Entangled Qubit States Research Articles

Harmonic flow-field representations of quantum bits and gates

We describe a general procedure for mapping arbitrary n-qubit states to two-dimensional (2D) vector fields. The mappings use complex rational function representations of individual qubits, producing classical vector field configurations that can be interpreted in terms of 2D inviscid fluid flows or electric fields. Elementary qubits are identified with localized defects in 2D harmonic vector fields, and multiqubit states find natural field representations via complex superpositions of vector field products. In particular, separable states appear as highly symmetric flow configurations, making them both dynamically and visually distinct from entangled states. The resulting real-space representations of entangled qubit states enable an intuitive visualization of their transformations under quantum logic operations. We demonstrate this for the quantum Fourier transform and the period finding process underlying Shor's algorithm, along with other quantum algorithms. Due to its generic construction, the mapping procedure suggests the possibility of extending concepts such as entanglement or entanglement entropy to classical continuum systems, and thus may help guide new experimental approaches to information storage and nonstandard computation. Published by the American Physical Society 2024

Dynamics of entangled Greenberger — Horne — Zeilinger states in three qubits thermal Tavis — Cummings model

In this paper, we investigated the dynamics of systems of two and three identical qubits interacting resonantly with a selected mode of a thermal field of a lossless resonator. We found solutions of the quantum time-dependent Liouville equation for various three- and two-qubit entangled states of qubits. Based on these solutions, we calculated the criterion of the qubit entanglement — fidelity. The results of numerical calculations of the fidelity showed that increasing the average number of photons in a mode leads to a decrease in the maximum degree of entanglement. It is shown that the two-qubit entangled state is more stable with respect to external noise than the three-qubit entangled Greenberger — Horne — Zeilinger states (GHZ). Moreover, a genuine entangled GHZ-state is more stable to noise than a GHZ-like entangled state.

Entanglemnt in nonlinear three-qubits Jaynes — Cummings

In this paper, we investigated the dynamics of entanglement of pairs of qubits in a system of three identical qubits that interact non-resonantly with the selected mode of a microwave resonator without loss with the Kerr medium by means of single-photon transitions. We have found solutions to the quantum time Schrodinger equation for the total wave function of the system for the initial separable, biseparable and true entangled states of qubits and the Fock initial state of the resonator field. Based on these solutions, the criterion of entanglement of qubit pairs — negativity is calculated. The results of numerical simulation of the negativity of qubit pairs have shown that the presence of disorder and Kerr nonlinearity in the case of an initial non-entangled state of a pair of qubits can lead to a significant increase in the degree of their entanglement. In the case of an initial entangled state of a pair of qubits, the disorder and the Kerr medium can lead to a significant stabilization of the initial entanglement.

Robust Engineering of Maximally Entangled States by Identical Particle Interferometry

AbstractThis study proposes a procedure for the robust preparation of maximally entangled states of identical fermionic qubits, studying the role played by particle statistics in the process. The protocol exploits externally activated noisy channels to reset the system to a known state. The subsequent interference effects generated at a beam splitter result in a mixture of maximally entangled Bell states and NOON states. It also discusses how every maximally entangled state of two fermionic qubits distributed over two spatial modes can be obtained from one another by fermionic passive optical transformations. Using a pseudospin‐insensitive, non‐absorbing, parity check detector, the proposed technique is thus shown to deterministically prepare any arbitrary maximally entangled state of two identical fermions. These results extend recent findings related to bosonic qubits. Finally, it analyzes the performance of the protocol for both bosons and fermions when the externally activated noisy channels are not used and the two qubits undergo standard types of noise. The results supply further insights toward viable strategies for noise‐protected entanglement exploitable in quantum‐enhanced technologies.

Sharing entanglement of the Werner state by arbitrarily many independent observers

The problem of sharing quantum correlations is an interesting problem in the study of quantum information theory. Silva et al. proposed the study of sharing quantum nonlocality at first. They studied the fundamental limits on nonlocality, asking whether a single pair of entangled qubits could generate a long sequence of nonlocal correlations. At the same time, the sequential scenario was also introduced first, in which Alice and Bob each have half of a pair of entangled qubit states. The first Bob measures his half and then passes his part to a second Bob who measures again and so on. Obviously, even partial preservation of entanglement in a shared state in spite of a few sequences of local operations performed by the sharing parties can be important for information processing schemes in which entanglement is utilized as a resource. Thus, the problem of sharing quantum entanglement has also been extensively investigated. Recently, Srivastava et al. proved that there exist a class of T-states whose entanglement can be shared by arbitrarily many independent observers in [<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.1103/PhysRevA.105.062413"><i>Phys. Rev. A</i> 2022 <b>105</b> 062413</ext-link>]. Here, we want to find whether there are other entangled states that can be shared entanglement arbitrarily many times. In this paper, we consider the problem of sharing quantum entanglement when the initial shared state is a two-qubit entangled Werner state. The goal is to maximize the number of Bobs that can share entanglement with a single Alice. By suitably choosing the entanglement witness operator and the unsharp measurement settings by the Bobs, we prove that there exist two-qubit entangled initial shared Werner states whose entanglement can be detected by arbitrarily many sequential observers Bobs with a single Alice. Then, we also consider the special case of the Werner state, that is, the maximally entangled state as the initial shared state. In this case, its entanglement can also be witnessed arbitrarily many times, and the number of Bobs increases with the decrease of parameter.

DYNAMICS OF THE THREE-QUBITS TAVIS — CUMMINGS MODEL

In this article, we have studied the entanglement dynamics of three identical qubits (natural or artificial two-level atoms) resonantly interacting with the one mode of the thermal field of a microwave lossless resonator via one-photon transitions. An exact solution of the quantum time Schrodinger equation is found for the total wave function of the system for the initial separable and entangled states of qubits and the Fock initial state of the resonator. On the basis of this solution, an exact solution of the quantum Liouville equation for the total time-dependent density matrix of the system in the case of a thermal field of the resonator is constructed. The exact solution for the full density matrix is used to calculate the criterion of entanglement of pairs of qubits negativity. The resultsof numerical simulation of the time dependence of the negativity of pairs of qubits showed that with an increase in the intensity of the thermal resonator field, the degree of entanglement of pairs of qubits decreases. It is also shown that In the model under consideration, for any initial states of qubits and intensities of the thermal field of the resonator, the effect of sudden death of entanglement takes place. This behavior of the entanglement parameter in the model under consideration differs from that in the two-qubit model. For two-qubit model, the effect of the sudden death of entanglement takes place only for the initial entangled states of qubits and intense thermal fields of the resonator.

Annihilating Entanglement Between Cones

Every multipartite entangled quantum state becomes fully separable after an entanglement breaking quantum channel acted locally on each of its subsystems. Whether there are other quantum channels with this property has been an open problem with important implications for entanglement theory (e.g., for the distillation problem and the PPT squared conjecture). We cast this problem in the general setting of proper convex cones in finite-dimensional vector spaces. The max-entanglement annihilating maps transform the k-fold maximal tensor product of a cone {textsf{C}}_1 into the k-fold minimal tensor product of a cone {textsf{C}}_2, and the pair ({textsf{C}}_1,{textsf{C}}_2) is called resilient if all max-entanglement annihilating maps are entanglement breaking. Our main result is that ({textsf{C}}_1,{textsf{C}}_2) is resilient if either {textsf{C}}_1 or {textsf{C}}_2 is a Lorentz cone. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation: As a warm-up, we use the multiplication tensors of real composition algebras to construct a finite family of generalized distillation protocols for Lorentz cones, containing the distillation protocol for entangled qubit states by Bennett et al. (Phys Rev Lett 76(5):722, 1996) as a special case. Then, we construct an infinite family of protocols using solutions to the Hurwitz matrix equations. After proving these results, we focus on maps between cones of positive semidefinite matrices, where we derive necessary conditions for max-entanglement annihilation similar to the reduction criterion in entanglement distillation. Finally, we apply results from the theory of Banach space tensor norms to show that the Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied.

Entangled Qubit States and Linear Entropy in the Probability Representation of Quantum Mechanics.

The superposition states of two qubits including entangled Bell states are considered in the probability representation of quantum mechanics. The superposition principle formulated in terms of the nonlinear addition rule of the state density matrices is formulated as a nonlinear addition rule of the probability distributions describing the qubit states. The generalization of the entanglement properties to the case of superposition of two-mode oscillator states is discussed using the probability representation of quantum states.

Rabi Oscillations, Entanglement and Teleportation in the Anti-Jaynes-Cummings Model

This paper provides a scheme for generating maximally entangled qubit states in the anti-Jaynes-Cummings interaction mechanism, so called entangled anti-polariton qubit states. We demonstrate that in an initial vacuum-field, Rabi oscillations in a cavity mode in the anti-Jaynes-Cummings interaction process, occur in the reverse sense relative to the Jaynes-Cummings interaction process and that time evolution of entanglement in the anti-Jaynes-Cummings interaction process takes the same form as in the Jaynes-Cummings interaction process. With the generated anti-polariton qubit state as one of the initial qubits, we present quantum teleportation of an atomic quantum state by applying entanglement swapping protocol achieving an impressive maximal teleportation fidelity~$F_\rho=1$.

Observation of the Dipole Blockade Effect in Detecting Rydberg Atoms by the Selective Field Ionization Method

The dipole blockade effect at laser excitation of mesoscopic ensembles of Rydberg atoms lies in the fact that the excitation of one atom to a Rydberg state blocks the excitation of other atoms due to the shift in the collective energy levels of interacting Rydberg atoms. It is used to obtain the entangled qubit states based on single neutral atoms in optical traps. In this paper, we present our experimental results on the observation of the dipole blockade for mesoscopic ensembles of 1-5 atoms when they are detected by the selective field ionization method. We investigated the spectra of the three-photon laser excitation $ 5S_{1/2} \to 5P_{3/2} \to 6S_{1/2} \to nP_{3/2} $ of cold Rb Rydberg atoms in a magneto-optical trap. We have found that for mesoscopic ensembles this method allows only a partial dipole blockage to be observed. This is most likely related to the presence of parasitic electric fields reducing the interaction energy of Rydberg atoms, the decrease in the probability of detecting high states, and the strong angular dependence of the interaction energy of Rydberg atoms in a single interaction volume.

Transferring entangled states of photonic cat-state qubits in circuit QED

We propose a method for transferring quantum entangled states of two photonic cat-state qubits (cqubits) from two microwave cavities to the other two microwave cavities. This proposal is realized by using four microwave cavities coupled to a superconducting flux qutrit. Because of using four cavities with different frequencies, the inter-cavity crosstalk is significantly reduced. Since only one coupler qutrit is used, the circuit resource is minimized. The entanglement transfer is completed with a singlestep operation only, thus this proposal is quite simple. The third energy level of the coupler qutrit is not populated during the state transfer, therefore decoherence from the higher energy level is greatly suppressed. Our numerical simulations show that high-fidelity transfer of two-cqubit entangled states from two transmission line resonators to the other two transmission line resonators is feasible with current circuit QED technology. This proposal is universal and can be applied to accomplish the same task in a wide range of physical systems, such as four microwave or optical cavities, which are coupled to a natural or artificial three-level atom.

Apollonius Representation and Complex Geometry of Entangled Qubit States

A representation of one qubit state by points in complex plane is proposed, such that the computational basis corresponds to two fixed points at a finite distance in the plane. These points represent common symmetric states for the set of quantum states on Apollonius circles. It is shown that, the Shannon entropy of one qubit state depends on ratio of probabilities and is a constant along Apollonius circles. For two qubit state and for three qubit state in Apollonius representation, the concurrence for entanglement and the Cayley hyperdeterminant for tritanglement correspondingly, are constant on the circles as well. Similar results are obtained also for n-tangle hyperdeterminant with even number of qubit states. It turns out that, for arbitrary multiple qubit state in Apollonius representation, fidelity between symmetric qubit states is also constant on Apollonius circles. According to these, the Apollonius circles are interpreted as integral curves for entanglement characteristics. The bipolar and the Cassini representations for qubit state are introduced, and their relations with qubit coherent states are established. We proposed the differential geometry for qubit states in Apollonius representation, defined by the metric on a surface in conformal coordinates, as square of the concurrence. The surfaces of the concurrence, as surfaces of revolution in Euclidean and Minkowski spaces are constructed. It is shown that, curves on these surfaces with constant Gaussian curvature becomes Cassini curves.

Complete list of tight Bell inequalities for two parties with four binary settings

We give the complete list of 175 facet Bell inequalities for the case where Alice and Bob each choose their measurements from a set of four binary outcome measurements. For each inequality we compute the maximum quantum violation for qubits, the resistance to noise, and the minimal detection efficiency required for closing the detection loophole with maximally entangled qubit states, in the case where both detectors have the same efficiency (symmetric case).

On-chip frequency combs and telecommunications signal processing meet quantum optics

Entangled optical quantum states are essential towards solving questions in fundamental physics and are at the heart of applications in quantum information science. For advancing the research and development of quantum technologies, practical access to the generation and manipulation of photon states carrying significant quantum resources is required. Recently, integrated photonics has become a leading platform for the compact and cost-efficient generation and processing of optical quantum states. Despite significant advances, most on-chip nonclassical light sources are still limited to basic bi-photon systems formed by two-dimensional states (i.e., qubits). An interesting approach bearing large potential is the use of the time or frequency domain to enabled the scalable onchip generation of complex states. In this manuscript, we review recent efforts in using on-chip optical frequency combs for quantum state generation and telecommunications components for their coherent control. In particular, the generation of bi- and multi-photon entangled qubit states has been demonstrated, based on a discrete time domain approach. Moreover, the on-chip generation of high-dimensional entangled states (quDits) has recently been realized, wherein the photons are created in a coherent superposition of multiple pure frequency modes. The time- and frequency-domain states formed with on-chip frequency comb sources were coherently manipulated via off-the-shelf telecommunications components. Our results suggest that microcavity-based entangled photon states and their coherent control using accessible telecommunication infrastructures can open up new venues for scalable quantum information science.

Frequency Control of Single Quantum Emitters in Integrated Photonic Circuits.

Generating entangled graph states of qubits requires high entanglement rates with efficient detection of multiple indistinguishable photons from separate qubits. Integrating defect-based qubits into photonic devices results in an enhanced photon collection efficiency, however, typically at the cost of a reduced defect emission energy homogeneity. Here, we demonstrate that the reduction in defect homogeneity in an integrated device can be partially offset by electric field tuning. Using photonic device-coupled implanted nitrogen vacancy (NV) centers in a GaP-on-diamond platform, we demonstrate large field-dependent tuning ranges and partial stabilization of defect emission energies. These results address some of the challenges of chip-scale entanglement generation.

Harvesting Multiqubit Entanglement from Ultrastrong Interactions in Circuit Quantum Electrodynamics.

We analyze a multiqubit circuit QED system in the regime where the qubit-photon coupling dominates over the system's bare energy scales. Under such conditions a manifold of low-energy states with a high degree of entanglement emerges. Here we describe a time-dependent protocol for extracting these quantum correlations and converting them into well-defined multipartite entangled states of noninteracting qubits. Based on a combination of various ultrastrong-coupling effects, the protocol can be operated in a fast and robust manner, while still being consistent with experimental constraints on switching times and typical energy scales encountered in superconducting circuits. Therefore, our scheme can serve as a probe for otherwise inaccessible correlations in strongly coupled circuit QED systems. It also shows how such correlations can potentially be exploited as a resource for entanglement-based applications.

Accurate calculation of the geometric measure of entanglement for multipartite quantum states

This article proposes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction. Numerical examples are benchmarked and compared. Furthermore, we search for highly entangled qubit states to show the applicability of this method.

Absolutely Maximally Entangled States of Seven Qubits Do Not Exist.

Pure multiparticle quantum states are called absolutely maximally entangled if all reduced states obtained by tracing out at least half of the particles are maximally mixed. We provide a method to characterize these states for a general multiparticle system. With that, we prove that a seven-qubit state whose three-body marginals are all maximally mixed, or equivalently, a pure ((7,1,4))_{2} quantum error correcting code, does not exist. Furthermore, we obtain an upper limit on the possible number of maximally mixed three-body marginals and identify the state saturating the bound. This solves the seven-particle problem as the last open case concerning maximally entangled states of qubits.

Loss-tolerant parity measurement for distant quantum bits

We propose a scheme to measure the parity of two distant qubits, while ensuring that losses on the quantum channel between them does not destroy coherences within the parity subspaces. This capability enables deterministic preparation of highly entangled qubit states whose fidelity is not limited by the transmission loss. The key observation is that for a probe electromagnetic field in a particular quantum state, namely a superposition of two coherent states of opposite phases, the transmission loss stochastically applies a near-unitary back-action on the probe state. This leads to a parity measurement protocol where the main effect of the transmission losses is a decrease in the measurement strength. By repeating the non-destructive (weak) parity measurement, one achieves a high-fidelity entanglement in spite of a significant transmission loss.

Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers

Although superconducting systems provide a promising platform for quantum computing, their networking poses a challenge because they cannot be interfaced to light, the medium used to send quantum signals through channels at room temperature. We show that mechanical oscillators can mediate such coupling and light can be used to measure the joint state of two distant qubits. The measurement provides information on the total spin of the two qubits such that entangled qubit states can be postselected. Entanglement generation is possible without ground-state cooling of the mechanical oscillators for systems with optomechanical cooperativity moderately larger than unity; in addition, our setup tolerates a substantial transmission loss. The approach is scalable to the generation of multipartite entanglement and represents a crucial step towards quantum networks with superconducting circuits.