Multiparticle Entangled States Research Articles

A Dynamic Semi-Quantum Private Comparison Protocol for Size Relations

Abstract Semi-quantum private comparison allows multiple ``classical'' users who have restricted quantum capabilities to compare their private data with the assistance of a quantum third party. In this work, we propose a novel dynamic semi-quantum private comparison protocol using a circular transmission mode along with $d$-dimensional single-particle states. The protocol enables the comparison of data size relations among several ``classical'' users, while the third party can only determine the relative sizes without accessing the users' secret information. Security evaluations demonstrate that the designed protocol withstands typical external and internal attacks. Compared to previous works, this protocol offers several improvements: first, it supports dynamic addition or removal of users, enhancing applicability in practical scenarios; second, it eliminates the need for pre-shared keys, reducing quantum resource consumption; third, it avoids the use of high-dimensional multi-particle entangled states, thereby enhancing the feasibility of implementation. Therefore, the proposed protocol may have more practical potential compared to previous protocols.

Hierarchical Controlled Joint Remote Implementation of the Partially Unknown Operations of m Qudits via m High-Dimensional Entangled States.

We present a protocol for the hierarchical controlled joint remote implementation of the partially unknown operations of m qudits belonging to some restricted sets by using m multiparticle high-dimensional entangled states as the quantum channel. All the senders share the information of the partially unknown operations and cooperate with each other to implement the partially unknown operations on the remote receiver's quantum system. The receivers are hierarchized in accordance with their abilities to reconstruct the desired state. The agents in the upper grade need only cooperate with one of the lower-grade agents, and the agents in the lower grade need the cooperation of all the other agents. The protocol has the advantage of having high channel capacity by using a high-dimensional entangle state as the quantum channel for the hierarchial controlled joint remote implementation of partially unknown quantum operations of m qudits.

A Multiparty Quantum Private Equality Comparison Scheme Relying on |GHZ3⟩ States

In this work, we present a new protocol that accomplishes multiparty quantum private comparison leveraging maximally entangled |GHZ3⟩ triplets. Our intention was to develop a protocol that can be readily executed by contemporary quantum computers. This is possible because the protocol uses only |GHZ3⟩ triplets, irrespective of the number n of millionaires. Although it is feasible to prepare multiparticle entangled states of high complexity, this is overly demanding on a contemporary quantum apparatus, especially in situations involving multiple entities. By relying exclusively on |GHZ3⟩ states, we avoid these drawbacks and take a decisive step toward the practical implementation of the protocol. An important quantitative characteristic of the protocol is that the required quantum resources are linear both in the number of millionaires and the amount of information to be compared. Additionally, our protocol is suitable for both parallel and sequential execution. Ideally, its execution is envisioned to take place in parallel. Nonetheless, it is also possible to be implemented sequentially if the quantum resources are insufficient. Notably, our protocol involves two third parties, as opposed to a single third party in the majority of similar protocols. Trent, commonly featured in previous multiparty protocols, is now accompanied by Sophia. This dual setup allows for the simultaneous processing of all n millionaires’ fortunes. The new protocol does not rely on a quantum signature scheme or pre-shared keys, reducing complexity and cost. Implementation wise, uniformity is ensured as all millionaires use similar private circuits composed of Hadamard and CNOT gates. Lastly, the protocol is information-theoretically secure, preventing outside parties from learning about fortunes or inside players from knowing each other’s secret numbers.

Entanglement-enhanced quantum metrology: From standard quantum limit to Heisenberg limit

Entanglement-enhanced quantum metrology explores the utilization of quantum entanglement to enhance measurement precision. When particles in a probe are prepared into a suitable quantum entangled state, they may collectively accumulate information about the physical quantity to be measured, leading to an improvement in measurement precision beyond the standard quantum limit and approaching the Heisenberg limit. The rapid advancement of techniques for quantum manipulation and detection has enabled the generation, manipulation, and detection of multi-particle entangled states in synthetic quantum systems such as cold atoms and trapped ions. This article aims to review and illustrate the fundamental principles and experimental progresses that demonstrate multi-particle entanglement for quantum metrology, as well as discuss the potential applications of entanglement-enhanced quantum sensors.

Controlled bidirectional remote implementations of partially unknown quantum operations

By blending the ideas of controlled teleportation, bidirectional teleportation and remote implementation of quantum operations, we investigate the bidirectional transmission of quantum operations under the control of one supervisor. Firstly, we provide a method for generating a class of multi-particle entangled states, including five-particle and seven-particle entangled states, using a nine-particle entangled state as an example. Then using our constructed five-particle entangled state as a quantum channel, we propose a new controlled bidirectional protocol for remotely implementing partially known quantum operations (PUQOs for short) of one qubit within the two restricted sets satisfying specific conditions. Subsequently, exploiting a nine-particle entangled state as the quantum channel, we extend it to the case of two-qubit quantum operations which come from eight restricted sets. Replacing two PUQO of two qubits by a PUQO of one qubit and a PUQO of two qubits, we put forward another new asymmetric controlled bidirectional protocol for remotely implementing PKQOs via a seven-particle entangled state as the quantum channel. In these protocols, by using universal recovered operations performed by the receivers, the senders can simultaneously exchange their PUQOs as long as the controller collaborates, where each PUQO acts on the corresponding unknown state owned by the remote recipient.

A quantum blind signature scheme based on dense coding for non-entangled states

In some schemes, quantum blind signatures require the use of difficult-to-prepare multiparticle entangled states. By considering the communication overhead, quantum operation complexity, verification efficiency and other relevant factors in practical situations, this article proposes a non-entangled quantum blind signature scheme based on dense encoding. The information owner utilizes dense encoding and hash functions to blind the information while reducing the use of quantum resources. After receiving particles, the signer encrypts the message using a one-way function and performs a Hadamard gate operation on the selected single photon to generate the signature. Then the verifier performs a Hadamard gate inverse operation on the signature and combines it with the encoding rules to restore the message and complete the verification. Compared with some typical quantum blind signature protocols, this protocol has strong blindness in privacy protection, and higher flexibility in scalability and application. The signer can adjust the signature operation according to the actual situation, which greatly simplifies the complexity of the signature. By simultaneously utilizing the secondary distribution and rearrangement of non-entangled quantum states, a non-entangled quantum state representation of three bits of classical information is achieved, reducing the use of a large amount of quantum resources and lowering implementation costs. This improves both signature verification efficiency and communication efficiency while, at the same time, this scheme meets the requirements of unforgeability, non-repudiation, and prevention of information leakage.

Efficient dynamic quantum secret sharing in pre-measurement and post-measurement phases

This study introduces a novel dynamic quantum secret sharing (DQSS) protocol that utilizes entanglement swapping, Bell measurements, and single-particle measurements to enable agent addition and revocation in both the pre-measurement and post-measurement phases. Since the dealer is only required to prepare Bell states for execution, the proposed DQSS offers greater flexibility and practicality compared to other existing protocols that rely on multiparticle entangled states and are limited to agent modifications in one phase. Furthermore, the proposed DQSS not only exhibits superior qubit efficiency to other related protocols but also demonstrates resilience against several notable attack methods, including Trojan horse and collusion attacks.

Implementing quantum anonymous multi-party ranking: the influence and application of the law of large numbers

Secure multi-party ranking is not only a pivotal component within the domain of secure multi-party computation but also holds extensive real-world applicability, given its efficacy in safeguarding the integrity and privacy of data. In this paper, we propose a verifiable quantum anonymous multi-party ranking protocol, which leverages the power of multi-particle entangled states in conjunction with the law of large numbers. The protocol achieves the secure ranking of participants’ private data while verifying their identities through the assistance of a semi-honest third party. We prove that the protocol is resistant to different types of attacks from internal or external attackers. In addition, the proposed protocol employs qubits as the information carriers, which improves the feasibility of the protocol. We demonstrate the feasibility of the protocol by using the online analog quantum computer of IBM Corporation placed on the cloud. Our research represents an innovative initiative that merges the realms of quantum cryptography and statistical analysis to address pertinent practical challenges.

Multipartite quantum key agreement against d-dimensional collective-dephasing noise

In this paper, we introduce a novel model for collective-dephasing noise in [Formula: see text]-dimensional space. After that, we construct a multi-particle entangled state to resist the given collective-dephasing noise. Based on the measurement laws of multi-particle entangled state under two different bases, we propose a multipartite quantum key agreement protocol. In this protocol, multiple participants would obtain [Formula: see text]-dimensional secret key even if the quantum channel is influenced by collective-dephasing noise. The security analysis indicates that this protocol can resist both dishonest participant attack and the outsider attacks which include intercept-resend attack and entangle-measure attack. By comparing with the existing QKA protocols, it is clear that our protocol has greater universality from the perspective of dimensionality and number of participants.

Generating Multiparticle Entangled States by Self-Organization of Driven Ultracold Atoms.

We describe a mechanism for guiding the dynamical evolution of ultracold atomic motional degrees of freedom toward multiparticle entangled Dicke-squeezed states, via nonlinear self-organization under external driving. Two examples of many-body models are investigated. In the first model, the external drive is a temporally oscillating magnetic field leading to self-organization by interatomic scattering. In the second model, the drive is a pump laser leading to transverse self-organization by photon-atom scattering in a ring cavity. We numerically demonstrate the generation of multiparticle entangled states of atomic motion and discuss prospective experimental realizations of the models. For the cavity case, the calculations with adiabatically eliminated photonic sidebands show significant momentum entanglement generation can occur even in the "bad cavity" regime. The results highlight the potential for using self-organization of atomic motion in quantum technological applications.

Multi-party private size comparison protocol under the semi-quantum condition

Based on -dimensional multiparticle maximal entangled states, a novel multi-party private comparison protocol under semi-quantum condition is proposed. With the help of a semi-honest quantum third party, classical participants can determine the size relationship of their privacies while keeping them private in the devised protocol. Compared with some similar protocols, the presented protocol performs better in terms of security and qubit efficiency. In addition, the effectiveness and the correctness of our protocol are verified with some examples and proofs. By the decoy particles and the pre-shared keys, the presented protocol can defend against the internal and the external attacks.

A protocol to create a multi-particle entangled state for quantum-enhanced sensing

We propose a protocol for generating multi-particle entangled states using coherent manipulation of atoms trapped in an optical cavity. We show how entanglement can be adiabatically produced with two control beams and by exploiting cavity-mediated interactions between the atoms. Our methods will allow for optimal generation of entanglement for the measurement protocol we propose. We discuss a possible experimental implementation and compare the performance of the states produced with those of classical states and ideal maximally-entangled Dicke states. We find that our states always feature metrological gain and even outperform ideal Dicke states in the measurement of magnetic field gradients. Due to the easy scalability, our entanglement protocol is a promising tool for quantum state engineering.

Quantifying multiparticle entanglement with randomized measurements

Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the potential of randomized measurements in order to probe the amount of entanglement contained in multiparticle quantum systems as quantified by the multiparticle concurrence. We further present a detailed statistical analysis of the underlying measurement resources required for a confident estimation of the introduced quantifiers using analytical tools from the theory of random matrices. The introduced framework is demonstrated by a series of numerical experiments analyzing the concurrence of typical multiparticle entangled states as well as of ensembles of output states produced by random quantum circuits. Finally, we examine the multiparticle entanglement of mixed states produced by noisy quantum circuits consisting of single- and two-qubit gates with non-vanishing depolarization errors, thus showing that our framework is directly applicable in the noisy intermediate-scale regime.

Quantum detectable Byzantine agreement for distributed data trust management in blockchain

No system entity within a contemporary distributed cyber system can be entirely trusted. Hence, the classic centralized trust management method cannot be directly applied to it. Blockchain technology is essential to achieving decentralized trust management, its consensus mechanism is useful in addressing large-scale data sharing and data consensus challenges. Herein, an n-party quantum detectable Byzantine agreement (DBA) based on the GHZ state to realize the data consensus in a quantum blockchain is proposed, considering the threat posed by the growth of quantum information technology on the traditional blockchain. Relying on the nonlocality of the GHZ state, the proposed protocol detects the honesty of nodes by allocating the entanglement resources between different nodes. The GHZ state is notably simpler to prepare than other multi-particle entangled states, thus reducing preparation consumption and increasing practicality. When the number of network nodes increases, the proposed protocol provides better scalability and stronger practicability than the current quantum DBA. In addition, the proposed protocol has the optimal fault-tolerant found and does not rely on any other presumptions. A consensus can be reached even when there are n−2 traitors. The performance analysis confirms viability and effectiveness through exemplification. The security analysis also demonstrates that the quantum DBA protocol is unconditionally secure, effectively ensuring the security of data and realizing data consistency in the quantum blockchain.

Entanglement-enhanced test proposal for local Lorentz-symmetry violation via spinor atoms

Invariance under Lorentz transformations is fundamental to both the standard model and general relativity. Testing Lorentz-symmetry violation (LSV) via atomic systems attracts extensive interests in both theory and experiment. In several test proposals, the LSV violation effects are described as a local interaction and the corresponding test precision can asymptotically reach the Heisenberg limit via increasing quantum Fisher information (QFI), but the limited resolution of collective observables prevents the detection of large QFI. Here, we propose a multimode many-body quantum interferometry for testing the LSV parameter κ via an ensemble of spinor atoms. By employing an N-atom multimode GHZ state, the test precision can attain the Heisenberg limit Δκ∝1/(F2N) with the spin length F and the atom number N. We find a realistic observable (i.e. practical measurement process) to achieve the ultimate precision and analyze the LSV test via an experimentally accessible three-mode interferometry with Bose condensed spin-1 atoms for example. By selecting suitable input states and unitary recombination operation, the LSV parameter κ can be extracted via realizable population measurement. Especially, the measurement precision of the LSV parameter κ can beat the standard quantum limit and even approach the Heisenberg limit via spin mixing dynamics or driving through quantum phase transitions. Moreover, the scheme is robust against nonadiabatic effect and detection noise. Our test scheme may open up a feasible way for a drastic improvement of the LSV tests with atomic systems and provide an alternative application of multi-particle entangled states.

Multi-User Measurement-Device-Independent Quantum Key Distribution Based on GHZ Entangled State.

As a multi-particle entangled state, the Greenberger–Horne–Zeilinger (GHZ) state plays an important role in quantum theory and applications. In this study, we propose a flexible multi-user measurement-device-independent quantum key distribution (MDI-QKD) scheme based on a GHZ entangled state. Our scheme can distribute quantum keys among multiple users while being resistant to detection attacks. Our simulation results show that the secure distance between each user and the measurement device can reach more than 280 km while reducing the complexity of the quantum network. Additionally, we propose a method to expand our scheme to a multi-node with multi-user network, which can further enhance the communication distance between the users at different nodes.

Generation of the GHZ and the W State in a Series of Rydberg Atoms Trapped in Optical Lattices

In this work, we present a quantum control methodology to create multi-particle entangled states of two typical classes, the W and the Greenberger-Horne-Zeilinger (GHZ). The methodology is demonstrated on a generation of the W and GHZ three-atomic states via the mechanism of two-photon passage using overlapping chirped pulses and the interplay of the chirp rate, the one-photon and two-photon detuning, the peak Rabi frequency and the strength of the Rydberg-Rydberg interactions. A chain of N alkali 87Rb atoms in an optical lattice interacting with two laser fields is modeled within a semi-classical theory. The strategy to create different classes of multiparticle entangled states was revealed through performed dressed state analysis

Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits.

Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28} dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.

Quantum multicast communication over the butterfly network

We propose a scheme where one can exploit auxiliary resources to achieve quantum multicast communication with network coding over the butterfly network. In this paper, we propose the quantum 2-pair multicast communication scheme, and extend it to k-pair multicast communication over the extended butterfly network. Firstly, an EPR pair is shared between each adjacent node on the butterfly network, and make use of local operation and classical communication to generate entangled relationship between non-adjacent nodes. Secondly, each sender adds auxiliary particles according to the multicast number k, in which the CNOT operations are applied to form the multi-particle entangled state. Finally, combined with network coding and free classical communication, quantum multicast communication based on quantum measurements is completed over the extended butterfly network. Not only the bottleneck problem is solved, but also quantum multicast communication can be completed in our scheme. At the same time, regardless of multicast number k, the maximum capacity of classical channel is 2 bits, and quantum channel is used only once.

A novel dynamic quantum secret sharing in high-dimensional quantum system

This paper proposed a novel dynamic quantum secret sharing protocol in high-dimensional quantum system. Via transmitting the particles circularly and local unitary operations, the dealer and all agents can share the multi-particle entangled GHZ state in high-dimensional quantum system. The proposed protocol allows a dealer to share the predetermined dits without directly distributing any piece of shares to agents. To recover the secrets, dealer and all agents only need to perform the single-particle measurement operation and then implement the simple modular arithmetic operation according to their corresponding measurement results. Besides, in the proposed protocol, only a little fraction of entangled GHZ states are employed for eavesdropping check instead of lots of decoy (or detecting) particles used in previous protocols. Since the protocol is designed in the high-dimensional quantum system, it makes our protocol have higher resource capacity and better security in detecting the illegal eavesdropper than former protocols designed in two-dimensional quantum system. Security analyses indicate that the proposed protocol is immune to general attacks of intercept-and-resend, entangle-and-measure, collusion, and revoked a dishonest agent. Furthermore, the efficiency of proposed DQSS protocol in noise environment is deduced through quantum fidelity. The obtained results indicate that the efficiency of proposed protocol decreases with the increase in channel noise parameter and it has a quite different efficiency in four types of noise, i.e., dit-flip, d-phase-flip, amplitude-damping and depolarizing.