Quantum Information Processing Tasks Research Articles

Resource-efficient quantum principal component analysis

Abstract 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 principal component analysis. 
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 $\lambda$ with error $\epsilon$ and success probability larger than $\lambda(1-\eta)$ requests a query complexity {$\mathcal{\widetilde{O}}(\epsilon^{-1})$} and a sample complexity {$\mathcal{\widetilde{O}}(\epsilon^{-2}\eta^{-1})$}, respectively. To our knowledge, our result is the first quantum speedup that achieves asymptotic linear scaling in $1/\epsilon$ 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 principal component analysis 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.

Mode entanglement in fermionic and bosonic Harmonium

Mode entanglement in many-body quantum systems is an active area of research. It provides crucial insight into the suitability of many-body systems for quantum information processing tasks. Local super-selection rules must be taken into account when assessing the amount of physically accessible entanglement. This requires amending well-established entanglement measures by incorporating local parity and local particle number constraints. In this paper, we report on mode entanglement present in the analytically solvable system of N-Harmonium. To the knowledge of the authors, this is the first analytic study of the physically accessible mode and mode-mode entanglement of an interacting many-body system in a continuous state space. We find that super-selection rules dramatically reduce the amount of physically accessible entanglement, which vanishes entirely in some cases. Our results strongly suggest the need to re-evaluate intra and inter-mode entanglement in other fermionic and bosonic systems.

Continuous Variable Quantum Teleportation in a Dissipative Environment: Comparison of Non‐Gaussian Operations Before and After Noisy Channel

AbstractThis article explores the relative advantages in continuous‐variable quantum teleportation when non‐Gaussian operations, namely, photon subtraction, addition, and catalysis, are performed before and after interaction with a noisy channel. The resource state for teleporting unknown coherent and squeezed vacuum states is generated using two distinct strategies: i) Implementation of non‐Gaussian operations on two mode squeezed vacuum (TMSV) state before interaction with a noisy channel, ii) Implementation of non‐Gaussian operations after interaction of TMSV state with a noisy channel. The results show that non‐Gaussian operations can enhance teleportation fidelity in a dissipative environment. However, the most advantageous non‐Gaussian operation and appropriate strategy depend on the state and channel parameters. The results suggest that employing such strategies can be advantageous in other non‐Gaussian continuous variable quantum information (QIP) processing tasks in a dissipative environment.

Tripartite Svetlichny test with measurement dependence

The Bell test, as an important method for detecting nonlocality, is widely used in device-independent quantum information processing tasks. The security of these tasks is based on an assumption called measurement independence. Since this assumption is difficult to be guaranteed in practical Bell tests, it is meaningful to consider the effect of reduced measurement independence (i.e., measurement dependence) on Bell tests. Some research studies have shown that nonlocality can be detected even if measurement dependence exists. However, the relevant results are all based on bipartite Bell tests, and the results for multipartite Bell tests are still missing. In this paper, we explore this problem in the tripartite Svetlichny test. By considering flexible lower and upper bounds on the degree of measurement dependence, we obtain the relation among measurement dependence, guessing probability, and the maximal value of Svetlichny inequality. Our results reveal the case in which genuine nonlocality is nonexistent; at this point, the outcomes of the Bell test cannot be applied in device-independent quantum information processing tasks.

Enhanced quantum resources via two distant atom-cavity systems under the influence of atomic dissipation

Quantum resources such as entanglement and coherence are the holy grail for modern quantum technologies. Although the unwanted environmental effects tackle quantum information processing tasks, suprisingly these key quantum resources may be protected and even enhanced by the implementation of some special hybrid open quantum systems. Here, we aim to show how a dissipative atom-cavity-system can be accomplished to generate enhanced quantum resources. To do so, we consider a couple of dissipative cavities, where each one contains two effective two-level atoms interacting with a single-mode cavity field. In practical applications, a classical laser field may be applied to drive each atomic subsystem. After driving the system, a Bell-state measurement is performed on the output of the system to quantify the entanglement and coherence. The obtained results reveal that the remote entanglement and coherence between the atoms existing inside the two distant cavities are not only enhanced, but can be stabilized, even under the action of dissipation. In contrast, the local entanglement between two atoms inside each dissipative cavity attenuates due to the presence of unwanted environmental effects. Nevertheless, the local coherence may show the same behavior as the remote coherence. Besides, the system provides the steady state entanglement in various interaction regimes, particularly in the strong atom-cavity coupling and with relatively large detuning. More interestingly, our numerical analyses demonstrate that the system may show a memory effect due to the fact that the death and revival of the entanglement take place during the interaction. Our proposed model may find potential applications for the implementation of long distance quantum networks. In particular, it facilitates the distribution of quantum resources between the nodes of large-scale quantum networks for secure communication.

Efficient Verification of Ground States of Frustration-Free Hamiltonians

Ground states of local Hamiltonians are of key interest in many-body physics and also in quantum information processing. Efficient verification of these states are crucial to many applications, but very challenging. Here we propose a simple, but powerful recipe for verifying the ground states of general frustration-free Hamiltonians based on local measurements. Moreover, we derive rigorous bounds on the sample complexity by virtue of the quantum detectability lemma (with improvement) and quantum union bound. Notably, the number of samples required does not increase with the system size when the underlying Hamiltonian is local and gapped, which is the case of most interest. As an application, we propose a general approach for verifying Affleck-Kennedy-Lieb-Tasaki (AKLT) states on arbitrary graphs based on local spin measurements, which requires only a constant number of samples for AKLT states defined on various lattices. Our work is of interest not only to many tasks in quantum information processing, but also to the study of many-body physics.

A Two‐Step Entanglement Concentration for the Less‐Entangled Four‐Photon Cluster States

AbstractEntanglement concentration serves as an essential tool to obtain the maximally entangled states from the less‐entangled states in quantum information processing tasks. An efficient two‐step entanglement concentration protocol (ECP) is proposed to concentrate the less‐entangled four‐photon cluster states with four unknown coefficients into the maximally entangled states in this paper. The protocol utilizes parity‐check gate and photon‐polarized controlled‐Z gate, constructed with a single semiconductor quantum dot in a single optical microcavity (quantum dot‐cavity coupled system) and several linear optical elements. The discarded quantum states can be recycled in the next round concentration to achieve a higher success probability. Under conditions of strong coupling and weak side leakage rate, the ECP can tend toward ideal fidelity and efficiency. Compared to the previously proposed ECPs that utilize various auxiliary tools such as additional entangled states and complex quantum logic gates, the ECP significantly simplifies the analysis process and enables efficient implementation. Thus, the ECP is more economical and feasible in future optical systems.

Graph-theoretical optimization of fusion-based graph state generation

Graph states are versatile resources for various quantum information processing tasks, including measurement-based quantum computing and quantum repeaters. Although the type-II fusion gate enables all-optical generation of graph states by combining small graph states, its non-deterministic nature hinders the efficient generation of large graph states. In this work, we present a graph-theoretical strategy to effectively optimize fusion-based generation of any given graph state, along with a Python package OptGraphState. Our strategy comprises three stages: simplifying the target graph state, building a fusion network, and determining the order of fusions. Utilizing this proposed method, we evaluate the resource overheads of random graphs and various well-known graphs. Additionally, we investigate the success probability of graph state generation given a restricted number of available resource states. We expect that our strategy and software will assist researchers in developing and assessing experimentally viable schemes that use photonic graph states.

Quantum Correlation Resource Recycling via Sequential Measurements: Theoretical Models and Optical Experiments

Quantum correlation is a key resource for a variety of quantum information processing and communication tasks, the efficient utilization of which has been a longstanding concern, and it is also one of the main challenges in the application of quantum technology. In this review, we focus on the interaction between quantum measurements and quantum correlations by designing appropriate measurement strategies, specifically exploring the trade-off between information gain and disturbance degree in weak measurements to ensure that quantum correlations from the same source can be shared among multiple independent observers. We introduce the basic knowledge and classification of quantum measurements, investigate the weak measurement scenario, and show the theoretical model construction of quantum correlation recycling in the original works. We summarize the theoretical and experimental development process and the latest progress in this field. Finally, we provide an outlook for more quantum resource applications that can profit from the optimization of quantum measurement strategies.

Manipulating the direction of one-way steering in an optomechanical ring cavity

Quantum steering refers to the apparent possibility of exploiting nonseparable quantum correlations to remotely influence the quantum state of an observer via local measurements. Different from entanglement and Bell nonlocality, quantum steering exhibits an inherent asymmetric property, which makes it relevant for many asymmetric quantum information processing tasks. Here, we study Gaussian quantum steering between two mechanical modes in an optomechanical ring cavity. Using experimentally feasible parameters, we show that the state of the two considered modes can exhibit two-way steering and even one-way steering. Instead of using unbalanced losses or noises, we propose a simple practical way to control the direction of one-way steering. A comparative study between the steering and entanglement of the studied modes shows that both steering and entanglement undergo a sudden death-like behavior. In particular, steering is found more fragile against thermal noise remaining constantly upper-bounded by entanglement. The proposed scheme may be meaningful for one-sided device-independent quantum key distribution, where the security of such protocol depends fundamentally on the direction of steering.

Variational quantum state discriminator for supervised machine learning

Abstract Quantum state discrimination (QSD) is a fundamental task in quantum information processing with numerous applications. We present a variational quantum algorithm that performs the minimum-error QSD, called the variational quantum state discriminator (VQSD). The VQSD uses a parameterized quantum circuit that is trained by minimizing a cost function derived from the QSD, and finds the optimal positive-operator valued measure (POVM) for distinguishing target quantum states. The VQSD is capable of discriminating even unknown states, eliminating the need for expensive quantum state tomography. Our numerical simulations and comparisons with semidefinite programming demonstrate the effectiveness of the VQSD in finding optimal POVMs for minimum-error QSD of both pure and mixed states. In addition, the VQSD can be utilized as a supervised machine learning algorithm for multi-class classification. The area under the receiver operating characteristic curve obtained in numerical simulations with the Iris flower dataset ranges from 0.97 to 1 with an average of 0.985, demonstrating excellent performance of the VQSD classifier.

Optimal entanglement generation in GHZ-type states

The entanglement production is key for many applications in the realm of quantum information, but so is the identification of processes that allow to create entanglement in a fast and sustained way. Most of the advances in this direction have been circumscribed to bipartite systems only, and the rate of entanglement in multipartite system has been much less explored. Here we contribute to the identification of processes that favor the fastest and sustained generation of tripartite entanglement in a class of 3-qubit GHZ-type states. By considering a three-party interaction Hamiltonian, we analyze the dynamics of the 3-tangle and the entanglement rate to identify the optimal local operations that supplement the Hamiltonian evolution in order to speed-up the generation of three-way entanglement, and to prevent its decay below a predetermined threshold value. The appropriate local operation that maximizes the speed at which a highly-entangled state is reached has the advantage of requiring access to only one of the qubits, yet depends on the actual state of the system. Other universal (state-independent) local operations are found that conform schemes to maintain a sufficiently high amount of 3-tangle. Our results expand our understanding of entanglement rates to multipartite systems, and offer guidance regarding the strategies that improve the efficiency in various quantum information processing tasks.

Physical entanglement between localized orbitals

The goal of the present work is to guide the development of quantum technologies in the context of fermionic systems. For this, we first elucidate the process of entanglement swapping in electron systems such as atoms, molecules or solid bodies. This demonstrates the significance of the number-parity superselection rule and highlights the relevance of localized few-orbital subsystems for quantum information processing tasks. Then, we explore and quantify the entanglement between localized orbitals in two systems, a tight-binding model of non-interacting electrons and the hydrogen ring. For this, we apply the first closed formula of a faithful entanglement measure, derived in (arXiv:2207.03377) as an extension of the von Neumann entropy to genuinely correlated many-orbital systems. For both systems, long-distance entanglement is found at low and high densities η, whereas for medium densities, , practically only neighboring orbitals are entangled. The Coulomb interaction does not change the entanglement pattern qualitatively except for low and high densities where the entanglement increases as function of the distance between both orbitals.

Generalized Quantum Measurements on a Higher-Dimensional System via Quantum Walks.

Quantum measurements play a fundamental role in quantum mechanics. Especially, generalized quantum measurements provide a powerful and versatile tool to extract information from quantum systems. However, how to realize them on an arbitrary higher-dimensional quantum system remains a challenging task. Here we propose a simple recipe for the implementation of a general positive-operator valued measurement (POVM) on a higher-dimensional quantum system via a one-dimensional discrete-time quantum walk with a two-dimensional coin. Furthermore, using single photons and linear optics, we realize experimentally a symmetric, informationally complete (SIC) POVM on a three-dimensional system with high fidelity. As an application, we realize a qutrit state tomography with SIC-POVM and confirm that the infidelity scaling achieved by the qutrit SIC-POVM is as good as that based on mutually unbiased bases. Our study paves the way to explore physics and information in higher-dimensional quantum systems and finds applications in various quantum information processing tasks that rely on generalized quantum measurements.