Quantum Information Processing Tasks Research Articles

Robust projective measurements through measuring code-inspired observables

Quantum measurements are ubiquitous in quantum information processing tasks, but errors can render their outputs unreliable. Here, we present a scheme that implements a robust projective measurement through measuring code-inspired observables. Namely, given a projective POVM, a classical code, and a constraint on the number of measurement outcomes each observable can have, we construct commuting observables whose measurement is equivalent to the projective measurement in the noiseless setting. Moreover, we can correct t errors on the classical outcomes of the observables’ measurement if the classical code corrects t errors. Since our scheme does not require the encoding of quantum data onto a quantum error correction code, it can help construct robust measurements for near-term quantum algorithms that do not use quantum error correction. Moreover, our scheme works for any projective POVM, and hence can allow robust syndrome extraction procedures in non-stabilizer quantum error correction codes.

Non-Markovian noise mitigation in quantum teleportation: enhancing fidelity and entanglement

Maintaining quantum coherence and entanglement in the presence of environmental noise, particularly within non-Markovian contexts, represents a significant challenge for the progression of quantum information science and technology. This study offers a substantial advancement by investigating the dynamics of a two-qubit system subjected to diverse noise conditions, encompassing relaxation, dephasing, and their cumulative effects. By employing quantum-state-diffusion equations specifically crafted for non-Markovian environments, we introduce an innovative strategy to counteract the detrimental influences of environmental noise on quantum teleportation fidelity and entanglement concurrence. Our results underscore the potential for external interventions to markedly improve the resilience of quantum information processing tasks over prolonged durations, especially in settings where dephasing noise prevails. A key revelation is the intricate relationship between dephasing noise and the initial state of entanglement, which profoundly impacts the occurrence of entanglement sudden death. This research not only deepens our comprehension of quantum system dynamics under noisy circumstances but also furnishes practical directives for engineering robust quantum systems, a necessity for the development of scalable quantum technologies.

Improved experimental scheme for the generation of pair coherent state in traveling-wave optical fields

Abstract Pair coherent state (PCS) is a two-mode non-Gaussian state recently generated within spatially confined superconducting cavities. Under typical conditions, it is unsuitable for performing global quantum missions in open space. Several methods have been proposed to generate this state with the capability to propagate unrestrictedly. However, these methods employed an excessive amount of unnecessary physical resources or relied on coherent displacement within the low regime. This paper presents a novel experimental approach to generate this state, specifically designed for facilitating long-distance quantum information processing and communication tasks. The method involves the utilization of two weak cross-Kerr nonlinear media, two balanced beam splitters, and an on/off photodetector. Furthermore, the input comprises three CSs with high amplitudes. These physical resources are potentially accessible within existing technology. The analysis of success probability and fidelity demonstrates that the PCS can be successfully generated with a high coherent parameter amplitude, even in scenarios where the photodetector efficiency is low, provided that the coherent amplitudes are sufficiently high.

Quantum data compression under localized features

In this paper, we first introduce the local quantum information processing task by compressing the density operator based on local quantum Bernoulli noises. Then, the local quantum compression theorem is given, that is, the local quantum entropy is the minimum achievable rate of local compression. Finally, we prove the theorem with the proof of the direct coding theorem and the inverse theorem. The direct coding theorem shows that a scheme with such a local compression rate exists, and that this local compression rate converges to the local quantum entropy. The inverse theorem shows that the compression scheme with the rate below the local entropy is unachievable. With the continuous development of quantum technology, local quantum data compression technology will have broad application prospects and development space.

Can imaginarity be broadcast via real operations?

Imaginarity has proven to be a valuable resource in various quantum information processing tasks. A natural question arises: can the imaginarity of quantum states be broadcast via real operations? In this work, we present explicit structures for nonreal states whose imaginarity can be broadcast and cloned. That is, for a nonreal state, its imaginarity can be cloned if and only if it is a direct sum of several maximally imaginary states under orthogonal transformation, and its imaginarity can be broadcast if and only if it is a direct sum of a real state and some nonreal qubit states which are mixtures of two orthogonal maximally imaginary states under orthogonal transformation. In particular, we show that for a nonreal pure state, its imaginarity cannot be broadcast unless it is a maximally imaginary state. Furthermore, we derive a trade-off relation on the imaginarity broadcasting of pure states in terms of the measure of irreversibility of quantum states concerning real operations and the geometric measure of imaginarity. In addition, we demonstrate that any faithful measure of imaginarity is not superadditive.

Measurement Dependence can Affect Security in a Quantum Network

AbstractNetwork Nonlocality is an advanced study of quantum nonlocality that comprises network structure beyond Bell's theorem. The development of quantum networks has the potential to bring a lot of technological applications in several quantum information processing tasks. Here, the focus is on how the role of the independence of the measurement choices by the end parties in a network works and can be used to affect the security in a quantum network. In both three‐parties two‐sources bilocal network and four‐parties three‐sources star network scenarios, this study is able to show, a practical way to understand the relaxation of the assumptions to enhance a real security protocol if someone wants to breach in a network communication. Theoretically, it have been proved that by relaxing the independence of the measurement choices of only one end party, a Standard Network Nonlocality (SNN) and more stronger Full Network Nonlocality (FNN) can be created and the maximum quantum violation by the classical no‐signalling local model can be obtained. The distinguish between two types of network nonlocality, SNN and FNN, can also be made. It has been shown that FNN is a stronger correlation than SNN in the sense that the former comes in a scenario where all the sources must be nonlocal in nature.

Exponentially faster preparation of quantum dimers via driven-dissipative stabilization

We propose a rapid, high-fidelity, and noise-resistant scheme to generate many-body entanglement between multiple qubits stabilized by dissipation into a 1D bath. Using a carefully designed time-dependent drive, our scheme achieves a provably exponential speedup over state-of-the-art dissipative stabilization schemes in 1D baths, which require a timescale that diverges as the target fidelity approaches unity and scales exponentially with the number of qubits. To prepare quantum dimer pairs, our scheme only requires local 2-qubit control Hamiltonians, with a protocol time that is independent of system size. This provides a scalable and robust protocol for generating a large number of entangled dimer pairs on-demand, serving as a fundamental resource for many quantum metrology and quantum information processing tasks. Published by the American Physical Society 2024

The Simplified Quantum Circuits for Implementing Quantum Teleportation

AbstractIt is crucial to design quantum circuits as small as possible and as shallow as possible for quantum information processing tasks. Quantum circuits are designed with simplified gate‐count, cost, and depth for implementing quantum teleportation among various entangled channels. Here, the gate‐count/cost/depth of the Greenberger‐Horne‐Zeilinger‐based quantum teleportation is reduced from 10/6/8 to 9/4/6, the two‐qubit‐cluster‐based quantum teleportation is reduced from 9/4/5 to 6/3/5, the three‐qubit‐cluster‐based quantum teleportation is reduced from 12/6/7 to 8/4/5, the Brown‐based quantum teleportation is reduced from 25/15/17 to 18/8/7, the Borras‐based quantum teleportation is reduced from 36/25/20 to 15/8/11, and the entanglement‐swapping‐based quantum teleportation is reduced from 13/8/8 to 10/5/5. Note that, no feed‐forward recover operation is required in the simplified schemes. Moreover, the experimentally demonstrations on IBM quantum computer indicate that the simplified and compressed schemes can be realized with good fidelity.

Improved Entanglement‐Based High‐Dimensional Optical Quantum Computation with Linear Optics

AbstractQuantum gates are the essential block for quantum computers. High‐dimensional quantum gates exhibit remarkable advantages over their 2D counterparts for some quantum information processing tasks. Here, a family of entanglement‐based optical controlled‐SWAP gates on is presented. With the hybrid encoding, the control qubits and target qudits are encoded in photonic polarization and spatial degrees of freedom, respectively. The circuit is constructed using only () linear optics, beating an earlier result of 14 linear optics with . The circuit depth five is much lower than an earlier result of 11 with . Besides, the fidelity of the presented circuit can reach 99.4%, and it is higher than the previous counterpart with . The scheme is constructed in a deterministic way without any borrowed ancillary photons or measurement‐induced nonlinearities. Moreover, the approach allows .

Contextual quantum metrology

We demonstrate that the contextuality of measurement selection can enhance the precision of quantum metrology with a simple linear optical experiment. Contextuality is a nonclassical property known as a resource for various quantum information processing tasks. Recent studies show that contextuality by anomalous weak values can be utilized to enhance metrological precision, unraveling the role of contextuality in quantum metrology. Our contextual quantum metrology (coQM) scheme can elevate the precision of the optical polarimetry as much as 6 times the precision limit given by the Quantum Fisher Information. We achieve the contextuality-enabled enhancement with two mutually complementary measurements, whereas, in the conventional method, some optimal measurements to achieve the precision limit are either theoretically challenging to find or experimentally infeasible to realize. These results highlight that the contextuality of measurement selection is applicable in practice for quantum metrology.

Families of Schmidt-number witnesses for high dimensional quantum states

Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with a Schmidt number less than k.

Gaussian tripartite entanglement in the simultaneous measurement of position and momentum

By utilizing the positive partial transpose criterion, we certify Gaussian tripartite entanglement in the dynamics of the simultaneous measurement process of position and momentum raised by Arthurs and Kelly, considering a measurement configuration where the system under examination is a squeezed coherent state. Hence, the system is classified as a fully inseparable. Moreover, using the residual tripartite Rényi-2 entanglement as a quantifier measure, we determine the amount and behavior of the entanglement in the three-mode system as in all its reduced and global mode bipartitions. Besides, we compare the entanglement structure of the Arthurs-Kelly dynamics with that of the set of linear three-mode continuous-variable cluster states. The certification and quantification of entanglement in the simultaneous measurements process of the canonical pair pave the way for integrating this scheme into quantum information processing tasks.

Pretty good measurement for bosonic Gaussian ensembles

The pretty good measurement is a fundamental analytical tool in quantum information theory, giving a method for inferring the classical label that identifies a quantum state chosen probabilistically from an ensemble. Identifying and constructing the pretty good measurement for the class of bosonic Gaussian states is of immediate practical relevance in quantum information processing tasks. Holevo recently showed that the pretty good measurement for a bosonic Gaussian ensemble is a bosonic Gaussian measurement that attains the accessible information of the ensemble [IEEE Trans. Inf. Theory 66(9) (2020) 5634]. In this paper, we provide an alternate proof of Gaussianity of the pretty good measurement for a Gaussian ensemble of multimode bosonic states, with a focus on establishing an explicit and efficiently computable Gaussian description of the measurement. We also compute an explicit form of the mean square error of the pretty good measurement, which is relevant when using it for parameter estimation. Generalizing the pretty good measurement is a quantum instrument, called the pretty good instrument. We prove that the post-measurement state of the pretty good instrument is a faithful Gaussian state if the input state is a faithful Gaussian state whose covariance matrix satisfies a certain condition. Combined with our previous finding for the pretty good measurement and provided that the same condition holds, it follows that the expected output state is a faithful Gaussian state as well. In this case, we compute an explicit Gaussian description of the post-measurement and expected output states. Our findings imply that the pretty good instrument for bosonic Gaussian ensembles is no longer merely an analytical tool, but that it can also be implemented experimentally in quantum optics laboratories.

Resource-efficient quantum principal component analysis

Principal component analysis (PCA) is an important dimensionality reduction method in machine learning and data analysis. Recently, the quantum version of PCA has been established to diagonalize quantum states. Although these quantum algorithms promise quantum advantages, they require substantial resources beyond the reach of state-of-the-art quantum technologies. This work aims to reduce resource requirements and improve the efficiency of quantum PCA. Assuming that the quantum state is accessed through a purified quantum query model and a sampling model, we propose quantum algorithms that use minimal resource requirements for ancillary qubits to reveal properties of eigenvectors and eigenvalues of a state. In particular, we show that estimating eigenvalue λ with error ε and success probability larger than λ(1−η) requests a query complexity O~(ϵ−1) and a sample complexity O~(ϵ−2η−1) , respectively. To our knowledge, our result is the first quantum speedup that achieves asymptotic linear scaling in 1/ϵ for quantum PCA. As applications, we discuss estimating the minimum relative entropy of entanglement of bipartite pure-states and performing quantum state discrimination tasks. We show that quantum speedups are maintained when the pure state has a low Schmidt number and states of discrimination have a low rank. This study opens up a new quantum PCA method for high-dimensional quantum data analysis and discusses its application in quantum information processing tasks.

Error correction based artificial neural network in multi-modes CV-QKD with simultaneous type-I and type-II parametric-down conversion entangled photon source

We model simultaneous type-I and type-II phase matching in a single non-linear crystal (NLC), based on a double periodically poled lithium niobate crystal. We also discuss entanglement based continuous variable quantum key distribution (CV-QKD), and the security of such scheme is analyzed considering an eavesdropper being capable of individual attacks. We further demonstrate efficiency of the artificial neural network (ANN) algorithm during post-processing or errors correction in such CV-QKD protocols. Results show that employing simultaneous type-I and type-II SPDC process in single NLC is a potential source to generate high dimensional (or hyper-entangled) states, strongly required for quantum information processing tasks, an example of CV-QKD. Security analysis of such a CV-QKD protocol shows a strong advantage of employing the above entangled photon state source, given that it provides a higher secure key rate and thus a secure communication within a larger distance. In addition, the suggested error correction algorithm is less time consuming and highly efficient, since full synchronization is achieved just after a few number of updates of trusted parties’ tree-parity-machines. Our results sufficiently demonstrate that the suggested CV-QKD is able to distribute secure keys in nearby inter-city areas, and therefore allows lower-cost secure communication networks.

Uncertainty relation and the constrained quadratic programming

The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in terms of their variance, by utilizing the generalized Gell-Mann representation in qudit systems. We find that the tight state-independent lower bound of the variance sum can be characterized as a quadratic programming problem with nonlinear constraints in optimization theory. As illustrative examples, we derive analytical solutions for these quadratic programming problems in lower-dimensional systems, which align with the state-independent lower bounds. Additionally, we introduce a numerical algorithm tailored for solving these quadratic programming instances, highlighting its efficiency and accuracy. The advantage of our approach lies in its potential ability to simultaneously achieve the optimal value of the quadratic programming problem with nonlinear constraints but also precisely identify the extremal state where this optimal value is attained. This enables us to establish a tight state-independent lower bound for the sum of variances, and further identify the extremal state at which this lower bound is realized.

Tight Upper Bound for the Maximal Expectation Value of the N$N$‐Partite Generalized Svetlichny Operator

AbstractGenuine multipartite non‐locality is not only of fundamental interest but also serves as an important resource for quantum information theory. The ‐partite scenario and provide an analytical upper bound on the maximal expectation value of the generalized Svetlichny inequality achieved by an arbitrary ‐qubit system is considered. Furthermore, the constraints on quantum states for which the upper bound is tight are also presented and illustrated by noisy generalized Greenberger‐Horne‐Zeilinger states. Especially, the new techniques proposed to derive the upper bound allow more insights into the structure of the generalized Svetlichny operator and enable us to systematically investigate the relevant properties. As an operational approach, the variation of the correlation matrix defined makes it more convenient to search for suitable unit vectors that satisfy the tightness conditions. Finally, the results give feasible experimental implementations in detecting the genuine multipartite non‐locality and can potentially be applied to other quantum information processing tasks.

Entanglement Detection: A Scoping Review

Quantum entanglement is a critical physical process in quantum mechanics and quantum information theory. It is a required process in quantum computing, quantum teleportation, and quantum cryptography. Entanglement detection affects the performance of quantum information processing tasks. Entanglement detection has grown in popularity over the years, and various entanglement detection methods are available, though some have application and system scale limitations. This scoping review sought to identify various measurement methods for entanglement detection in both bipartite and multipartite entanglement systems. Secondary resource indexed literatures were selected based on specific keywords from literatures published between 2017 and 2021. The goal of this study is to present a proposed conceptual framework of entanglement detection based on previous work as a guidance and reference founded on one’s specific requirements.

Nonadiabatic Holonomic Quantum Computation Based on Rydberg Ground State Blockade

Quantum gates are crucial for quantum computation and quantum information processing. However, their effectiveness is often hindered by systematic errors and decoherence. Therefore, achieving resilient quantum gates to these factors is of great significance. We present a method to construct nonadiabatic holonomic single- and two-qubit gates in a Rydberg ground-state-blockade regime. Our approach utilizes a far-off-resonant technique for the single-qubit gate and a modified Rydberg antiblockade for the two-qubit gate. The reduction of the population of single- and two-excitation Rydberg states and the nonadiabatic holonomic process during the construction of the gates ensure robustness to decoherence and systematic errors, respectively. Numerical results demonstrate the fidelity and robustness of our scheme. The proposed scheme holds promise for future applications in quantum computation and quantum information processing tasks.

Eigenvalue-based quantum state verification of three-qubit W class states

In quantum many-body systems, W class states are typical examples of states with genuine multipartite entanglement. They have been found to be valuable resources in many quantum information processing tasks. However, the characterization and verification of W class states still remains an intractable problem. Here we first propose an eigenvalue-based verification protocol consisting of four practical adaptive local projective measurement tests, and obtain the optimal test probabilities with particle swarm optimization algorithm. The efficiency achieved by this protocol is far from satisfactory when compared with the theoretical upper bound. Then by utilizing the symmetry of the target states and a class of specific unitaries, we optimize the original verification strategy based on group theory. In this case, our new protocol can realize the efficient verification of three-qubit W class states.