Entanglement Concentration Research Articles

Multicore Quantum Computing

Any architecture for practical quantum computing must be scalable. An attractive approach is to create multiple cores, computing regions of fixed size that are well-spaced but interlinked with communication channels. This exploded architecture can relax the demands associated with a single monolithic device: the complexity of control, cooling and power infrastructure as well as the difficulties of cross-talk suppression and near-perfect component yield. Here we explore interlinked multicore architectures through analytic and numerical modelling. While elements of our analysis are relevant to diverse platforms, our focus is on semiconductor electron spin systems in which numerous cores may exist on a single chip. We model shuttling and microwave-based interlinks and estimate the achievable fidelities, finding values that are encouraging but markedly inferior to intra-core operations. We therefore introduce optimsed entanglement purification to enable high-fidelity communication, finding that $99.5\%$ is a very realistic goal. We then assess the prospects for quantum advantage using such devices in the NISQ-era and beyond: we simulate recently proposed exponentially-powerful error mitigation schemes in the multicore environment and conclude that these techniques impressively suppress imperfections in both the inter- and intra-core operations.

Simple proof of security of the multiparty prepare and measure QKD

The majority of research to date has concentrated on the quantum key distribution (QKD) between two parties. In general, the QKD protocols proposed for the multiparty scenario often involve the usage of a maximally entangled state, such as GHZ, which is challenging to implement in practice. This paper examines the prepare and measure version of multiparty communication through quantum key distribution. It is sufficient to have the capability of preparing and measuring a single qubit state. The security of the multiparty prepare and measure QKD is demonstrated by utilizing the well-known techniques of quantum error correction and entanglement purification. We begin by establishing the security of the entangled-based version and progress through a series of reductions to arrive at our equivalent multiparty prepare and measure version of QKD. We establish the security proof of multiparty entangled-based version by combining FTQC and classical statistics on the GHZ basis. Then proved the conditional security of the multiparty prepare-and-measure QKD by the equivalency.

Entanglement distillation toward minimal bond cut surface in tensor networks

In tensor networks, a geometric operation of pushing a bond cut surface toward a minimal surface corresponds to entanglement distillation. Cutting bonds defines a reduced transition matrix on the bond cut surface and the associated quantum state naturally emerges from it. We justify this picture quantitatively by evaluating the trace distance between the maximally entangled states and the states on bond cut surfaces in the multi-scale entanglement renormalization ansatz (MERA) and matrix product states in a canonical form. Our numerical result for the random MERA is in a reasonable agreement with our proposal. The result sheds new light on a deeper understanding of the Ryu-Takayanagi formula for entanglement entropy in holography and the emergence of geometry from the entanglement structure.

Open-Air Microwave Entanglement Distribution for Quantum Teleportation

Microwave technology plays a central role in current wireless communications, standing among them mobile communication and local area networks (LANs). The microwave range shows relevant advantages with respect to other frequencies in open-air transmission, such as low absorption losses and low energy consumption, and it is additionally the natural working frequency in superconducting quantum technologies. Entanglement distribution between separate parties is at the core of secure quantum communications. Therefore, understanding its limitations in realistic open-air settings, specially in the rather unexplored microwave regime, is crucial for transforming microwave quantum communications into a mainstream technology. Here, we investigate the feasibility of an open-air entanglement distribution scheme with microwave two-mode squeezed states. First, we study the reach of direct entanglement transmission in open-air, obtaining a maximum distance of approximately 500 meters in a realistic setting with state-of-the-art experimental parameters. Afterwards, we adapt entanglement distillation and entanglement swapping protocols to microwave technology in order to reduce environmental entanglement degradation. While entanglement distillation helps to increase quantum correlations in the short-distance low-squeezing regime by up to $46\%$, entanglement swapping increases the reach by $14\%$. Then, we compute the fidelity of a continuous-variable quantum teleportation protocol using open-air-distributed entanglement as a resource. Finally, we adapt the machinery to explore the limitations of quantum communication between satellites, where the thermal noise impact is substantially reduced and diffraction losses are dominant.

Tight constraints on probabilistic convertibility of quantum states

We develop two general approaches to characterising the manipulation of quantum states by means of probabilistic protocols constrained by the limitations of some quantum resource theory. First, we give a general necessary condition for the existence of a physical transformation between quantum states, obtained using a recently introduced resource monotone based on the Hilbert projective metric. In all affine quantum resource theories (e.g. coherence, asymmetry, imaginarity) as well as in entanglement distillation, we show that the monotone provides a necessary and sufficient condition for one-shot resource convertibility under resource-non-generating operations, and hence no better restrictions on all probabilistic protocols are possible. We use the monotone to establish improved bounds on the performance of both one-shot and many-copy probabilistic resource distillation protocols. Complementing this approach, we introduce a general method for bounding achievable probabilities in resource transformations under resource-non-generating maps through a family of convex optimisation problems. We show it to tightly characterise single-shot probabilistic distillation in broad types of resource theories, allowing an exact analysis of the trade-offs between the probabilities and errors in distilling maximally resourceful states. We demonstrate the usefulness of both of our approaches in the study of quantum entanglement distillation.

Reactive Extrusion as a Pretreatment in Cassava (Manihot esculenta Crantz) and Pea (Pisum sativum L.) Starches to Improve Spinnability Properties for Obtaining Fibers.

Starch is a biocompatible and economical biopolymer in which interest has been shown in obtaining electrospun fibers. This research reports that cassava (CEX) and pea (PEX) starches pretreated by means of reactive extrusion (REX) improved the starches rheological properties and the availability of amylose to obtain fibers. Solutions of CEX and PEX (30–36% w/v) in 38% v/v formic acid were prepared and the rheological properties and electrospinability were studied. The rheological values indicated that to obtain continuous fibers without beads, the entanglement concentration (Ce) must be 1.20 and 1.25 times the concentration of CEX and PEX, respectively. In CEX, a higher amylose content and lower viscosity were obtained than in PEX, which resulted in a greater range of concentrations (32–36% w/v) to obtain continuous fibers without beads with average diameters ranging from 316 ± 65 nm to 394 ± 102 nm. In PEX, continuous fibers without beads were obtained only at 34% w/v with an average diameter of 170 ± 49 nm. This study showed that starches (20–35% amylose) pretreated through REX exhibited electrospinning properties to obtain fibers, opening the opportunity to expand their use in food, environmental, biosensor, and biomedical applications, as vehicles for the administration of bioactive compounds.

Developing Electrospun Ethylcellulose Nanofibrous Webs: An Alternative Approach for Structuring Castor Oil.

The development of environment-friendly natural polymer gel-like dispersions in oil media, with functional properties, in terms of formulation design and synthesis protocol, is still a cutting-edge research area for many applications. The aim of this work was to study the manufacture of electrospun ethylcellulose (EC) nanofibrous webs and to examine their usage to thicken vegetable oils as an alternative approach. The role of concentration, molecular weight (Mw), and binary solvent systems on the electrospinnability of EC and subsequently on the rheological properties of EC nanofiber dispersions in castor oil was investigated. It was observed that, for each Mw, defect-free nanofibers were produced above a critical concentration, corresponding to about 2.5 the entanglement concentration (Ce). The average fiber diameter increased with both Mw and EC concentrations. Dielectric constant and dipole moment of binary solvent systems influenced the morphology of the EC nanofiber web. The morphology of the micro- and nanoarchitectures generated played a key role in the physical stabilization and rheological behavior of electrospun EC dispersions. The storage modulus (G') of EC dispersions was correlated with both the spinning solution concentration and average fiber diameter. Furthermore, electrospun EC nanofiber dispersions were compared with EC oleogels obtained by traditional thermogelation from thermorheological and tribological points of view. Overall, this work proposes an efficient and innovative approach to produce bio-based oleogel-like dispersions with great potential in different sectors such as pharmaceuticals, food, or lubricants.

Optimal two-qubit gates in recurrence protocols of entanglement purification

We propose and investigate a method to optimize recurrence entanglement purification protocols. The approach is based on a numerical search in the whole set of SU(4) matrices with the aid of a quasi-Newton algorithm. Our method evaluates average concurrences where the probabilistic occurrence of mixed entangled states is also taken into account. We show for certain families of states that optimal protocols are not necessarily achieved by bilaterally applied controlled-NOT gates. As we discover several optimal solutions, the proposed method offers some flexibility in experimental implementations of entanglement purification protocols and interesting perspectives in quantum information processing.

Phase-matching quantum key distribution based on orbital angular momentum under atmospheric turbulence

We propose a phase-matching quantum key distribution (PM-QKD) protocol based on orbital angular momentum (OAM) to exceed the linear key-rate bound without quantum repeater in the paper, named OAM-PM-QKD protocol, where the coherent state consisting of OAM with opposite topological charges is used as the information carrier. With the equivalent entanglement distillation model, we analyze its security and then derive its key generation rate. The numerical simulation results show that the proposed OAM-PM-QKD protocol is able to exceed the linear key-rate bound when the transmission distance exceeds 230 km, and the maximum secure transmission distance is also longer than those of original PM-QKD protocol due to no misalignment in the basis. Furthermore, the influence of the atmospheric turbulence (AT) on the key generation rate is also discussed. The stronger the strength of AT is, the shorter the transmission distance is.

Almost complete solution for the NP-hard separability problem of Bell diagonal qutrits

With a probability of success of 95% we solve the separability problem for Bell diagonal qutrit states with positive partial transposition (PPT). The separability problem, i.e. distinguishing separable and entangled states, generally lacks an efficient solution due to the existence of bound entangled states. In contrast to free entangled states that can be used for entanglement distillation via local operations and classical communication, these states cannot be detected by the Peres–Horodecki criterion or PPT criterion. We analyze a large family of bipartite qutrit states that can be separable, free entangled or bound entangled. Leveraging a geometrical representation of these states in Euclidean space, novel methods are presented that allow the classification of separable and bound entangled Bell diagonal states in an efficient way. Moreover, the classification allows the precise determination of relative volumes of the classes of separable, free and bound entangled states. In detail, out of all Bell diagonal PPT states 81.0% pm 0.1% are determined to be separable while 13.9 pm 0.1% are bound entangled and only 5.1 pm 0.1% remain unclassified. Moreover, our applied criteria are compared for their effectiveness and relation as detectors of bound entanglement, which reveals that not a single criterion is capable to detect all bound entangled states.

Monitored open fermion dynamics: Exploring the interplay of measurement, decoherence, and free Hamiltonian evolution

The interplay of unitary evolution and local measurements in many-body systems gives rise to a stochastic state evolution and to measurement-induced phase transitions in the pure state entanglement. In realistic settings, however, this dynamics may be spoiled by decoherence, e.g., dephasing, due to coupling to an environment or measurement imperfections. We investigate the impact of dephasing and the inevitable evolution into a non-Gaussian, mixed state, on the dynamics of monitored fermions. We approach it from three complementary perspectives: (i) the exact solution of the conditional master equation for small systems, (ii) quantum trajectory simulations of Gaussian states for large systems, and (iii) a renormalization group analysis of a bosonic replica field theory. For weak dephasing, constant monitoring preserves a weakly mixed state, which displays a robust measurement-induced phase transition between a critical and a pinned phase, as in the decoherence-free case. At strong dephasing, we observe the emergence of a new scale describing an effective temperature, which is accompanied with an increased mixedness of the fermion density matrix. Remarkably, observables such as density-density correlation functions or the subsystem parity still display scale invariant behavior even in this strongly mixed phase. We interpret this as a signature of gapless, classical diffusion, which is stabilized by the balanced interplay of Hamiltonian dynamics, measurements, and decoherence.

Sensitivity of entanglement measures in bipartite pure quantum states

Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two entanglement measures for all quantum states, however, allows for meaningful conceptualization of sensitivity to entanglement, which will be greater for the entanglement measure that produces the larger numerical values. Here, we have investigated the partial order between the normalized versions of four entanglement measures based on Schmidt decomposition of bipartite pure quantum states, namely, concurrence, tangle, entanglement robustness and Schmidt number. We have shown that among those four measures, the concurrence and the Schmidt number have the highest and the lowest sensitivity to quantum entanglement, respectively. Further, we have demonstrated how these measures could be used to track the dynamics of quantum entanglement in a simple quantum toy model composed of two qutrits. Lastly, we have employed state-dependent entanglement statistics to compute measurable correlations between the outcomes of quantum observables in agreement with the uncertainty principle. The presented results could be helpful in quantum applications that require monitoring of the available quantum resources for sharp identification of temporal points of maximal entanglement or system separability.

Measurement-based logical qubit entanglement purification

Entanglement purification is the distilling of high-quality entanglement from low-quality entanglement and is a key element in the quantum repeater. As a new branch of entanglement purification, the measurement-based entanglement purification protocol (MBEPP) only requires one to perform the Bell state measurement to couple resource states with noisy pairs, and it tolerates more local noise than the conventional purification protocols. Existing MBEPPs usually focus on physical qubit entanglement. In this paper, we propose a measurement-based logical qubit entanglement purification protocol (MBLEPP) with quantum nondemolition detection (QND), where the qubit is encoded in the quantum parity code. The results show that this MBLEPP can also work with photon loss under the conditions that each block of the logical Bell state measurement contains at least one physical qubit, that at least one of the blocks is intact, and that the entanglement exists between all blocks. Moreover, we also consider the MBLEPP with imperfect QND. We show that below a certain QND error threshold, this MBLEPP can still work. In this way, this MBLEPP not only obtains high-fidelity entanglement but also tolerates photon loss and the error from imperfect QND. This MBLEPP combines the benefits of the MBEPP and quantum error correction code and may have potential application in long-distance quantum communication.

Note on surface growth approach for bulk reconstruction * *J.R.S. was supported by the National Natural Science Foundation of China (11675272). This work was also supported by the National Natural Science Foundation of China (12105113) and China Postdoctoral Science Foundation (2019M653137)

In this paper, we show using several examples that the bulk geometry of asymptotically AdS spacetimes can be effectively reconstructed using an intuitive and visual method called the surface growth scheme. This new approach for bulk reconstruction was originally proposed in a recent paper, along with its explicit realization using the one-shot entanglement distillation tensor network and the surface/state correspondence. In this paper, we directly analyze the growth of the bulk minimal surfaces to implement this scheme. Our study provides further support for the surface growth approach in entanglement wedge reconstruction.

Impact of zinc salt counterion on poly(ethylene oxide) solution viscosity, conductivity, and ability to generate electrospun MOF/nanofiber composites

The effect of seeding poly(ethylene oxide), PEO, aqueous solutions with zinc acetate (ZA) and zinc chloride (ZC) on solution properties (e.g., viscosity and electrical conductivity) and the ability to electrospin nanofibers was investigated. The impacts of the type of Zn counterion and overall salt concentration on solution viscosity and electrical conductivity were correlated to the ability to electrospin nanofibers, as well as the resulting fiber morphology. In dilute PEO solutions, Zn salt addition reduced the PEO hydrodynamic radius ( R h ) and viscosity likely as a result of PEO chain envelopment of Zn cations, while in semi-dilute entangled regimes, Zn salt addition increased R h and viscosity likely due to interactions a single Zn cation with multiple polymer chains. The addition of Zn salts had limited effects on the overlap concentration ( c* ), but increased the entanglement concentration ( c e ), and the presence of either ZA or ZC enabled electrospinning of bead-free fibers at lower PEO concentrations (than without salt) because of the increased electrical conductivity of the solution. However, increasing the ZA concentration in solution had limited effect on fiber diameter and morphology, while raising the ZC concentration in solution resulted in the fusion of fibers into webs and films likely due to charge carryover. The resulting salt-doped PEO nanofibers were used as a template to synthesize a zeolitic imidazolate framework, ZIF-8, through a vapor-deposition approach exploiting the embedded Zn as nucleation sites for heterogeneous growth in a ‘Fiber-first’ strategy. • Aqueous poly(ethylene oxide) solutions were seeded with zinc salts. • Zinc salts, notably Zn acetate, reduced polymer concentration required to spin bead-free fibers. • Zinc chloride, especially at higher loadings, led to electrospun fused webs instead of fibers. • Zinc counterion type impacted solution conductivity and affected bead-free fiber development. • Zinc salt seeding enabled the vapor-phase growth of the zeolitic imidazolate framework ZIF-8.

Enumerating all bilocal Clifford distillation protocols through symmetry reduction

Entanglement distillation is an essential building block in quantum communication protocols. Here, we study the class of near-term implementable distillation protocols that use bilocal Clifford operations followed by a single round of communication. We introduce tools to enumerate and optimise over all protocols for up to n=5 (not necessarily equal) Bell-diagonal states using a commodity desktop computer. Furthermore, by exploiting the symmetries of the input states, we find all protocols for up to n=8 copies of a Werner state. For the latter case, we present circuits that achieve the highest fidelity with perfect operations and no decoherence. These circuits have modest depth and number of two-qubit gates. Our results are based on a correspondence between distillation protocols and double cosets of the symplectic group, and improve on previously known protocols.

Facile, Energy-Efficient Microscale Fibrillation of Polyacrylamides under Ambient Conditions.

Insight into fiber formation can provide new rationale for the design and preparation of fibers with programmed mechanical properties. While synthetic bioinspired fibers have shown impressive tensile properties, the fiber formation process remains poorly understood. Moreover, these systems are highly complex and their formation is environmentally and economically costly. Controlled fiber formation under ambient conditions from polyacrylamide solutions with properties comparable to natural fibers such as wool and coir is demonstrated. Photopolymerization and subsequent microscale fibrillation of different acrylamides in water/ethanol mixtures yield a simple and energy-efficient route to fiber formation. This strategy reduces required processing energy by two-to-three orders of magnitude. Through extensive experimental elucidation, insight into precise fiber forming conditions of polymeric solutions is achieved. Ethanol is utilized as a chain transfer agent to control the molecular weight of the polyacrylamides, and the entanglement regimes of the solutions are determined through rheological characterization showing fiber formation above the entanglement concentration. Unique from previously reported hydrogel microfibers, it is shown that fibers with good mechanical properties can be obtained without the need for composites or crosslinkers. The reported approach offers a platform for fiber formation under ambient conditions with molecular-level understanding of theirassembly.

Genuine entanglement, distillability and quantum information masking under noise

Genuineness and distillability of entanglement play a key role in quantum information tasks, and they are easily disturbed by the noise. We construct a family of multipartite states without genuine entanglement and distillability sudden death across every bipartition, respectively. They are realized by establishing the noise as the multipartite high-dimensional Pauli channels. Further, we construct a locally unitary channel as another noise such that the multipartite Greenberger–Horne–Zeilinger state becomes the Dür’s multipartite state. We also show that the quantum information masking still works under the noise we constructed and thus show a novel quantum secret sharing scheme under noise. The evolution of a family of three-qutrit genuinely entangled states distillable across every bipartition under noise is also investigated.

Ideal Quantum Teleamplification up to a Selected Energy Cutoff Using Linear Optics.

We introduce a linear optical technique that can implement ideal quantum teleamplification up to the nth Fock state, where n can be any positive integer. Here teleamplification consists of both quantum teleportation and noiseless linear amplification (NLA). This simple protocol consists of a beam splitter and an (n+1) splitter, with n ancillary photons and detection of n photons. For a given target fidelity, our technique improves success probability and physical resource costs by orders of magnitude over current alternative teleportation and NLA schemes. We show how this protocol can also be used as a loss-tolerant quantum relay for entanglement distribution and distillation.

Optimal Entanglement Swapping in Quantum Repeaters.

We formulate the problem of finding the optimal entanglement swapping scheme in a quantum repeater chain as a Markov decision process and present its solution for different repeaters' sizes. Based on this, weare able to demonstrate that the commonly used "doubling" scheme for performing probabilistic entanglement swapping of probabilistically distributed entangled qubit pairs in quantum repeaters does not always produce the best possible raw rate. Focusing on this figure of merit, without considering additional probabilistic elements for error suppression such as entanglement distillation on higher "nesting levels," our approach reveals that a power-of-two number of segments has no privileged position in quantum repeater theory; the best scheme can be constructed for any number of segments. Moreover, classical communication can be included into our scheme, and we show how this influences the raw waiting time for different numbers of segments, confirming again the optimality of "nondoubling" in some relevant parameter regimes. Thus, our approach provides the minimal possible waiting time of quantum repeaters in a fairly general physical setting.