Entanglement Correlations Research Articles

Quantum Private Comparison Based on Four-Particle Cluster State

A quantum private comparison (QPC) protocol enables two parties to securely compare their private data without disclosing the actual values to one another, utilizing quantum mechanics to maintain confidentiality. Many current QPC protocols mainly concentrate on comparing the equality of private information between two users during a single execution, which restricts their scalability. To overcome this limitation, we present an efficient QPC protocol aimed at evaluating the equality of private information between two groups of users in one execution. This is achieved by leveraging the entanglement correlations present in each particle of a four-particle cluster state. In our approach, users encode their private data using bit flip or phase shift operators on the quantum sequence they receive, which is then sent back to a semi-trusted party which then determines whether the secrets of the two groups are equal and communicates the results to the users. By employing this method and facilitating the distributed transmission of the quantum sequence, our protocol achieves a qubit efficiency of 50%. Security analyses reveal that neither external attacks nor insider threats can successfully compromise the confidentiality of private data.

Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review

AbstractThe detection and certification of entanglement and quantum correlations in materials is of fundamental and far‐reaching importance, and has seen significant recent progress. It impacts both the understanding of the basic science of quantum many‐body phenomena as well as the identification of systems suitable for novel technologies. Frameworks suitable to condensed matter that connect measurements to entanglement and coherence have been developed in the context of quantum information theory. These take the form of entanglement witnesses and quantum correlation measures.The underlying theory of these quantities, their relation to condensed matter experimental techniques, and their application to real materials are comprehensively reviewed. In addition, their usage in, e.g., protocols, the relative advantages and disadvantages of witnesses and measures, and future prospects in, e.g., correlated electrons, entanglement dynamics, and entangled spectroscopic probes, are presented. Consideration is given to the interdisciplinary nature of this emerging research and substantial ongoing progress by providing an accessible and practical treatment from fundamentals to application. Particular emphasis is placed on quantities accessible to collective measurements, including by susceptibility and spectroscopic techniques. This includes the magnetic susceptibility witness, one‐tangle, concurrence and two‐tangle, two‐site quantum discord, and quantum coherence measures such as the quantum Fisher information.

Effects of DM and KSEA interactions on entanglement, Fisher and Wigner-Yanase information correlations of two XYZ-Heisenberg-qubit states under a magnetic field

We employ entanglement negativity, local quantum uncertainty (LQU), and local quantum Fisher information (LQFI) to characterize thermal entanglement between two XYZ-Heisenberg-qubit states under the influence of Dzyaloshinsky-Moriya(DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions, as well as a magnetic field and thermal equilibrium temperature. A comparative examination reveals similar behaviors among these correlation measures. For the antiferromagnetic scenario, we observe that increasing the DM interaction parameter D z enhances thermal entanglement. Conversely, in the ferromagnetic case, the behavior of thermal entanglement differs with varying D z . Additionally, employing Kraus operators, we explore the performance of these quantifiers under decoherence. Notably, LQFI exhibits greater robustness than negativity and LQU, even displaying a frozen phenomenon at some time under dephasing effects.

Transfer of nonclassical correlations between bosonic field and atomic ensemble through electromagnetically induced transparency

Dark state polariton, as an important concept in the mechanism of electromagnetic induced transparency (EIT), can map the state of bosonic fields to atomic ensembles. To reflect the mapping ability of dark state polariton, we choose the odd and even bosonic coherent states as the probe field in EIT process, and employ spin squeezing, entanglement, and quantum correlation to characterize nonclassical correlations of atomic ensembles during the manipulation of the driving field. It is shown that the differences between the odd and even coherent states are comprehensively reflected in the three characterizations of nonclassical correlations generated through dark state polaritons. The even bosonic coherent states can perfectly transfer bosonic squeezing into atomic ensembles, resulting in spin squeezing. Although the odd bosonic coherent states cannot induce the spin squeezing, they have an advantage over the even bosonic coherent states in generating quantum entanglement and quantum correlations. Furthermore, we demonstrate that atomic ensembles can achieve significant spin squeezing with squeezing degree ∝ 1/N 2/3 through the one-axis twisting (OAT) model and two-axis twisting (TAT) model under the large N limit with the low excitation conditions, and the EIT mechanism was used to transfer the generated spin squeezing to the bosonic field, providing a feasible strategy for obtaining significant bosonic squeezing.

Entanglement harvesting and quantum discord of alpha vacua in de Sitter space

The CPT invariant vacuum states of a scalar field in de Sitter space, called α-vacua, are not unique. We explore the α-vacua from the quantum information perspective by a pair of static Unruh-DeWitt (UDW) detectors coupled to a scalar field with either monopole or dipole coupling, which are in time-like zero separation or space-like antipodal separation. The analytical form of the reduced final state of the UDW detector is derived. We study the entanglement harvesting and quantum discord of the reduced state, which characterize the quantum entanglement and quantum correlation of the underlying α-vacua, respectively. Our results imply that the quantum entanglement gravitated by de Sitter gravity behaves quite differently for time-like and space-like separations. It experiences “sudden death” for the former and grows for the latter as the measuring time or the value of α increases. This demonstrates the nonlocal nature of quantum entanglement. For the quantum discord, we find no “sudden death” behavior, and it experiences superhorizon suppression, which explains the superhorizon decoherence in the inflationary universe scenario. Overall, the time-like or space-like quantum entanglement and correlation behave differently on their dependence of α, measuring time and spectral gaps, with details discussed in this work.

Quantum entanglement and classical correlation have the same form

In agreement with the data, the quantum correlation between spins violates Bell’s inequality by following a cosine curve when one analyzer is rotated relative to the other. In contrast, the linear correlation attributed to hidden variables has never been observed. Besides these well-established facts, we show here that classical covariance, Pearson correlation, between spins projected as up or down on the analyzer axes also follows the cosine form hitherto uniquely ascribed to the quantum mechanical expectation value. The common cause for the classical correlation is the conservation of intrinsic angular momentum that aligns the two spins antiparallel at the breakup. Thus, as long as the spins retain their orientations relative to each other, the measurement of one spin in a chosen frame of reference also discloses the opposite orientation of the other in that frame. Realizing that classical correlation has the same functional form as quantum entanglement sheds light on the foundations of modern physics and quantum computing.

New Quantum Private Comparison Using Four-Particle Cluster State.

Quantum private comparison (QPC) enables two users to securely conduct private comparisons in a network characterized by mutual distrust while guaranteeing the confidentiality of their private inputs. Most previous QPC protocols were primarily used to determine the equality of private information between two users, which constrained their scalability. In this paper, we propose a QPC protocol that leverages the entanglement correlation between particles in a four-particle cluster state. This protocol can compare the information of two groups of users within one protocol execution, with each group consisting of two users. A semi-honest third party (TP), who will not deviate from the protocol execution or conspire with any participant, is involved in assisting users to achieve private comparisons. Users encode their inputs into specific angles of rotational operations performed on the received quantum sequence, which is then sent back to TP. Security analysis shows that both external attacks and insider threats are ineffective at stealing private data. Finally, we compare our protocol with some previously proposed QPC protocols.

Generation of stationary entanglement and quantum discord in an optomechanical system through three-level atoms

In this paper, we investigate the stationary entanglement and quantum discord between the cavity and mechanical oscillator mode of an optomechanical system whose cavity contains three-level atoms. We examine how sharing entanglement and correlations would be affected by increasing the level of atoms injected into the cavity. In particular, using the appropriate preference of injected atoms to the cavity and optical cavity detuning, we found the impact of atoms and couplings on the degree of steady-state entanglement and quantum discord. Consequently, the stationary entanglement and quantum discord together rise to a certain range of normalized detuning and atom injection levels. Furthermore, both entanglement and Gaussian quantum discord are enhanced when three-level atoms are present, and the maximum entanglement manifests closest to the ringing case. Moreover, we are aware that the system’s physical parameters affect the generation of stationary entanglement and quantum correlation. Therefore, these results may provide a platform for a valuable asset in the practical realization of continuous variable entanglement and quantum information processing.

Microwave quantum memcapacitor effect

Developing the field of neuromorphic quantum computing necessitates designing scalable quantum memory devices. Here, we propose a superconducting quantum memory device in the microwave regime, termed a microwave quantum memcapacitor. It comprises two linked resonators, the primary one is coupled to a Superconducting Quantum Interference Device, which allows for the modulation of the resonator properties through external magnetic flux. The auxiliary resonator, operated through weak measurements, provides feedback to the primary resonator, ensuring stable memory behavior. This device operates with a classical input in one cavity while reading the response in the other, serving as a fundamental building block toward arrays of microwave quantum memcapacitors. We observe that a bipartite setup can retain its memory behavior and gains entanglement and quantum correlations. Our findings pave the way for the experimental implementation of memcapacitive superconducting quantum devices and memory device arrays for neuromorphic quantum computing.

Generation of scalable many-body Bell correlations in spin chains with short-range two-body interactions

Dynamical generation of strong and scalable quantum resources, like many-body entanglement and Bell correlations, in spin-1/2 chains is possible with all-to-all interactions, either for constant interaction strength realizing one-axis twisting protocol or for power-law decaying potentials. We show, however, that such quantum resources can also be dynamically generated with a finite range of interactions. We identify a threshold range and indicate a threshold time when scalable quantum correlations appear. Finally, we show that the certification of generated states is accessible in modern quantum simulator platforms. Published by the American Physical Society 2024

Investigating entangled photons to quantify quantum correlations in dual optomechanical cavities.

Quantum correlations that go beyond quantum entanglement have a significant role in the fields of quantum information processing and quantum computation. In essence, when we describe a quantum system using pure states, quantum entanglement and quantum correlation are essentially indistinguishable. However, this equivalence breaks down when dealing with general mixed states. To contribute to understanding this distinction, we have considered a straightforward model for both generating and measuring these quantum correlations. We focus on two macroscopic mechanical resonators situated in separate Fabry–Perot cavities and coupled through the photon hopping process. Our model allows us to conduct a comprehensive examination and quantification of quantum correlations that extend beyond entanglement between these mechanical modes. Our approach begins with the determination of the global covariance matrix, serving as the foundation for calculating two key metrics: the Entropy of Formation and the Gaussian quantum Discord. These metrics enable us to quantify the extent of quantum entanglement and quantum correlations, respectively. Our analysis, based on these quantifiers, reveals that quantum discord serves as a more appropriate metric for characterizing the quantum correlations between the mechanical modes in an optomechanical quantum system, especially in the presence of robust photon hopping.

Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation. Essentially, for quantum systems prepared in pure states, it is difficult to differentiate between quantum entanglement and quantum correlation. Nonetheless, this indistinguishability is no longer holds for mixed states. To contribute to a better understanding of this differentiation, we have explored a simple model for both generating and measuring these quantum correlations. Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities, coupled through the photon hopping process. this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes. The key ingredient in analyzing quantum correlation in this system is the global covariance matrix. It forms the basis for computing two essential metrics: the logarithmic negativity ( ENm ) and the Gaussian interferometric power ( PGm ). These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations, respectively. Our study reveals that the Gaussian interferometric power ( PGm ) proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system, particularly in scenarios featuring resilient photon hopping.

Multipartite entanglement serves as a faithful detector for quantum phase transitions

We investigate quantum phase transitions (QPTs) in various spin chain systems using the multipartite entanglement measure τSEF based on the monogamy inequality of squared entanglement of formation (EOF). Our results demonstrate that τSEF is more effective and reliable than bipartite entanglement or bipartite correlation measures such as EOF, von Neumann entropy, and quantum discord in characterizing QPTs. τSEF not only detects critical points that may go unnoticed by other detectors but also avoids the issue of singularity at non-critical points encountered by other measures. Furthermore, by applying τSEF , we have obtained the phase diagram for the XY spin chain with three and four interactions and discovered a new quantum phase.

Quantum Metrology Assisted by Machine Learning

AbstractQuantum metrology aims to measure physical quantities based on fundamental quantum principles, enhancing measurement precision through resources like quantum entanglement and quantum correlations. This field holds promise for advancing quantum‐enhanced sensors, including atomic clocks and magnetometers. However, practical constraints exist in the four fundamental steps of quantum metrology, including initialization, sensing, readout, and estimation. Valuable resources, such as coherence time, impose limitations on the performance of quantum sensors. Machine learning, enabling learning and prediction without explicit knowledge, provides a powerful tool in optimizing quantum metrology with limited resources. This article reviews the fundamental principles, potential applications, and recent advancements in quantum metrology assisted by machine learning.

Circular semi-quantum secret sharing based on hybrid single particle and GHZ-type states

Semi-quantum secret sharing (SQSS) is a branch of quantum cryptography, with the advantage of fewer quantum resources. In this paper, we present a SQSS protocol based on hybrid single particle and GHZ-type states. Our protocol adopts circular transport structure to share secret information between classical and quantum parties, employing the entanglement correlation and uncertainty of GHZ-type states to guarantee the security of the transmission. Security analysis indicates that the proposed SQSS protocol enables resilience against various potential attacks such as measure-resend, entangle-measure, internal, and Trojan attacks. Furthermore, our protocol is easy to generalize to multi-party scenarios without increasing the complexity of state preparation. Compared with some typical SQSS protocols, our protocol has higher qubit efficiency without the need for entanglement swapping operations. The proposed SQSS protocol has the potential for broader applications in practical scenarios.

Semi‐Quantum Secure Multiparty Summation and its Applications to Anonymous Auction and Ranking

AbstractSemi‐quantum secure summation allows multiple parties with limited quantum capabilities to perform collective calculations under the premise of protecting privacy. However, current approaches are confined to low‐dimensional quantum states as information carriers and are restricted to scenarios involving two or three parties. This limitation hinders their universality and ability to fulfill the requirements of practical secure multiparty computations. To address these challenges, a novel semi‐quantum secure multiparty summation (SQSMS) protocol is proposed based on high‐dimensional entangled states and single‐particle states. The protocol leverages the entanglement correlation to guarantee the security of the transmission, enabling resistance against various potential attacks. Then, by utilizing the IBM Qiskit platform, corresponding quantum circuits and simulation results are presented to validate the feasibility and correctness of the protocol. Furthermore, building upon the foundation of the SQSMS protocol, semi‐quantum anonymous auction and anonymous ranking protocols are further constructed. Compared with previous approaches, the designed protocols cater to the requirements of their respective counterparts. Consequently, the approach may have broad applications in semi‐quantum secure multiparty computation scenarios.

Entanglement and quantum correlations in the honeycomb graphene lattice within the Hubbard model

Entanglement and quantum correlations in the honeycomb graphene lattice within the Hubbard model

Quantifying quantum correlations beyond entanglement via robust photon hopping in an optomechanical system

Quantum correlations beyond quantum entanglement represent vital resources in quantum information processing as well as in quantum computation. In fact, both quantum entanglement and quantum correlation are the same when the quantum system is described by pure states. However, this is not exactly the case when general mixed states are considered. In order to clarify this, a simple model has been proposed for the production and quantification of these quantum correlations between two mechanical resonators that are macroscopic in two Fabry–Pérot cavities optomechanical coupled by the photon hopping process. In this model, we analyze and investigate the quantification of the quantum correlation beyond the entanglement between the mechanical modes. We determine the global covariance matrix of the model from which we derive the expression of the entropy of formation ([Formula: see text]) as well as the Gaussian quantum discord ([Formula: see text]), which quantify the amount of quantum entanglement and quantum correlations, respectively. The analysis based on these two quantum correlations quantifiers shows that quantum discord is more appropriate to characterize the quantum correlations between the mechanical modes in an optomechanical quantum system in the presence of robust photon hopping.

Entanglement Correlation from a Non-degenerate Three-Level Laser with a Parametric Amplifier and Coupled to Vacuum Reservoir

The quantum properties of a non-degenerate three-level laser with the parametric amplifier and coupled to a thermal reservoir are thoroughly analyzed with the use of the pertinent master equation and stochastic differential equations associated with the normal ordering. Applying solutions of resulting differential equations, quadrature variance, the mean and variance of photon number, the photon number correlation are calculated. However, the two-mode driving light has no effect on the squeezing properties of the cavity modes. Employing the same solutions, one can also obtain anti normally ordered characteristic function defined in the Heisenberg picture. For a linear gain coefficient of (A = 100), for a cavity damping constant of K= 0:8, μ = 0.16 and for thermal reservoir nth = 0, the maximum intra cavity photon entanglement is found at steady state and at threshold to be 70%.

Classical and quantum correlations between two qubits interacting with a field in thermal spin states

In this manuscript, we introduce a quantum physical model consisting of two-atom system that interact with a quantized field initially prepared in the thermal spin states (TSSs). We study the effect of the main parameters of the model on the dynamical behavior atom–atom coherence, atoms-field entanglement, atom–atom entanglement and classical correlation. We show how the quantumness measures can be influenced by the spin number and thermal noise in the absence and presence of time-dependent coupling effect. We obtain that, despite the destructive influence of thermal noise, a considerable amount of coherence, entanglement and classical correlation still remain during the time evolution according the values of spin number. The results also show that the TSSs can offer the advantage of generating the maximal amount of coherence, entanglement and classical correlation during the dynamics.