Entanglement Recovery Research Articles

Entanglement recovery by weak measurement reversal in tripartite systems

Entanglement protection from noisy environments is an essential task in practical quantum information and communication. In this paper, we investigate the entanglement recovery of an amplitude-damped tripartite GHZ state by a weak-measurement reversal procedure. In particular, we emphasize the key importance of the inequivalency of probability amplitudes of the tripartite system under the recovery technique. We explore the maximal and non-maximal tripartite entangled state scenarios under amplitude damping noise in the absence and presence of weak measurement reversal procedures. Importantly, the non-maximal entangled state turns out to be a good choice for the entanglement recovery via weak-measurement reversal procedure.

A thermodynamically consistent constitutive equation describing polymer disentanglement under flow

We derive a thermodynamically consistent framework for incorporating entanglement dynamics into constitutive equations for flowing polymer melts. We use this to combine the convected constraint release (CCR) dynamics of Ianniruberto–Marriccui into a finitely extensible version of the Rolie–Poly model, and also include an anisotropic mobility as in the Giesekus model. The reversible dynamics are obtained from a free energy that describes both a finitely extensible conformation tensor and an ideal gas of entanglements along the chain. The dissipative dynamics give rise to coupled kinetic equations for the conformation tensor and entanglements, whose coupling terms describe shear-induced disentanglement. The relaxation dynamics of the conformation tensor follow the GLaMM and Rolie–Poly models, and account for reptation, retraction, and CCR. We propose that the relaxation time τν for entanglement recovery is proportional to the Rouse time τR which governs polymer stretch within the tube. This matches recent molecular dynamics simulations and corresponds to relaxing the entanglement number before the entire polymer anisotropy has relaxed on the longer reptation time τd. Our model suggests that claimed signatures of slow re-entanglement on the reptation time in step-strain experiments may be interpreted as arising from anisotropies in reptation dynamics.

Indistinguishability-Enhanced Entanglement Recovery by Spatially Localized Operations and Classical Communication

We extend a procedure exploiting spatial indistinguishability of identical particles to recover the spoiled entanglement between two qubits interacting with Markovian noisy environments. Here, the spatially localized operations and classical communication (sLOCC) operational framework is used to activate the entanglement restoration from the indistinguishable constituents. We consider the realistic scenario where noise acts for the whole duration of the process. Three standard types of noises are considered: a phase damping, a depolarizing, and an amplitude damping channel. Within this general scenario, we find the entanglement to be restored in an amount proportional to the degree of spatial indistinguishability. These results elevate sLOCC to a practical framework for accessing and utilizing quantum state protection within a quantum network of spatially indistinguishable subsystems.

Effective entanglement recovery via operators

Entanglement is one of essential quantum resources in quantum information processing, playing an important role during quantum communication and computation. While any system unavoidably interacts with its surrounding environment, this thus will result in decoherence or dissipation effect. With this in mind, a natural question arises: how to recover quantum entanglement under decoherence inducing by the environmental noises. In this work, our attempt is to propose an effective strategy to optimally achieve entanglement recovery. Specifically, we derive a nontrivial condition satisfied by any operation U, i.e. , which will definitely recover the entanglement of an arbitrary two-qubit system, and more importantly offer an explicit physical explanation towards the intrinsic mechanics of the entanglement recovery. By means of derivations, we obtain the appropriate operational strength to realize optimal entanglement recovery through taking advantage of our proposed methods. As illustrations, we apply some local operations complying with our presented strategy on validly protecting entanglement, including -symmetry operation, quantum weak measurement and quantum reversal measurement.

Delay of re-entanglement kinetics by shear-induced nucleation precursors in isotactic polypropylene melt

Rheological measurements were carried out to in-situ monitor the re-entanglement process of large amplitude oscillatory shear flow (LAOS) modified partially disentangled isotactic polypropylene (i-PP) melt. The characteristic entanglement recovery time (τent) was essentially longer than the average reptation time (τD) of fully entangled melt. At temperatures above 200 °C, the Arrhenius temperature dependence of τent and τD are the same, displaying a normal chain diffusion-controlled mechanism with flow activation energy of 41.4 kJ/mol. However, when the temperature is lower than 200 °C, τent is unexpectedly longer than expectation extrapolated from high temperatures, and a much higher activation energy of 98.6 kJ/mol is observed for the re-entanglement process. Based on our understanding, the re-entanglement process of shear-induced disentanglements in i-PP melt was postponed by the existence of quasi-ordered clusters created by shear at relatively low temperatures and their dissipation turns to be the rate-determining step for the whole recovery. Moreover, morphological study under polarized optical microscope showing much higher nucleation density which originates from the flow-induced precursors corroborates our hypothesis. Meanwhile, the surviving time of LAOS-generated nucleation precursors is comparable to the recovery time of disentangled chains, suggesting that the delay effect of nucleation precursors on chain diffusion may last over the entire re-entanglement process. Notwithstanding the obstruction of “extra” physical entanglements for chain diffusion, the molecular weight (Mw) dependence of entanglement recovery still follows the reptation model-based power law: τent=(a+b)Mw3.4, where a and b is the contribution of chain diffusion and dissipation of precursors, respectively.

Entanglement fluctuation theorems

Pure state entanglement transformations have been thought of as irreversible, with reversible transformations generally only possible in the limit of many copies. Here, we show that reversible entanglement transformations do not require processing on the many copy level, but can instead be undertaken on individual systems, provided the amount of entanglement which is produced or consumed is allowed to fluctuate. We derive necessary and sufficient conditions for entanglement manipulations in this case. As a corollary, we derive an equation which quantifies the fluctuations of entanglement, which is formally identical to the Jarzynski fluctuation equality found in thermodynamics. One can also relate a forward entanglement transformation to its reverse process in terms of the entanglement cost of such a transformation, in a manner equivalent to the Crooks relation. We show that a strong converse theorem for entanglement transformations is formally related to the second law of thermodynamics, while the fact that the Schmidt rank of an entangled state cannot increase is related to the third law of thermodynamics. Achievability of the protocols is done by introducing an entanglement battery, a device which stores entanglement and uses an amount of entanglement that is allowed to fluctuate but with an average cost which is still optimal. This allows us to also solve the problem of partial entanglement recovery, and in fact, we show that entanglement is fully recovered. Allowing the amount of consumed entanglement to fluctuate also leads to improved and optimal entanglement dilution protocols.

Dynamics of Supramolecular Self-Healing Recovery in Extension

Self-healing materials are prized for their ability to recover mechanical properties after damage. Supramolecular polymer networks have been demonstrated to have the ability to recover without the need for extraneous material components or the use of external stimuli. Surprisingly, there is little quantitative measure of self-healing dynamics and recovery. In this work, we develop a tool using a filament stretching rheometer to probe self-healing dynamics in creep and constant rate of extension. We experimentally determine the effect of process time scales, τH and τW, on the degree of recovery for two distinct supramolecular architectures. These results are put into the context of molecular time scales such as disengagement time, the Rouse time, and bond lifetime. We find that entangled polymers undergo sequential healing, whereby at short times, dynamics are dominated by entanglement recovery followed by recovery of associations. For an unentangled polymer, recovery is seemingly dominated by association ...

Better bounds on optimal measurement and entanglement recovery, with applications to uncertainty and monogamy relations

We extend the recent bounds of Sason and Verd\'u relating R\'enyi entropy and Bayesian hypothesis testing [arXiv:1701.01974] to the quantum domain and show that they have a number of different applications. First, we obtain a sharper bound relating the optimal probability of correctly distinguishing elements of an ensemble of states to that of the pretty good measurement, and an analogous bound for optimal and pretty good entanglement recovery. Second, we obtain bounds relating optimal guessing and entanglement recovery to the fidelity of the state with a product state, which then leads to tight tripartite uncertainty and monogamy relations.

Disentanglement effects on welding behaviour of polymer melts during the fused-filament-fabrication method for additive manufacturing

Although 3D printing has the potential to transform manufacturing processes, the strength of printed parts often does not rival that of traditionally-manufactured parts. The fused-filament fabrication method involves melting a thermoplastic, followed by layer-by-layer extrusion of the molten viscoelastic material to fabricate a three-dimensional object. The strength of the welds between layers is controlled by interdiffusion and entanglement of the melt across the interface. However, diffusion slows down as the printed layer cools towards the glass transition temperature. Diffusion is also affected by high shear rates in the nozzle, which significantly deform and disentangle the polymer microstructure prior to welding. In this paper, we model non-isothermal polymer relaxation, entanglement recovery, and diffusion processes that occur post-extrusion to investigate the effects that typical printing conditions and amorphous (non-crystalline) polymer rheology have on the ultimate weld structure. Although we find the weld thickness to be of the order of the polymer size, the structure of the weld is anisotropic and relatively disentangled; reduced mechanical strength at the weld is attributed to this lower degree of entanglement.

Effect of chain entanglement on the melt-crystallization behavior of poly(l-lactide) acid

Chain entanglements and the entanglement degree determine many processes and behaviors of polymers. In this work, poly(l-lactide) acid (PLLA) samples with markedly decreased entanglements were obtained via a freeze extraction method and the kinetics of entanglement recovery process of freeze-extracted samples was monitored by dynamic rheology approach. The crystallization kinetics of freeze-extracted PLLA samples was further studied by polarized optical microscope, which revealed that the entanglement degree greatly influences the crystallization of PLLA and lower degree of entanglement or disentanglement was conducive to the melt-crystallization of PLLA. The spherulites grew faster in partially disentangled melt than in well entangled melt.

The dependence time of melting behavior on rheological aspects of disentangled polymer melt: a route to the heterogeneous melt

To enhance the time scale for entanglement recovery, ultra high molecular weight polyethylene (UHMWPE) with a molecular weight of approximately 9.2 × 106 gmol−1 has been used. Rheological experiments were performed to monitor the melting kinetics of the disentangled melt prepared via solution casting. The successive frequency and strain sweep experiments showed that the processes of recovery of entanglements were quite clear in our experiments. It was observed that the entangled state influenced the border of the linear viscoelastic regime and the non-linear region. Complete re-entanglement time obtained by dynamics time-sweep experiment changed with the entanglement density and became unexpectedly longer in the disentangled sample. Meanwhile, the time-sweep experiments performed in the disentangled melt displayed that the gradual increasing of storage modulus in the initial has lagged behind and the time required for the modulus build up was relevant to the heating rate on melting. We suggested that an unusual behavior of melting kinetics of the disentangled sample caused the resultant heterogeneous melt having differences in local chain mobility, and hence an “immediate” loss in the disentangled state did not occur. Therefore, the level-off storage modulus on the onset of the following time-sweep experiment may be associated with the mixing of the distinguishable state of the heterogeneous distribution on melting.

Casting solvent effects on molecular dynamics of weak dynamic asymmetry polymer blend films via broadband dielectric spectroscopy

The effects of solvent casting parameters on the molecular dynamics of poly(methyl methacrylate)/poly(styrene-co-maleic anhydride) (PMMA/SMA) blend films was investigated using broadband dielectric spectroscopy. Through changing the solvent type and solution concentration, blend film samples with different entanglement intensity were prepared, and they can significantly affect the glass transition temperature (Tg) and segmental dynamics of the films. In films cast from a methyl ethyl ketone (MEK) solution at various concentrations, Tg and relaxation time (τmax) increase with increasing solution concentration due to an increased entanglement density, decreased molecular mobility and entanglement recovery. No obvious distribution broadening is observed due to the unchanged heterogeneous dynamics. In the case of films cast from chloroform, MEK and tetrahydrofuran solution, Tg and τmax of the resultant films are hardly affected, while Tg and τmax of films cast from a N, N-Dimethylformamide (DMF) solution are much higher than the other three due to a higher entanglement degree and strong interaction contributions. Moreover, the poor dissolving capacity of DMF may result in more heterogeneous dynamics and subsequently a larger dc conductivity process and broader and more symmetric α-relaxation spectra. Neither the dynamics nor the distribution width of the subglass relaxation processes is affected by the casting solvent or solution concentration, indicating little change in the local environment of the segments.

Influence of Annealing on Chain Entanglement and Molecular Dynamics in Weak Dynamic Asymmetry Polymer Blends

The influence of annealing above the glass transition temperature (T(g)) on chain entanglement and molecular dynamics of solution-cast poly(methyl methacrylate)/poly(styrene-co-maleic anhydride) (PMMA/SMA) blends was investigated via a combination of dynamic rheological measurement and broadband dielectric spectroscopy. Chain entanglement density increases when the annealing temperature and/or time increases, resulting from the increased efficiency of chain packing and entanglement recovery. The results of the annealing treatment without cooling revealed that the increase of the entanglement density occurred during the annealing process instead of the subsequent cooling procedure. Annealing above T(g) exerts a profound effect on segmental motion, including the transition temperature and dynamics. Namely, T(g) shifts to higher temperatures and the relaxation time (τ(max)) increases due to the increased entanglement density and decreased molecular mobility. Either T(g) or τ(max) approaches an equilibrium value gradually, corresponding to the equilibrium entanglement density that might be obtained through the theoretical predictions. However, no obvious distribution broadening is observed due to the unchanged heterogeneous dynamics. Furthermore, side group rotational motion could be freely achieved without overcoming the chain entanglement resistance. Hence, neither the dynamics nor the distribution width of the subglass relaxation (β- and γ-relaxation) processes is affected by chain entanglement resulting from annealing, indicating that the local environment of the segments is unchanged.

Reentanglement Kinetics of Freeze-Dried Polymers above the Glass Transition Temperature

Rheology experiments were performed to monitoring the kinetics of the entanglement recovery process of freeze-dried polystyrene. Complete reentanglement time requires unexpected long time, which does not monotonically reduce with the concentration of precursor solution. The entanglement recovery was treated as the complementary process of stress relaxation in Doi–Edwards model and was found to agree well with the exponential law. We clarified that freeze-drying is an effective way to achieve disentanglement for polymer chains. The correlation between recovery time and the concentration of precursor solution is in good agreement with previous results from molecular dynamics (MD) simulations.

Measurement-induced quantum entanglement recovery

By using photon pairs created in parametric down conversion, we report on an experiment, which demonstrates that measurement can recover the quantum entanglement of two qubit system in a pure dephasing environment. The concurrence of the final state with and without measurement are compared and analyzed. Furthermore, we verify that recovered states can still violate Bell's inequality, that is, to say, such recovered states exhibit nonlocality. In the context of quantum entanglement, sudden death and rebirth provide clear evidence, which verifies that entanglement dynamics of the system is sensitive not only to its environment, but also on its initial state.

Some Issues in Quantum Information Theory

Quantum information theory is a new interdisciplinary research field related to quantum mechanics, computer science, information theory, and applied mathematics. It provides completely new paradigms to do information processing tasks by employing the principles of quantum mechanics. In this review, we first survey some of the significant advances in quantum information theory in the last twenty years. We then focus mainly on two special subjects: discrimination of quantum objects and transformations between entanglements. More specifically, we first discuss discrimination of quantum states and quantum apparatus in both global and local settings. Secondly, we present systematical characterizations and equivalence relations of several interesting entanglement transformation phenomena, namely entanglement catalysis, multiple-copy entanglement transformation, and partial entanglement recovery.

Partial recovery of quantum entanglement

Suppose Alice and Bob try to transform an entangled state shared between them into another one by local operations and classical communications. Then in general a certain amount of entanglement contained in the initial state will decrease in the process of transformation. However, an interesting phenomenon called partial entanglement recovery shows that it is possible to recover some amount of entanglement by adding another entangled state and transforming the two entangled states collectively. In this paper, we are mainly concerned with the feasibility of partial entanglement recovery. The basic problem we address is whether a given state is useful in recovering entanglement lost in a specified transformation. In the case where the source and target states of the original transformation satisfy the strict majorization relation, a necessary and sufficient condition for partial entanglement recovery is obtained. For the general case we give two sufficient conditions. We also give an efficient algorithm for the feasibility of partial entanglement recovery in polynomial time. As applications, we establish some interesting connections between partial entanglement recovery and the generation of maximally entangled states, quantum catalysis, mutual catalysis, and multiple-copy entanglement transformation.

Recovery of Shear-Modified Polybutadiene Solutions

Abstract We have investigated the recovery of the overshoot in the transient viscosity, the first normal stress coefficient, and the dynamic modulus for entangled polybutadiene solutions subjected to nonlinear shear flow. The molecular-weight dependences of the various time scales (linear viscoelastic relaxation time, entanglement recovery time, and timescale for decay of stress following cessation of shearing) are all consistent with the usual 3.4 power law. Nevertheless, the time for recovery of the stress overshoot and plateau value of the dynamic modulus were substantially longer (by as much as two orders of magnitude) than the linear viscoelastic relaxation time calculated from the Newtonian viscosity and the equilibrium recoverable compliance. These results indicate that complete entanglement recovery requires cooperative chain motions over a length scale exceeding that associated with linear relaxation. This persistence of a disentangled state means that a state of low viscosity and reduced elasticity is retained for an extended time, suggesting that shear modification can be used to facilitate the processing of polymers.

Reentanglement Kinetics in Sheared Polybutadiene Solutions

Interrupted shear measurements were used to follow the reentanglement kinetics and associated molecular weight dependence for solutions of near-monodisperse polybutadiene (PB). The time-dependent recovery of the overshoot in the shear stress was measured for PB having weight-average molecular weights (Mw) equal to 61, 90, 107, and 167 kg/mol, corresponding to a range of 17−47 entanglements per chain in solution. The times for recovery of the stress overshoot were 1.5 decades longer (30 times greater) than the corresponding linear viscoelastic relaxation times, the latter determined from dynamic shear data or from stress relaxation following cessation of flow. Notwithstanding the differing time scales, the Mw dependences for entanglement recovery and linear viscoelastic relaxation were equivalent (power law exponent ∼ 3.4).