Tripartite States Research Articles

Generation of a tripartite photonic state via a double-Λ configuration in a four-level system

Triphotons have a more abundant energy structure compared to biphotons. Furthermore, as the number of photons increases, excellent properties such as entangled multi-qubit states, high security, flexibility, and information capacity are observed. This leads to a growing demand for multi-body quantum information processing. Here, a method is proposed to generate a three-photon entangled state using a single six-wave mixing process in an atomic ensemble. The research examines the temporal correlation characteristics of the triphoton produced in photon coincidence counting measurements, with a focus on the linear and nonlinear susceptibilities of the six-wave mixing process. These properties primarily depend on the fifth-order nonlinear coupling coefficients responsible for the damping Rabi oscillations and the group delay determined by the longitudinal detuning function. To enhance the nonlinear interaction between the optical field and the atomic ensemble, placing the atomic ensemble in a high-quality cavity and utilizing laser cooling techniques to eliminate the internal Doppler broadening effect in the atomic gas hold promise.

A universal framework for entanglement detection under group symmetry

One of the fundamental questions in quantum information theory is determining entanglement of quantum states, which is generally an NP-hard problem. In this paper, we prove that all PPT (π―A⊗πB) -invariant quantum states are separable if and only if all extremal unital positive (πB,πA) -covariant maps are decomposable where πA,πB are unitary representations of a compact group and π A is irreducible. Moreover, an extremal unital positive (πB,πA) -covariant map L is decomposable if and only if L is completely positive or completely copositive. We then apply these results to prove that all PPT quantum channels of the form Φ(ρ)=aTr(ρ)dIdd+bρ+cρT+(1−a−b−c)diag(ρ) are entanglement-breaking, and that there is no A-BC PPT-entangled (U⊗U―⊗U) -invariant tripartite quantum state. The former strengthens some conclusions in (Vollbrecht and Werner 2001 Phys. Rev. A 64 062307; Kopszak et al 2020 J. Phys. A: Math. Theor. 53 395306), and the latter resolves some open questions raised in (Collins et al 2018 Linear Algebra Appl. 555 398–411).

Monogamy of quantum correlations shared in a cavity-freeoptomechanical system

In this work, we discuss the monogamy property of quantum correlations (entanglement and steering) distributed in a cavity-free optomechanical system. In a tripartite pure Gaussian state, we verify the hierarchy of the studied quantum correlations. We investigate in detail the CKW-type monogamy inequalities, based on Gaussian Rényi-2 entropy entanglement, as well as, Gaussian steering. We quantify genuine tripartite entanglement by using the minimum residual Gaussian entanglement. In addition, we consider the minimum residual Gaussian steering as a quantifier of genuine tripartite steering. Our results indicate that, in the one-mode versus two-mode Gaussian state, the correlations hierarchy was respected; in the considered pure state, the monogamy of entanglement and steering distribution was proven and the studied genuine tripartite correlations have similar time evolution under the same conditions.

Evidence of a significant full tripartite entanglement in a mixed spin-(1/2,1) Heisenberg tetramer

We rigorously analyze the full tripartite entanglement of a mixed spin-(1/2,1) Heisenberg tetramer in the presence of an external magnetic field. The tetramer consists of two mixed spin-(1/2,1) dimers arranged to form a square plaquette, with distinct exchange couplings J and J1 between spins from the same and different dimers, respectively. The full tripartite entanglement is classified according to the tripartite negativity NABC defined as a geometric mean of all possible bipartite negativities NA|BC, NB|AC, and NC|AB, when the degrees of freedom of the fourth spin D of the tetrapartite system ABCD are traced out. We demonstrate that for J1/J>1, both trimeric subsystems 1/2-1-1 and 1/2-1/2-1 exhibit tripartite entanglement mediated through the central spin. This entanglement becomes more robust upon the application of an external magnetic field. The opposite limit J1/J<1 leads to the spontaneous emergence of full tripartite entanglement solely within the subsystem 1/2-1-1. However, the increasing magnetic field swiftly disrupts the three-particle correlation across the relevant ground-state phase boundary. Additionally, we identify that in the isotropic limit J1/J=1, the ground-state degeneracy significantly reduces the strength of full tripartite entanglement and favors nontrivial subtypes of full nonseparable states with none or just one spin-dimer entanglement. Finally, we discuss in detail the thermal stability of all fully tripartite nonseparable states.

Conditions on detecting tripartite entangled state in psychophysical experiments

This paper explores the sensitivity of the human visual system to quantum entangled light. We examine the possibility of human subjects perceiving multipartite entangled state through psychophysical experiments. Our focus begins with a bipartite entangled state to make a comparative study with the literature by taking into account additive noise for false positive on bipartite entanglement perception by humans. After that, we limit our similar investigation to a tripartite entangled state for simplicity in higher dimensions. To model the photodetection by humans, we employ the probability of seeing determined for coherently amplified photons in Fock number states, including an additive noise. Our results indicate that detecting bipartite and tripartite entanglement with the human eye is possible for a certain range of additive noise levels and visual thresholds. Finally, we discuss several alternative amplification methods.Graphical abstract

Detection and measure of genuine entanglement based on the realignment of density matrices for tripartite quantum states

As one of the important types of entanglement, genuine multipartite entanglement plays a key role in both foundational and practical aspects of quantum information theory. In this manuscript, we study the genuine multipartite entanglement in tripartite quantum systems based on the enhanced realignment criterion. A family of sufficient conditions for detecting genuine tripartite entanglement are presented. Moreover, lower bounds of the genuine multipartite entanglement concurrence are derived. The detection power and advantages of our results are illustrated through several examples.

Sharing Genuine Entanglement of Generalized Tripartite States by Multiple Sequential Observers

Sharing Genuine Entanglement of Generalized Tripartite States by Multiple Sequential Observers

Effect of acceleration on information delocalization

We study the impact of acceleration on information delocalization under the Unruh (anti-Unruh) effect for two types of tripartite entangled states, namely the GHZ and W states. Our findings indicate that the anti-Unruh effect can result in stronger delocalization of quantum information, as measured by tripartite mutual information (TMI). Additionally, we show that the W state is more stable than the GHZ state under the influence of uniformly accelerated motion. Lastly, we extend our analysis to N-partite entangled states and product states.

Enhancement of multimode entanglement and asymmetric steering by noiseless linear amplification

Quantum entanglement and Einstein-Podolsky-Rosen (EPR) steering is an important resource for quantum information. However, it is very fragile and prone to decoherence. Recently, it has been shown that the noiseless linear amplification (NLA) which can be applied to any channel with loss and noise can effectively counteract the effect of quantum decoherence. Besides, the initial quantum correlation can even be exceed by using this method. Thus, it is a useful tool in enhancing quantum entanglement. In this paper, we apply NLA to the tripartite GHZ entangled state and analyze quantum entanglement and steering after NLA. The results showed that the NLA can effectively improve quantum entanglement and expand the range of quantum steering. Simultaneously, they also provide useful direction for the distillation of quantum state using NLA in practical quantum communication.

Intra‐Cavity Laser Manipulation of High‐Dimensional Non‐Separable States

AbstractNon‐separable states of structured light have the analogous mathematical forms with quantum entanglement, which offer an effective way to simulate quantum process. However, the classical multi‐partite non‐separable states analogue to multi‐particle entanglements can only be controlled by bulky free‐space modulation of light through coupling multiple degrees of freedom (DoFs) with orbital angular momentum (OAM) to achieve high dimensionality and other DoFs to emulate multi‐parties. In this paper, a scheme is proposed to directly emit multi‐partite non‐separable states from a simple laser cavity to mimic multi‐particle quantum entanglement. Through manipulating three DoFs as OAM, polarization, and wavevector inside a laser cavity, the eight‐dimensional (8D) tripartite states and all Greenberger‐Horne‐Zeilinger (GHZ)‐like states can be generated and controlled on demand. In addition, an effective method is proposed to perform state tomography employing convolutional neural network (CNN), for measuring the generated GHZ‐like states with highest fidelity up to 95.11%. This work reveals a feasibility of intra‐cavity manipulation of high‐dimensional multipartite non‐separable states, opening a compact device for quantum‐classical analogy and paving the path for advanced quantum scenarios.

Quantum mutual information redistribution in a pure tripartite state by a number partitioning algorithm

Quantum mutual information redistribution in a pure tripartite state by a number partitioning algorithm

Effect of relativistic acceleration on tripartite entanglement of Gaussian states

The performance of quantum information protocols can be impacted by the noninertial motion of parties such as in a gravitational field. Previous studies have primarily focused on the degradation of entanglement for global modes, revealing that bipartite entanglement vanishes in the limit of large acceleration, whereas tripartite entanglement does not. In this study, we examine the impact of acceleration on tripartite Gaussian resource states encoded in spatially localized wave packets. Contrarily to prior findings, we observe that genuine tripartite entanglement (GTE) vanishes in the limit of large acceleration for various initial states and observer trajectories.

Entanglement recovery by weak measurement reversal in tripartite systems

Entanglement protection from noisy environments is an essential task in practical quantum information and communication. In this paper, we investigate the entanglement recovery of an amplitude-damped tripartite GHZ state by a weak-measurement reversal procedure. In particular, we emphasize the key importance of the inequivalency of probability amplitudes of the tripartite system under the recovery technique. We explore the maximal and non-maximal tripartite entangled state scenarios under amplitude damping noise in the absence and presence of weak measurement reversal procedures. Importantly, the non-maximal entangled state turns out to be a good choice for the entanglement recovery via weak-measurement reversal procedure.

Polygamy Relation of Quantum Correlations with Equality

AbstractThis study provides a generalized definition of polygamy relations for any quantum correlation measures. Instead of the usual polygamy inequality, a polygamy relation with equality is given by introducing the polygamy weight. From the polygamy relation with equality, it presents polygamy inequalities satisfied by the βth power of the quantum correlation measures. Taking concurrence of assistance as an example, it further illustrates the significance and advantages of these relations. It also obtains a polygamy relation with equality by considering the one‐to‐group entanglements for any quantum entanglement measures that do not satisfy the polygamy relations. It demonstrates that such relations for tripartite states can be generalized to multipartite systems.

Soliton pulse pairs at multiple colours in normal dispersion microresonators

AbstractSoliton microcombs are helping to advance the miniaturization of a range of comb systems. These combs mode lock through the formation of short temporal pulses in anomalous dispersion resonators. Here, a new microcomb is demonstrated that mode locks through the formation of pulse pairs in coupled normal dispersion resonators. Unlike conventional microcombs, pulses in this system cannot exist alone, and instead phase lock in pairs wherein pulses in each pair feature different optical spectra. The pairwise mode-locking modality extends to multiple pulse pairs and beyond two rings, and it greatly constrains mode-locking states. Two- (bipartite) and three-ring (tripartite) states containing many pulse pairs are demonstrated, including crystal states. Pulse pairs can also form at recurring spectral windows. We obtained the results using an ultra-low-loss Si3N4 platform that has not previously produced bright solitons on account of its inherent normal dispersion. The ability to generate multicolour pulse pairs over multiple rings is an important new feature for microcombs. It can extend the concept of all-optical soliton buffers and memories to multiple storage rings that multiplex pulses with respect to soliton colour and that are spatially addressable. The results also suggest a new platform for the study of topological photonics and quantum combs.

Hawking effect can generate physically inaccessible genuine tripartite nonlocality

We explore the acceleration effect on the genuine tripartite nonlocality (GTN) for one or two accelerated detector(s) coupled to the vacuum field with initial mixed tripartite states. We show that the Hawking radiation degrades the physically accessible GTN, which suffers from “sudden death” at certain critical Hawking temperature. An novel phenomenon has been observed first time that the Hawking effect can generate the physically inaccessible GTN for fermion fields in curved spacetime, the “sudden birth” of the physically inaccessible GTN. This result shows that the GTN can pass through the event horizon of black hole for certain mixed initial states. We also derived analytically the tradeoff relations of genuine tripartite entanglement (GTE) and quantum coherence under the influence of Hawking effect.

Sharing tripartite nonlocality sequentially by arbitrarily many independent observers

Bipartite entangled states whose violations of the Clauser-Horne-Shimony-Holt Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs exist [Brown and Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider their analogs for tripartite systems: a tripartite entangled state is shared among Alice, Bob, and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie, who measures again with other measurements, and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies can share genuine nonlocality of the Greenberger-Horne-Zeilinger state via the violation of the Svetlichny inequality with Alice and Bob [S. Saha et al., Quantum Inf. Process. 18, 42 (2019); Zhang and Fei, Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of the Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with a single Alice and single Bob.

Geometric discord of tripartite quantum systems

We study the quantification of geometric discord for tripartite quantum systems. Firstly, we obtain the analytic formula of geometric discord for tripartite pure states. It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems, the results presented here show that this property is no longer true in tripartite systems. Furthermore, we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination, that is, we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement. Lastly, we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence. It is interesting that the frozen phenomenon exists for geometric discord in this scenario.

Ancilla-Assisted Generation of Photons from Vacuum via Time-Modulation of Extracavity Qubit.

We propose a scheme for the generation of photons from a vacuum via time-modulation of a quantum system indirectly coupled to the cavity field through some ancilla quantum subsystem. We consider the simplest case when the modulation is applied to an artificial two-level atom (we call 't-qubit', that can be located even outside the cavity), while the ancilla is a stationary qubit coupled via the dipole interaction both to the cavity and t-qubit. We find that tripartite entangled states with a small number of photons can be generated from the system ground state under resonant modulations, even when the t-qubit is far detuned from both the ancilla and the cavity, provided its bare and modulation frequencies are properly adjusted. We attest our approximate analytic results by numeric simulations and show that photon generation from vacuum persists in the presence of common dissipation mechanisms.

Quantum steering as a resource for secure tripartite quantum state sharing

Quantum state sharing (QSS) is a protocol by which a (secret) quantum state may be securely split into shares, shared between multiple potentially-dishonest players, and reconstructed. Crucially, the players are each assumed to be dishonest, and so QSS requires that only a collaborating authorized subset of players can access the original secret state; any dishonest unauthorized conspiracy cannot reconstruct it. We analyze a QSS protocol involving three untrusted players and demonstrate that quantum steering is the required resource enabling the protocol to proceed securely. We analyze the level of steering required to share any single-mode Gaussian secret which enables the states to be shared with the optimal use of resources.