Equatorial States Research Articles

Enhancing hierarchical remote preparation of an arbitrary n-qudit equatorial state by weak measurement and measurement reversal

Based on the demand for safer and more efficient quantum network communication, we propose two deterministic protocols to achieve the remote preparation of an arbitrary n-qudit equatorial states among multiple agents by selecting appropriate entanglement resources. The level of the agents varies depending on their authorities to restore the secret state. The superior agent requires the cooperation of the residual superior agents and any one of the subordinate agents, while the subordinate agent needs the help of all the other agents. To be emphasized, the recovery operations are deduced by general formulas that distinctly elucidate their relevance with the measurement outcomes. Additionally, we discuss the impact of amplitude damping noise and utilize weak measurement and measurement reversal to suppress noise.

Developing an Approach for Equitable and Reasonable Utilization of International Rivers: The Nile River

The absence of a basin-wide apportionment agreement on using the Nile River equitably has been a long-standing source of disagreement among Nile riparian states. This study introduces a new approach that the riparian states can consider that quantifies the Nile River’s apportionment. The approach includes (1) developing a basin-wide database of indicators representative of the United Nations Watercourse Convention (UNWC) relevant factors and circumstances, (2) developing an ensemble of indicator weighting scenarios using various weighting methods, and (3) developing six water-sharing methods to obtain a range of apportionments for Egypt, Sudan, Ethiopia and the group of the White Nile Equatorial States for each weighting scenarios. The results illustrate a relatively narrow range of country-level water apportionments, even though some individual factor weights vary from 3% to 26%. Considering the entire Nile River, the water apportionment for Ethiopia ranges from 32% to 38%, Sudan and South Sudan from 25% to 33%, Egypt from 26% to 35%, and the Equatorial States from 5% to 7%. We trust that the six proposed equitable water-sharing methods may aid in fostering basin-wide negotiations toward a mutual agreement and address the dispute over water sharing.

Deterministic remote preparation of multi-qubit equatorial states through dissipative channels

We investigate the influence of a noisy environment on the remote preparation of the multi-qubit equatorial state, and specifically deduce the final states and fidelities of the remote preparation of the three-qubit and four-qubit equatorial states under diverse types of noisy environments, namely, amplitude damping, bit flip, phase damping, phase flip, bit-phase flip, depolarization, and non-Markov environments. The results show that when the decoherence factors of the front six noises are equal, the influence degrees of phase damped noise, bit flip noise, phase flip noise, and bit-phase flip noise are similar, while the information loss caused by the amplitude damped noise and depolarizing noise is less. In particular, the bit flip noise and depolarizing noise may have more complex effects on the remote state preparation (RSP) schemes depending on the phase information of the target states, even for the ideal cases where the fidelity values are always 1 for specific phase relations. In the non-Markov environment, owing to the back and forth of information between the environment and systems, fidelities exhibit oscillating behavior and the minimum value may stay greater than zero for a long evolutionary time. These results are expected to have potential applications for understanding and avoiding the influence of noise on remote quantum communication and quantum networks.

On the importance of equatorial metal-centered excited states in the photophysics of cyclometallated Ir(III) complexes.

In the present contribution, the following three cyclometallated Ir(III) complexes were theoretically investigated using density functional theory calculations to explain their different photophysical properties: [Ir(ppy)2(bpy)]+, where Hppy is 2-phenylpyridine and bpy is 2,2'-bipyridine, [Ir(ppy)2(pbpy)]+, where pbpy is 6-phenyl-2,2'-bipyridine, and [Ir(ppy)2(dpbpy)]+, where dpbpy is 6,6'-diphenyl-2,2'-bipyridine. Despite sharing the same molecular skeleton, with the only difference being the addition of one or two phenyl groups attached to the ancillary bpy ligand, the complexes show different emission quantum yields in CH2Cl2 solution (0.196, 0.049 and 0.036, respectively). Such a behavior was previously justified as a consequence of a different ability to non-radiatively decay through an axial metal-centered (MC) triplet state. In the present contribution, a new non-radiative decay path has been characterized to be mediated by the so-called equatorial MC states, in which an Ir-Nbpy bond is elongated instead of an Ir-Nppy bond as observed in the axial MC states. The decay path involving the equatorial MC states is more favorable than that associated with the axial MC states, and the different ability to decay through the former better explains the photoemission properties exhibited by the three complexes.

Cyclic controlled remote state preparation in the three-dimensional system

In this work, we propose a novel protocol for cyclic controlled remote state preparation (CCRSP) with single-qutrit equatorial states. In this protocol, three distant parties, Alleyn, Breden and Carden, are not only senders but also receivers. Alleyn wants to remotely prepare a single-qutrit equatorial state at Breden’s site, while at the same time, Breden (Carden) wishes to help Carden (Alleyn) remotely preparing another single-qutrit equatorial state. It is shown that, only if the three senders and the controller collaborate with each other, the CCRSP can be completed. To present this protocol more clearly, only maximally entangled channel is considered.

Hierarchical remote preparation of arbitrary dimensional equatorial states

Hierarchical remote preparation of equatorial states has practical applications but has not been studied before. We first propose a deterministic protocol for two-dimensional equatorial states via a four-qubit cluster state. The sender can asymmetrically transmit the secret state to any one of the three agents who are ranked in terms of their authorities. A set of useful measurement bases is elaborately constructed which plays a key role in the protocol. Then the protocol is generalized to high-dimensional system. Further, taking advantage of cluster state’s symmetry, we give a universal protocol with multiple agents. The high-grade agent needs the assistance of the remaining high-grade agents as well as one of the low-grade agents. While the low-grade agent needs the cooperation of all the other agents. The agents’ recovery operators are expressed by a general formula which clearly reveals the relationship with the measurement results. Additionally, the impact of two kinds of noise is analyzed.

An asymmetric controlled bidirectional remote preparation protocol of three- and four-qubit equatorial states

A scheme for asymmetric controlled bidirectional remote state preparation by utilizing 15-qubit entangled state as quantum channel is proposed. In this paper, we present a new protocol that Alice prepares a three-qubit equatorial state for Bob and Bob prepares a four-qubit equatorial state for Alice at the same time under Charlie’s control. The success of this scheme cannot be separated from the controller Charlie. In addition, we give some analysis and conclusions by comparing with other schemes. The auxiliary qubits and operations are not required in our scheme. In particular, the success probability of the receivers restoring the prepared states can reach 100%. Thus, our scheme has better performance.

Quantum metrology with superposition spin coherent states: Insights from Fisher information

We present a closed-form analytical description for the metrological performance of a generic superposition of spin coherent states (SSCS) used as probes for quantum phase estimation. Working in this framework, we derive transparent analytical expressions for the pertinent quantum Fisher information and identify a general class of spin coherent states enabling quantum metrology with Heisenberg-limit precision. Bloch-sphere analysis of antipodal SSCS shows that the phase-estimation precision attainable with such states increases with the distance from the equator of the Bloch sphere, growing from the shot-noise limit level for the equatorial states all the way up to the Heisenberg limit for SSCS that can be represented as superpositions of the poles of the Bloch sphere.

Controlled cyclic remote state preparation of single-qutrit equatorial states

The scheme for controlled unidirectional cyclic remote state preparation of single-qutrit equatorial states is put forward. Alice, Bob, Charlie, and David share a seven-qutrit entangled state as the quantum channel. Under the control of David, Alice can remotely prepare a single-qutrit equatorial state at Bob’s site, Bob can remotely prepare a single-qutrit equatorial state at Charlie’s site, Charlie can remotely prepare a single-qutrit equatorial state at Alice’s site simultaneously. The direction of controlled unidirectional cyclic remote state preparation can be reversed by changing measured qutrits of the quantum channel. The scheme for controlled bidirectional cyclic remote state preparation of single-qutrit equatorial states is also proposed. The schemes can be generalized to controlled unidirectional and bidirectional multi-party cyclic remote state preparation of single-qudit equatorial states.

An extended period of extremely weak geomagnetic field suggested by palaeointensities from the Ediacaran Grenville dykes (SE Canada)

Long-term variations of the geomagnetic field, observed in the palaeomagnetic record, have the potential to shed much light on the evolution of Earth's deep interior. With a geomagnetic field characterised by anomalous directions and ultra-low intensities, the Ediacaran period (635-538 Ma) is a time of special interest. Steep and shallow directions, leading to virtual geomagnetic poles (VGPs) separated by angles of up to 90° and very close in age could have recorded a geomagnetic field switching between axial and equatorial dipole-dominated states. Alternatively, the field may simply have been highly nondipolar and subject to rapid reversals. Palaeointensity determinations of units that record the anomalous directions could potentially help to discriminate between morphologies but the spatial and temporal distribution of palaeomagnetic data require improvement. Here we present new palaeointensities from 6 dykes from the western end of the Grenville Dyke swarm that recorded directionally anomalous geomagnetic fields around ∼585 Ma. Results from double-heating Thellier experiments failed to satisfy the used selection criteria, but successful microwave Thellier, Shaw and pseudo-Thellier experiments lead to palaeointensities that show field strength values of 2.9 ± 2.2 μT and corresponding virtual dipole moments of 0.3-1.7×1022 Am2. These field strengths are an order of magnitude weaker than the present-day field. VGPs grouping in two distinct clusters with almost identical angular dispersions of VGPs (SB=18.5° and 18.9°) may argue for the presence of an equatorial dipole. In contrast, the palaeointensities associated with the steep and shallow components are indistinguishable. Although based on a low number of results, this observation, together with the overall very large VGP dispersion may rather support that the Grenville Dykes have recorded enhanced secular variation linked to a highly unstable and rapidly reversing field.

Deterministic Controlled Remote Preparation of Two-qutrit Equatorial States

We present a novel scheme for deterministically realizing remote preparation of three-dimensional quantum states in a controlled manner. In this scheme, to link the three legitimate parties, generalized Einstein-Podolsky-Rosen (EPR) states, generalized Greenberger-Horne-Zeilinger (GHZ) states or their combinations are employed to product the shared quantum resources. Then to complete the deterministic controlled remote state preparation (DCRSP) in a three-dimensional system, some suitable sets of mutually orthogonal quantum states are hired as the measuring bases. It is shown that, after performing projective measurements under the proper measuring bases, the remote preparation of two-qutrit equatorial states can be successfully realized under control of a third party with unit successful probability.

Multiparty probabilistic controlled joint remote preparation of an arbitrary <italic>m</italic>-qudit equatorial state with a pure entangled quantum channel

<p indent="0mm">The quantum equatorial state, a special kind of quantum state, has attracted much attention because of its potential for applications in quantum information processing. The remote preparations of arbitrary two-qudit, three-qudit equatorial and <italic>m</italic>-qudit equatorial states have been studied via different entangle quantum channels. In this paper, we propose two protocols for the controlled joint remote preparation of an arbitrary <italic>m</italic>-qudit equatorial state with a pure entangled quantum channel. The first is for the controlled joint remote preparation of the <italic>m</italic>-qudit equatorial state by using <italic>m</italic> multiparticle GHZ-class states as the quantum channel, and the second is for the controlled joint remote preparation of the <italic>m</italic>-qudit equatorial state via a multiparticle entangled state. All senders share information about the prepared state and perform <italic>m</italic>-particle projective measurements on their entangled particles according to their information about the prepared state. All controllers perform generalized X-basis measurements on their entangled particles. If a receiver cooperates with all the senders and controllers, he can prepare the original state probabilistically by performing unitary operations on his entangled particles and an auxiliary qubit. This protocol is more convenient for applications because it only requires nonmaximal entanglement for the controlled joint remote preparation of an arbitrary <italic>m</italic>-qudit equatorial state.

Does Living in Previously Exposed Malaria or Warm Areas is Associated with a Lower Risk of Severe COVID-19 Infection in Italy?

Incidence of Covid-19 positivity (21/2/2020-28/3/2020) in provinces of 4 Italian regions whose territory was described as previously exposed to Malaria was compared with those of other provinces of the same regions. The climate of such provinces was compared with the climate of the other provinces in some regions. Previously malarial areas show a lower risk than other provinces of the same regions: Mantua (Lombardy) RR=0.94 (CI95%0.89-0.99); Venice-Rovigo (Veneto) RR=0.61 (CI95%0.58-0.65); Ferrara-Ravenna (Emilia-Romagna) RR=0.37 (CI95%0.35-0.41); Cagliari-Oristano-SouthSardinia (Sardinia) RR=0.25 (0.17-0.31). The maximum temperature in March 2020 in those provinces was higher in mean 1.5° for other provinces. The lower frequency of COVID-19 in the provinces previously exposed to Malaria of four Italian regions does not reveal a causal link. The phenomenon has emerged independently in all the regions investigated. People born between the 1920s and 1950s were those most exposed to malaria years ago and today are the most exposed to the severest forms of COVID-19. A warmer climate seems to be associated with a lower risk of COVID, in line with the evidence highlighted in equatorial states where a lower lethality of the virus has emerged, however this regardless of the presence of Malaria. This may suggest that climate and not Malaria is the real risk factor, though further studies need to determine the role of the association climate / COVID.

Calorimetric distinction between the inter- and intra-molecular rearrangement processes in alkylcyclohexane liquids by means of spatial confinement

We report an investigation, by means of adiabatic calorimetry, on the thermal properties of ethylcyclohexane (ECH) confined to within silica-gel mesoscopic pores with an average pore size of 6 nm. As a result of confinement, crystallization was circumvented within the entire temperature range. The devitrification behavior of the confined glass was observed to mainly proceed in a two-step manner and these steps were attributed to the existence of distinct relaxation processes involving molecules in the inner-pore and pore-wall-interface regions. Additionally, two secondary relaxations, of smaller magnitudes, were identified: (1) one occurring within the glassy state, below the primary devitrification process; and (2) another occurring within the supercooled liquid state. Revisit of the data of similar investigations on crystallization-circumvented methylcyclohexane (MCH) indicated the existence of a relaxation process analogous to this latter one (2). The characteristic temperatures for the latter process in both ECH and MCH were found to be independent of the degree of confinement. On the other hand, the former secondary relaxation (1) occurring within the glassy state of ECH displayed pore-size dependent behavior. We interpreted the behavioral difference, between the two processes, as associated with the distinct origins of either intermolecular or intramolecular processes; namely, the relaxation (1) as ascribed to the so-called β-relaxation commonly observed in glasses and the relaxation (2) to the molecular rearrangement modes involving the positional conversion, of the substituted alkyl-group, between the axial and equatorial configurations. The energy difference between the axial and equatorial states inferred from the magnitude of heat-capacity jump at the glass transition temperature was rationalized to be (7.7 ± 0.3) kJ mol−1.

Efficient scheme for remote preparation of arbitrary n-qubit equatorial states

Recently, a scheme for deterministic remote preparation of arbitrary multi-qubit equatorial states was proposed by Wei et al. [Quantum Inf. Process. 17 70 (2018)]. It is worth mentioning that the construction of mutual orthogonal measurement basis plays a key role in quantum remote state preparation. In this paper, a simple and feasible remote preparation of arbitrary n-qubit equatorial states scheme is proposed. In our scheme, the success probability will reach unit. Moreover, there are no coefficient constraint and auxiliary qubits in this scheme. It means that the success probabilities are independent of the coefficients of the entangled channel. The advantage of our scheme is that the mutual orthogonal measurement basis is devised. To accomplish the quantum remote state preparation (RSP) schemes, some new sets of mutually orthogonal measurement basis are introduced.

Remote Blind State Preparation with Weak Coherent Pulses in the Field.

Quantum computing has seen tremendous progress in past years. Due to implementation complexity and cost, the future path of quantum computation is strongly believed to delegate computational tasks to powerful quantum servers on the cloud. Universal blind quantum computing (UBQC) provides the protocol for the secure delegation of arbitrary quantum computations, and it has received significant attention. However, a great challenge in UBQC is how to transmit a quantum state over a long distance securely and reliably. Here, we solve this challenge by proposing a resource-efficient remote blind qubit preparation (RBQP) protocol, with weak coherent pulses for the client to produce, using a compact and low-cost laser. We experimentally verify a key step of RBQP-quantum nondemolition measurement-in the field test over 100km of fiber. Our experiment uses a quantum teleportation setup in the telecom wavelength and generates 1000secure qubits with an average fidelity of (86.9±1.5)%, which exceeds the quantum no-cloning fidelity of equatorial qubit states. The results prove the feasibility of UBQC over long distances, and thus serves as a key milestone towards secure cloud quantum computing.

A universal protocol for controlled bidirectional quantum state transmission

In this paper, we propose a universal protocol for controlled bidirectional quantum state transmission. The bidirectional transmission of $$ n_{1} $$ - and $$ n_{2} $$ -qubit equatorial states can be realized by using the $$ 2n_{1} + 2n_{2} + 1 $$ -qubit entangled state as the quantum channel, where $$ n_{1} ,n_{2} $$ are arbitrary nonzero positive integers. First, the quantum channel is constructed by using Hadamard (H) and CNOT operations. Furthermore, after the protocol completed, the desired state can be obtained simultaneously, securely and determinately. Second, two examples are given. One is a symmetric protocol which can complete the bidirectional transmission of two-qubit equatorial state. The other is an asymmetric protocol, where Alice transmits a single-qubit equatorial state to Bob and Bob transmits a four-qubit equatorial state to Alice. To the best of our knowledge, it is the first time to realize the bidirectional transmission of arbitrary-qubit equatorial state. At last, we analyze the performance of the protocol. Some comparisons with other protocols are described.

Remote state preparation using Einstein–Podolsky–Rosen representations

Because Einstein–Podolsky–Rosen states are well-defined on the Weyl algebra, their canonical cyclic representations are suitable for demonstrating the process of remote state preparation. Local projection-valued measurements and the corresponding recovery unitary operator are formulated in this representation, whereupon generalized equatorial states are prepared remotely and faithfully.

Deterministic remote preparation of arbitrary multi-qubit equatorial states via two-qubit entangled states

We propose an efficient scheme for remotely preparing an arbitrary n-qubit equatorial state via n two-qubit maximally entangled states. Compared to the former scheme (Wei et al. in Quantum Inf Process 16:260, 2017) that has the 50% successful probability when the amplitude factors of prepared states are $$2^{-n{/}2}$$ , the probability would be increased to 100% by using of our modified proposal. The feasibility of our scheme for remote preparation arbitrary multi-qubit equatorial states is explicitly demonstrated by theoretical studies and concrete examples.

Monotonic Bargaining Solution for Allocating Critically Scarce Transboundary Water

As much as transboundary river basins can be niches for regional cooperation, they could also be causes for interstate water disputes. The risk of water conflict in these river basins is much higher during water scarcity. As a result, establishing a fair and efficient water allocation mechanism is key for the sustainable sharing of these river basins’ water. In this paper, the authors propose a monotonic water allocation mechanism for transboundary river basins under water scarcity by coupling the bankruptcy theory with the Asymmetric Kalai-Smorodinsky bargaining solution concept. The allocation framework takes into account the aspiration water claims of the sharing countries. Additionally, as a case study, the allocation solution was used to allot the contested water of the Nile among the basin countries. For the medium term water demands the framework allocated 61.67%, 89.80%,91.82% and 61.67% of their water claims to Ethiopia, Sudan, Egypt and to the assumed coalition countries on the White Nile referred in this paper as equatorial states (Uganda, Kenya, Tanzania, Burundi, Rwanda, and Democratic Republic of Congo) respectively. On the other hand, for the long term demands, the allocation scheme allocated 63.65%, 69.36%, 71.42% and 60.41% of their water demands to the riparian countries in the same order. In general, the authors hope that the water allocation scheme applied in this article can contribute to the ongoing efforts to design river sharing solutions to river sharing problems in transboundary river basins by understanding the strategic interaction among riparian countries.