection techniques, or photon-number-resolving detectors are unnecessary for complete identification of the parity-check measurement. By coordinating auxiliary time degrees of freedom and implementing multiple recycling conditions, the success of two ECPs can be heralded by detection signatures without compromising the incident qubits, thereby allowing their efficiencies to be close to 0.75, in principle. The combination of heralded detection and basic linear optical elements renders our practical ECPs accessible for experimental exploration with current technology.

Theoretical concept of error-rejecting entanglement purification of quantum-dots electronic spins in single-sided optical microcavity

We use the quantum-dots (QD) coupled with single-sided microcavities system to construct the error-rejecting controlled not (CNOT) gate of electronic spins system in QD; We have designed an error-rejecting entanglement purification protocol (EPP) of electronic spins system in QD by using the error-rejecting CNOT gate and unitary operation. It can extract the high entanglement from the mixed entanglement states of the electronic spins with low entangled states. This EPP can eliminate the operation errors caused by the nonideal interaction between photons and QD coupled with optical microcavities system, and improve the fidelity of the EPP through iteration. Our scheme is more practical in future long-distance quantum communications, especially providing significant benefits for solving decoherence problems in quantum networks and quantum repeaters.

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.

Recovery of damaged information via scrambling in indefinite causal order

Scrambling prevents the access to local information with local operators and therefore can be used to protect quantum information from damage caused by local perturbations. Even though partial quantum information can be recovered if the type of the damage is known, the initial target state cannot be completely recovered, because the obtained state is a mixture of the initial state and a maximally mixed state. Here, we demonstrate an improved scheme to recover damaged quantum information via scrambling in indefinite causal order. We show that scheme with indefinite causal order can record information of the damage and distill the initial state from the damaged state simultaneously. It allows us to retrieve initial information versus any damage. Moreover, by iterating the schemes, the initial quantum state can be completely recovered. In addition, we experimentally demonstrate our schemes on the cloud-based quantum computer, named as Quafu. Our work proposes a feasible scheme to protect whole quantum information from damage, which is also compatible with other techniques such as quantum error corrections and entanglement purification protocols. We expect that our scheme will be useful in the both quantum information recovery from the damage and systems bench-marking.

Interplay among entanglement, measurement incompatibility, and nonlocality

Nonlocality, manifested by the violation of Bell inequalities, indicates entanglement within a joint quantum system. A natural question is how much entanglement is required for a given nonlocal behavior. Here, we explore this question by quantifying entanglement using a family of generalized Clauser–Horne–Shimony–Holt-type Bell inequalities. Given a Bell-inequality violation, we derive analytical lower bounds on the entanglement of formation, a measure related to entanglement dilution. The bounds also lead to an analytical estimation of the negativity of entanglement. In addition, we consider one-way distillable entanglement tied to entanglement distillation and derive tight numerical estimates. With the additional assumptions of qubit-qubit systems, we find that the relationship between entanglement and measurement incompatibility is not simply a trade-off under a fixed nonlocal behavior. Furthermore, we apply our results to two realistic scenarios—non-maximally entangled and Werner states. We show that one can utilize the nonlocal statistics by optimizing the Bell inequality for better entanglement estimation.

Reducing hardware requirements for entanglement distribution via joint hardware-protocol optimization

We conduct a numerical investigation of fiber-based entanglement distribution over distances of up to 1600 km using a chain of processing-node quantum repeaters. We determine minimal hardware requirements while simultaneously optimizing over protocols for entanglement generation and entanglement purification, as well as over strategies for entanglement swapping. Notably, we discover that through an adequate choice of protocols the hardware improvement cost scales linearly with the distance covered. Our results highlight the crucial role of good protocol choices in significantly reducing hardware requirements, such as employing purification to meet high-fidelity targets and adopting a swap as soon as possible policy for faster rates. To carry out this analysis, we employ an extensive simulation framework implemented with NetSquid, a discrete-event-based quantum-network simulator, and a genetic-algorithm-based optimization methodology to determine minimal hardware requirements.

Microstructures and Rheological Properties of Short-Side-Chain Perfluorosulfonic Acid in Water/2-Propanol.

The viscosity and viscoelasticity of polyelectrolyte solutions with a single electrostatic interaction have been carefully studied experimentally and theoretically. Despite some theoretical models describe experimental results well, the influence of multiple interactions (electrostatic and hydrophobic) on rheological scaling is not yet fully resolved. Herein, we systematically study the microstructures and rheological properties of short-side-chain perfluorosulfonic acid (S-PFSA), the most promising candidate of a proton exchange membrane composed of a hydrophobic backbone with hydrophilic side-chains, in water/2-propanol. Small-angle X-ray scattering confirms that semiflexible S-PFSA colloidal particles with a length of ~38 nm and a diameter of 1-1.3 nm are formed, and the concentration dependence of the correlation length (ξ) obeys the power law ξ~c-0.5 consistent with the prediction of Dobrynin et al. By combining macrorheology with diffusing wave spectroscopy microrheology, the semidilute unentangled, semidilute entangled, and concentrated regimes corresponding to the scaling relationships ηsp~c0.5, ηsp~c1.5, and ηsp~c4.1 are determined. The linear viscoelasticity indicates that the entanglement concentration (ce) obtained from the dependence of ηsp on the polymer concentration is underestimated owing to hydrophobic interaction. The true entanglement concentration (cte) is obtained by extrapolating the plateau modulus (Ge) to the terminal modulus (Gt). Furthermore, Ge and the plateau width, τr/τe (τr and τe denote reptation time and Rouse time), scale as Ge~c2.4 and τr/τe~c4.2, suggesting that S-PFSA dispersions behave like neutral polymer solutions in the concentrated regime. This work provides mechanistic insight into the rheological behavior of an S-PFSA dispersion, enabling quantitative control over the flow properties in the process of solution coating.

Normal quantum channels and Markovian correlated two-qubit quantum errors

We study general ‘normally’ (Gaussian) distributed random unitary transformations. These distributions can be defined in terms of a diffusive random walk in the respective group manifold. On the one hand, a Gaussian distribution induces a unital quantum channel, which we will call ‘normal’. On the other hand, the diffusive random walk defines a unital quantum process, generated by a Lindblad master equation. In the single qubit case, we show different distributions may induce the same quantum channel.In the case of two qubits, we study normal quantum channels, induced by Gaussian distributions in SU(2)⊗SU(2) . They provide an appropriate framework for modeling quantum errors with classical correlations. In contrast to correlated Pauli errors, for instance, they conserve their Markovianity, and they lead to very different results in error correcting codes. This is illustrated with an application to entanglement distillation.

Physical-Entanglements-Supported Polymeric Form Stable Phase Change Materials with Ultrahigh Melting Enthalpy.

With the rapid development of new energy and the upgrading of electronic devices, structurally stable phase change materials (PCMs) have attracted widespread attentions from both academia and industries. Traditional cross-linking, composites, or microencapsulation methods for preparation of form stable PCMs usually sacrifice part of the phase change enthalpy and recyclability. Based on the basic polymer viscoelasticity and crystallization theories, here, a kind of novel recyclable polymeric PCM is developed by simple solution mixing ultrahigh molecular weight of polyethylene oxide (UHMWPEO) with its chemical identical oligomer polyethylene glycol (PEG). Rheological and leakage-proof experiments confirm that, even containing 90% of phase change fraction PEG oligomers, long-term of structure stability of PCMs can be achieved when the molecular weight of UHMWPEO is higher than 7000kg mol-1 due to their ultralong terminal relaxation time and large number of entanglements per chain. Furthermore, because of the reduced overall entanglement concentration, phase change enthalpy of PCMs can be greatly promoted, even reaching to ≈185 J g-1, which is larger than any PEG-based form stable PCMs in literatures. This work provides a new strategy and mechanism for designing physical-entanglements-supported form stable PCMs with ultrahigh phase change enthalpies.

No-go theorem for entanglement distillation using catalysis

No-go theorem for entanglement distillation using catalysis