Entangled Bell States Research Articles

Tomography of entangling two-qubit logic operations in exchange-coupled donor electron spin qubits

Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers.

Fast Photon-Mediated Entanglement of Continuously Cooled Trapped Ions for Quantum Networking.

We entangle two cotrapped atomic barium ion qubits by collecting single visible photons from each ion through invacuo 0.8NA objectives, interfering them through an integrated fiber beam splitter and detecting them in coincidence. This projects the qubits into an entangled Bell state with an observed fidelity lower bound of F>94%. We also introduce an ytterbium ion for sympathetic cooling to remove the need for recooling interruptions and achieve a continuous entanglement rate of 250 s^{-1}.

Polarization-entangled photon-pair source with van der Waals 3R-WS2 crystal

Ultracompact entangled photon sources are pivotal to miniaturized quantum photonic devices. Van der Waals (vdW) nonlinear crystals promise efficient photon-pair generation and on-chip monolithic integration with nanophotonic circuitry. However, it remains challenging to generate maximally entangled Bell states of photon pairs with high purity, generation rate, and fidelity required for practical applications. Here, we realize a polarization-entangled photon-pair source based on spontaneous parametric down conversion in an ultrathin rhombohedral tungsten disulfide (3R-WS2) crystal. This vdW entangled photonic source exhibits a high photon-pair purity with a coincidence-to-accidental ratio of above 800, a generation rate of 31 Hz, and two maximally polarization-entangled Bell states with fidelities exceeding 0.93 and entanglement degree over 0.97. These results stem from scalable optical nonlinearity, enhanced second-order susceptibility by electronic transitions, and a well-defined symmetry-enabled selection rule inherent in 3R-WS2. Our polarization entangled photon source can be integrated with photonic structures for generating more complex entangled states, thus paving an avenue for advanced quantum photonic systems toward computation and metrology.

Resumable probabilistic teleportation of a three qubit state using different quantum channels

In this paper we describe two different probabilistic teleportation protocols for teleporting the same unknown 3-qubit state from the sender Alice to the receiver Bob. The speciality of the state is that it remains a 2-qubit entangled state after any of the three involved qubits is eliminated by partial trace operation. One of the protocols utilizes a two and a three-qubit separate channels while in the other protocol, a five-qubit channel is utilized. One of the channels in the first protocol is a non-maximally entangled Bell state while the 5-qubit channel used in the case of the second protocol is non-maximally entangled. Both the teleportation schemes are probabilistic with the feature that in the case of failure of the teleportation, the state to be teleported is not lost to the sender. So the process can be repeated after failure till success is achieved. Moreover, one of the channels is recovered in the failure case. Both protocols are resumable in the above sense. The above is the speciality of the present work. We analyze the efficiency of our protocol which shows that the present two protocols are better performing than some existing ones.

Correlated noise enhancement of coherence and fidelity in coupled qubits

ABSTRACT It is generally assumed that environmental noise arising from thermal fluctuations are detrimental to preserving coherence and entanglement in a quantum system. In the simplest sense, dephasing and decoherence are tied to energy fluctuations driven by coupling between the system and the normal modes of the bath. Here, we explore the role of noise correlation in an open-loop model quantum communication system whereby the ‘sender’ and the ‘receiver’ are subject to local environments with various degrees of correlation or anti-correlation. We introduce correlation within the spectral density by solving multidimensional stochastic differential equations and introduce these into the Redfield equations of motion for the system density matrix. We find that correlation can enhance both the fidelity and purity of a maximally entangled (Bell) state. Moreover, by comparing the evolution of different initial Bell states, we show that one can effectively probe the correlation between two local environments. These observations may be useful in the design of high-fidelity quantum gates and communication protocols.

Macroscopic Bell state between a millimeter-sized spin system and a superconducting qubit

Entanglement is a fundamental property in quantum mechanics that systems share inseparable quantum correlation regardless of their mutual distances. Owing to the fundamental significance and versatile applications, the generation of quantum entanglement between macroscopic systems has been a focus of current research. Here we report on the deterministic generation and tomography of the macroscopically entangled Bell state in a hybrid quantum system containing a millimeter-sized spin system ( ∼1×1019 atoms) and a micrometer-sized superconducting qubit. The deterministic generation is realized by coupling the macroscopic spin system and the qubit via a microwave cavity. Also, we develop a joint tomography approach to confirming the deterministic generation of the Bell state, which gives a generation fidelity of 0.90±0.01 . Our work makes the macroscopic spin system the largest system (in the sense of atom number) capable of generating the maximally entangled quantum state.

Generating a maximally entangled state via a pure global noise environment

We studied the entangling power of two pure global noises, i.e. amplitude damping noise and classic noise. The entangling power of the two-qubit amplitude damping global noise periodically oscillates with time. Additionally, the entangling power of two-qubit global classical noise increases exponentially with time. The maximum entangling power of both of them exceeds that of the perfect entanglers. Based on this, we propose the conditions for generating a maximally entangled state with global noise acting on a two-qubit separable state. Only if the two-qubit composite system, which is initially in one of those product states: 12(|0⟩±|1⟩)⊗12(|0⟩±|1⟩) , |10⟩ and |01⟩ suffers an amplitude damping global noise, can we prepare this system in the maximally entangled state by appropriately controlling the evolution time of amplitude damping. Finally, we investigate the disentanglement of the maximum entangled Bell state using these two types of global noise. The two global noises cannot completely disentangle the Bell states Φ± . Under the influence of amplitude damping global noise, the entanglement of Bell state Ψ+ undergoes a cyclical variation, alternating between disappearance and recovery to reach maximum entanglement within one period. The entanglement of either Bell state Ψ+ or Ψ− is completely independent of global classical noise. The entanglement of Bell state Ψ− is also robust against amplitude damping global noise.

Room-Temperature Entanglement of the Nickel-Radical Molecular Complex (Et3NH)[Ni(hfac)2L] Reinforced by the Magnetic Field

Bipartite entanglement is comprehensively investigated in the mononuclear molecular complex (Et3NH)[Ni(hfac)2L], where HL denotes 2-(2-hydroxy-3-methoxy-5-nitrophenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-3-oxide-1-oxyl and hfacH stands for hexafluoroacetylacetone. From the magnetic point of view, the molecular compound (Et3NH)[Ni(hfac)2L] consists of an exchange-coupled spin-1 Ni2+ magnetic ion and a spin-12 nitronyl-nitroxide radical substituted nitrophenol. The nickel-radical molecular complex affords an experimental realization of a mixed spin-(12, 1) Heisenberg dimer with a strong antiferromagnetic exchange coupling, J/kB = 505 K, and two distinct g-factors, gRad = 2.005 and gNi = 2.275. By adopting this set of magnetic parameters, we demonstrate that the Zeeman splitting of a quantum ferrimagnetic ground-state doublet due to a weak magnetic field may substantially reinforce the strength of bipartite entanglement at low temperatures. The molecular compound (Et3NH)[Ni(hfac)2L] maintains sufficiently strong thermal entanglement, even at room temperature, vanishing only above 546 K. Specifically, the thermal entanglement in the nickel-radical molecular complex retains approximately 40% of the maximum value, corresponding to perfectly entangled Bell states at room temperature, which implies that this magnetic compound provides a suitable platform of a molecular qubit with potential implications for room-temperature quantum computation and quantum information processing.

Time evolution of entangled Bell states in coupled quantum dots in the presence of fluctuations

Time evolution of entangled Bell states in coupled quantum dots in the presence of fluctuations

A photonic engine fueled by entangled two atoms

Entangled states are an important resource for quantum information processing and for the fundamental understanding of quantum physics. An intriguing open question would be whether entanglement can improve the performance of quantum heat engines in particular. One of the promising platforms to address this question is to use entangled atoms as a non-thermal bath for cavity photons, where the cavity mirror serves as a piston of the engine. Here we theoretically investigate a photonic quantum engine operating under an effective reservoir consisting of quantum-correlated pairs of atoms. We find that maximally entangled Bell states alone do not help extract useful work from the reservoir unless some extra populations in the excited states or ground states are taken into account. Furthermore, high efficiency and work output are shown for the non-maximally entangled superradiant state, while negligible for the subradiant state due to lack of emitted photons inside the cavity. Our results provide insights in the role of quantum-correlated atoms in a photonic engine and present new opportunities in designing a better quantum heat engine.

From the classical Frenet–Serret apparatus to the curvature and torsion of quantum-mechanical evolutions. Part I. Stationary Hamiltonians

It is known that the Frenet–Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet–Serret apparatus specifies important geometric invariants, including the curvature and the torsion of a curve. It is also acknowledged in quantum information science that low complexity and high efficiency are essential features to achieve when cleverly manipulating quantum states that encode quantum information about a physical system. In this paper, we propose a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by dynamically evolving state vectors. Specifically, we propose a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced by a parallel-transported pure quantum state evolving unitarily under a stationary Hamiltonian specifying the Schrödinger equation. Our proposed constant curvature coefficient is given by the magnitude squared of the covariant derivative of the tangent vector [Formula: see text] to the state vector [Formula: see text] and represents a useful measure of the bending of the quantum curve. Our proposed constant torsion coefficient, instead, is defined in terms of the magnitude squared of the projection of the covariant derivative of the tangent vector [Formula: see text], orthogonal to both [Formula: see text] and [Formula: see text]. The torsion coefficient provides a convenient measure of the twisting of the quantum curve. Remarkably, we show that our proposed curvature and torsion coefficients coincide with those existing in the literature, although introduced in a completely different manner. Interestingly, not only we establish that zero curvature corresponds to unit geodesic efficiency during the quantum transportation in projective Hilbert space, but we also find that the concepts of curvature and torsion help enlighten the statistical structure of quantum theory. Indeed, while the former concept can be essentially defined in terms of the concept of kurtosis, the positivity of the latter can be regarded as a restatement of the well-known Pearson inequality that involves both the concepts of kurtosis and skewness in mathematical statistics. Finally, not only do we present illustrative examples with nonzero curvature for single-qubit time-independent Hamiltonian evolutions for which it is impossible to generate torsion, but we also discuss physical applications extended to two-qubit stationary Hamiltonians that generate curves with both nonzero curvature and nonvanishing torsion traced by quantum states with different degrees of entanglement, ranging from separable states to maximally entangled Bell states. In the Appendix C, we examine the different curvature and torsion characteristics of the three qubit [Formula: see text] and [Formula: see text] states under evolution by a quantum Heisenberg Hamiltonian.

Protecting quantum correlations of negative quantum states using weak measurement under non-Markovian noise

The weak measurement (WM) and quantum measurement reversal (QMR) are crucial in protecting the collapse of quantum states. The idea of WM and QMR has recently been used to protect and enhance quantum correlations and universal quantum teleportation (UQT) protocols. Here, we study the quantum correlations, maximal fidelity, and fidelity deviation of the two-qubit negative quantum states developed using discrete Wigner functions with(without) WM and QMR. To take into account the effect of a noisy environment, we evolve the states via non-Markovian amplitude damping and random telegraph noise quantum channels. To benchmark the performance of negative quantum states, we calculate their success probability. We compare our results with the two-qubit maximally entangled Bell state. Interestingly, we observe that some negative quantum states perform better with WM and QMR than the Bell state for different cases under evolution via noisy quantum channels.

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.

Protected simultaneous quantum remote state preparation scheme by weak and reversal measurements in noisy environments

We discuss a quantum remote state preparation protocol by which two parties, Alice and Candy, prepare a single-qubit and a two-qubit state, respectively, at the site of the receiver Bob. The single-qubit state is known to Alice while the two-qubit state which is a non-maximally entangled Bell state is known to Candy. The three parties are connected through a single entangled state which acts as a quantum channel. We first describe the protocol in the ideal case when the entangled channel under use is in a pure state. After that, we consider the effect of amplitude damping (AD) noise on the quantum channel and describe the protocol executed through the noisy channel. The decrement of the fidelity is shown to occur with the increment in the noise parameter. This is shown by numerical computation in specific examples of the states to be created. Finally, we show that it is possible to maintain the label of fidelity to some extent and hence to decrease the effect of noise by the application of weak and reversal measurements. We also present a scheme for the generation of the five-qubit entangled resource which we require as a quantum channel. The generation scheme is run on the IBMQ platform.

Reconfigurable Silicon Photonic Chip for the Generation Of Frequency-Bin-Entangled Qudits

Quantum optical microcombs in integrated ring resonators generate entangled photon pairs over many spectral modes, and allow the preparation of high-dimensional qudit states. Ideally, those sources should be programmable and have a high generation rate, with comb lines tightly spaced for the implementation of efficient qudit gates based on electro-optic frequency mixing. While these requirements cannot all be satisfied by a single resonator device, for which there is a trade-off between the high generation rate and tight bin spacing, a promising strategy is the use of multiple resonators, each generating photon pairs in specific frequency bins via spontaneous four-wave mixing. Based on this approach we present a programmable silicon photonics device for the generation of frequency-bin-entangled qudits, in which bin spacing, qudit dimension, and the bipartite quantum state can be reconfigured on chip. Using resonators with a radius of $22\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$, we achieve a high brightness [about $\mathrm{MHz}/(\mathrm{mW}{)}^{2}$] per comb line with a bin spacing of 15 GHz, and fidelities above 85% with maximally entangled Bell states up to a Hilbert space dimension of 16. By individually addressing each spectral mode, we realize states that cannot be generated on chip using a single resonator. We measure the correlation matrices of maximally entangled two-qubit and two-qutrit states on a set of mutually unbiased bases, finding fidelities exceeding 98%, and indicating that the source can find application in high-dimensional secure communication protocols.

Phonon-induced transition between entangled and nonentangled photon emission in constantly driven quantum-dot–cavity systems

Entangled photon pairs are essential for many applications in quantum technologies. Recent theoretical studies demonstrated that different types of entangled Bell states can be created in a constantly driven four-level quantum emitter-cavity system. Unlike other candidates for the realization of the four-level emitter, semiconductor quantum dots unavoidably interact with their environment, resulting in carrier-phonon interactions. Surprisingly, phonons change the entanglement of emitted photon pairs in a qualitative way, already at low temperatures on the order of 4 K. While one type of Bell state can still be generated using small driving strengths, the other type is suppressed due to phonon interactions in strongly-confined quantum dots. The degree of entanglement decreases with rising temperature and driving strength until it vanishes at a certain parameter value. Because it remains zero afterward, we encounter a phonon-induced transition between entangled and nonentangled photon emission that resembles a phase transition. The transition occurs at temperatures below 30 K and, independent of the driving strength, the concurrence as a function of the reduced temperature is found to obey a power law with exponent one near the transition point.

Entanglement of Trapped-Ion Qubits Separated by 230Meters.

We report on an elementary quantum network of two atomic ions separated by 230m. The ions are trapped in different buildings and connected with 520(2)m of optical fiber. At each network node, the electronic state of an ion is entangled with the polarization state of a single cavity photon; subsequent to interference of the photons at a beam splitter, photon detection heralds entanglement between the two ions. Fidelities of up to (88.0+2.2-4.7)% are achieved with respect to a maximally entangled Bell state, with a success probability of 4×10^{-5}. We analyze the routes to improve these metrics, paving the way for long-distance networks of entangled quantum processors.

Polarimetric Quantum-Strong Correlations with Independent Photons on the Poincaré Sphere

Controllable, quantum-strong correlations of polarization states can be implemented with multi-photon independent states. Polarization-based photonic quantum correlations can be traced back to the overlap of the polarization Stokes vectors on the Poincaré sphere between two polarization filters. The quantum Rayleigh scattering prevents a single photon from propagating in a straight line inside a dielectric medium, and it also provides a mechanism for the projective measurement of polarization. Complexities associated with single-photon sources and detectors can be eliminated because the quantum Rayleigh scattering in a dielectric medium destroys entangled photons. Entanglement-free, identical sources and processing devices give rise to correlations rather than these being caused by “quantum nonlocality”. These analytic developments were prompted by the vanishing expectation values of the Pauli spin vector for a single photon of maximally entangled photonic Bell states.

Demonstration of a Quantum Gate Using Electromagnetically Induced Transparency.

We demonstrate a native CNOT gate between two individually addressed neutral atoms based on electromagnetically induced transparency. This protocol utilizes the strong long-range interactions of Rydberg states to enable conditional state transfer on the target qubit when operated in the blockade regime. An advantage of this scheme is it enables implementation of multiqubit CNOT^{k} gates using a pulse sequence independent of qubit number, providing a simple gate for efficient implementation of digital quantum algorithms and stabilizer measurements for quantum error correction. We achieve a loss corrected gate fidelity of F_{CNOT}^{cor}=0.82(6), and prepare an entangled Bell state with F_{Bell}^{cor}=0.66(5), limited at present by laser power. We present a number of technical improvements to advance this to a level required for fault-tolerant scaling.

A new (w, t, n)-weighted threshold quantum secret sharing scheme based on two-qubit system

The weighted threshold structure of secret sharing has important application values in the hierarchical organization. In order to satisfy the actual needs of participants with different authority, only using single-particle transform of Bell state, we construct a new (w, t, n)-weighted threshold quantum secret sharing scheme in the two-qubit system based on the Chinese Remainder Theorem. The paper can share not only classical information but also quantum state information. Compared with the existing threshold schemes, the proposed scheme can greatly improve information transmission capacity by employing two-qubit entangled Bell state. Furthermore, the security analysis shows that our scheme cannot only detect a series of typical external attacks but resist forgery and collusion attacks.