Fidelity Of State Research Articles

Geometric quench in the fractional quantum Hall effect: Exact solution in quantum Hall matrix models and comparison with bimetric theory

We investigate the recently introduced geometric quench protocol for fractional quantum Hall (FQH) states within the framework of exactly solvable quantum Hall matrix models. In the geometric quench protocol a FQH state is subjected to a sudden change in the ambient geometry, which introduces anisotropy into the system. We formulate this quench in the matrix models and then we solve exactly for the post-quench dynamics of the system and the quantum fidelity (Loschmidt echo) of the post-quench state. Next, we explain how to define a spin-2 collective variable $\hat{g}_{ab}(t)$ in the matrix models, and we show that for a weak quench (small anisotropy) the dynamics of $\hat{g}_{ab}(t)$ agrees with the dynamics of the intrinsic metric governed by the recently discussed bimetric theory of FQH states. We also find a modification of the bimetric theory such that the predictions of the modified bimetric theory agree with those of the matrix model for arbitrarily strong quenches. Finally, we introduce a class of higher-spin collective variables for the matrix model, which are related to generators of the $W_{\infty}$ algebra, and we show that the geometric quench induces nontrivial dynamics for these variables.

High production rate of single-photon and two-photon Fock states for quantum state engineering.

We report the implementation of a high-rate source of single- and two-photon states. By combining the advantages of short pulses and cavities, heralding rates as high as 200 kHz have been obtained for the single photons, as well as 250 Hz for the two-photon states. In this setup, homodyne measurements are conditioned by the heralding of the quantum states thanks to the introduction of a low-loss optical delay line in the heralded states path. This enables the detection of most of the heralded events, and fidelities reaching 68.5% (91% with correction for detection efficiency) and 50.4% (85% with correction) were obtained for the single- and two-photon states, respectively. Such high rates and fidelities in the generation of elementary Fock states may open the path for the production of complex quantum states.

Decoherence of quantum systems sequentially interacting with a common environment

A composite quantum channel is derived for two independent quantum systems that interact sequentially with a common environment. One of the two quantum systems first interacts with the environment for a finite time, and after that the other one interacts with the same environment. In the process, the environment does not simultaneously interact with the two quantum systems. It is important to note that the second quantum system interacts with the environment that has been disturbed by the first one. As a result, the correlation between the two quantum systems, not directly interacting with each other, is created through the environment. An approximation to the composite quantum channel is also provided, which is applicable if a correlation time of the environment is not so long. When two independent qubits interact sequentially with a common bosonic environment via a dephasing coupling, it is explicitly shown that the time evolution of the second qubit can be non-Markovian due to the disturbance effect caused by the first qubit, even if the time evolution of the first qubit is Markovian. Entanglement, total, classical, and quantum correlations are calculated to find how the disturbance affects bipartite correlations. Furthermore, in state transmission through the composite quantum channel, it is found that the fidelity of quantum states can be enhanced by the disturbance effect.

12-Photon Entanglement and Scalable Scattershot Boson Sampling with Optimal Entangled-Photon Pairs from Parametric Down-Conversion.

Entangled-photon sources with simultaneously near-unity heralding efficiency and indistinguishability are the fundamental elements for scalable photonic quantum technologies. We design and realize a degenerate telecommunication wavelength entangled-photon source from an ultrafast pulsed laser pumped spontaneous parametric down-conversion (SPDC), which shows simultaneously 97% heralding efficiency and 96% indistinguishability between independent single photons without narrow-band filtering. Such a beamlike and frequency-uncorrelated SPDC source allows generation of the first 12-photon genuine entanglement with a state fidelity of 0.572±0.024. We further demonstrate a blueprint of scalable scattershot boson sampling using 12 SPDC sources and a 12×12 mode interferometer for three-, four-, and five-boson sampling, which yields count rates more than 4 orders of magnitude higher than all previous SPDC experiments.

Noiseless linear amplification for the single-photon entanglement of arbitrary polarization–time-bin qudit**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474168 and 11747161), the Priority Academic Program Development of Jiangsu Higher Education Institutions, China, and the China Postdoctoral Science Foundation (Grant No. 2018M642293).

Single-photon entanglement (SPE) is an important source in quantum communication. In this paper, we put forward a single-photon-assisted noiseless linear amplification protocol to protect the SPE of an arbitrary polarization–time-bin qudit from the photon transmission loss caused by the practical channel noise. After the amplification, the fidelity of the SPE can be effectively increased. Meanwhile, the encoded polarization–time-bin features of the qudit can be well preserved. The protocol can be realized under the current experimental conditions. Moreover, the amplification protocol can be extended to resist complete photon loss and partial photon loss during the photon transmission. After the amplification, we can not only increase the fidelity of the target state, but also solve the decoherence problem simultaneously. Based on the above features, our amplification protocol may be useful in future quantum communication.

High-performance source of spectrally pure, polarization entangled photon pairs based on hybrid integrated-bulk optics.

Entangled photon pair sources based on bulk optics are approaching optimal design and implementation, with high state fidelities, spectral purities and heralding efficiencies, but generally low brightness. Integrated entanglement sources, while providing higher brightness and low-power operation, often sacrifice performance in output state quality and coupling efficiency. Here we present a polarization-entangled pair source based on a hybrid approach of waveguiding and bulk optics, addressing every metric simultaneously. We show 96 % fidelity to the singlet state, 82 % Hong-Ou-Mandel interference visibility, 43 % average Klyshko efficiency, and a high brightness of 2.9 × 106 pairs/(mode·s·mW), while requiring only microwatts of pump power.

A Model for Immune Noise Towards High-Fidelity Quantum Secure Communication

In this paper, we examine unified framework of high-fidelity entangled quantum secure Communication channels under noise. We adopt system evolution density matrix to calculate the individual and average fidelity of initial states. We adjust intensity levels of noise with respect to the surroundings. Based on quantum entanglement and unitary transformation, we develop and implement a model for four types of noise that act on the quantum bits at different intensity levels. We analyze the model with quantum bits produced against the immune noise based on density matrix. Our propose model for immune noise is not only efficient and robust, but also achieves high-fidelity for secure quantum communication.

Quantum coherence as indicators of quantum phase transitions, factorization and thermal phase transitions in the anisotropic XY model

Quantifying quantum coherence has attracted considerable interests. In the present work, we employ two measures of quantum coherence recently proposed in terms of the skew information and the trace norm, respectively, to investigate the quantum phase transitions (QPTs), factorization in the XY model and the thermal phase transitions (TPTs) in the transverse field Ising model. Two quantifications of quantum nonlocality via the same distance measure of the quantum coherence are also studied for reference. It is shown that two types of quantum coherence are reliable in identifying QPTs and TPTs. However, only the quantum coherence based on the skew information can detect factorization. In addition, the quantum coherence and nonlocality measured via the same distance space have similar finite temperature scaling law, while the quantum coherence based on skew information and trace norm has different finite temperature scaling law. Moreover, the skew-information-based quantum coherence at finite temperature suggests that factorization vanishes when temperature exceeds 0.02 (Boltzmann constant $$k_{B} = 1$$ ), which is in agreement with the results of the fidelity for states with different distances of spin-pairs.

Two-qubit mixed states and teleportation fidelity: purity, concurrence, and beyond

To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fidelity of a teleported state depends on the resource state purity and entanglement, as characterized by concurrence. Concurrence and purity are functions of state parameters. However, it turns out that a state with larger purity and concurrence, may have comparatively smaller fidelity. By computing teleportation fidelity, concurrence and purity for two-qubit X-states, we show it explicitly. We further show that fidelity changes monotonically with respect to functions of parameters - other than concurrence and purity. A state with smaller concurrence and purity, but larger value of one of these functions has larger fidelity. These functions, thus characterize nonlocal classical and/or quantum properties of the state that are not captured by purity and concurrence alone. In particular, concurrence is not enough to characterize the entanglement properties of a two-qubit mixed state.

Entanglement of Three-Qubit Random Pure States.

We study entanglement properties of generic three-qubit pure states. First, we obtain the distributions of both the coefficients and the only phase in the five-term decomposition of Acín et al. for an ensemble of random pure states generated by the Haar measure on . Furthermore, we analyze the probability distributions of two sets of polynomial invariants. One of these sets allows us to classify three-qubit pure states into four classes. Entanglement in each class is characterized using the minimal Rényi-Ingarden-Urbanik entropy. Besides, the fidelity of a three-qubit random state with the closest state in each entanglement class is investigated. We also present a characterization of these classes in terms of the corresponding entanglement polytope. The entanglement classes related to stochastic local operations and classical communication (SLOCC) are analyzed as well from this geometric perspective. The numerical findings suggest some conjectures relating some of those invariants with entanglement properties to be ground in future analytical work.

Engineering multipartite steady entanglement of distant atoms via dissipation

We propose a scheme for generating an entangled state for three atoms trapped in separate optical cavities that are coupled to each other through two optical fibers based on coherent driving and dissipation, which are induced by the classical fields and the decay of non-local bosonic modes, respectively. In our scheme, the interaction time need not be controlled strictly in the overall dynamics process, and the cavity field decay can be changed into a vital resource. The numerical simulation shows that the fidelity of the target state is insensitive to atomic spontaneous emission, and our scheme is good enough to generate the W state of distant atoms with a high fidelity and purity. In addition, the present scheme can also be generalized to prepare the N-partite W state of distant atoms.

Weak measurement for improving the efficiency of remote state preparation in noisy

Quantum communication provides a new way for transmitting highly sensitive information. But the existence of quantum noise inevitably affects the security and reliability of a quantum communication system. The technique of weak measurement and its reversal measurement (WMRM) has been proposed to suppress the effect of quantum noise, especially, the amplitude-damping noise. Taking a GHZ based remote state preparation (RSP) scheme as an example, we discuss the effect of WMRM for suppressing four types of quantum noise that usually encountered in real-world, i.e., not only the amplitude-damping noise, but also the bit-flip, phase-flip (phase-damping) and depolarizing noise. And we give a quantitative study on how much a quantum output state can be improved by WMRM in noisy environment. It is shown that the technique of WMRM has certain effect for improving the fidelity of the output state in the amplitude-damping noise, and only has little effect for suppressing the depolarizing noise, while has no effect for suppressing the bit-flip and phase-flip (phase-damping) noise. Our result is helpful for improving the efficiency of entanglement-based quantum communication systems in real implementation.

Quantum phase transition in a two-dimensional quantum Ising model: Tensor network states and ground-state fidelity

The purpose of this paper is to describe how to describe the phase transition of quantum multibody system from the perspective of the basic concept of quantum information science - fidelity. For systems the traditional way of characterization that undergo a quantum phase transition is Landau’s introduction of order and the fluctuation. In particular, for phase transitions caused by spontaneous breaking symmetry, that is, different ground state wave functions are orthogonal to each other. This suggests that, contrary to the ups and downs of traditional expressions, the concept of irrelevant information and vital information can be introduced. By introducing the basic amount of ground lattice fidelity, quantifying irrelevant information and critical information which can identify the quantum phase transition of the system. It is worth emphasizing that no matter the internal order of quantum multibody systems is a traditional symmetry or other novel quantum order, they all can be applied such as topological order, single-grid ground state fidelity. In order to efficiently calculate the single-grid ground state fidelity of quantum multibody systems, tensor network algorithm is needed. This kind of algorithm is the result of the deepening of quantum entanglement in recent years. Quantum entanglement expounds the working principle of real-space renormalization group algorithm, especially density matrix re-grouping algorithm.

Effect of Quantum Noise on the Controlled Remote Preparation via the Brown State

Gao et al. have studied the controlled remote preparation of arbitrary two- and three-qubit states via the Brown state as the entangled channel. But these schemes are considered in ideal environment. In this paper, we take the scheme of preparing an arbitrary two-qubit state as an example and reinvestigate it in five-type noises: the bit flip, phase flip, bit-phase flip, phase-damping and amplitude-damping noise. The fidelity is adopted to describe how close the output state with the prepared state are. It is found that the fidelity of the output state is dependent on the coefficients of the prepared state and the noise parameter in five-type noises. Interestingly, the fidelity is irrelated to the participators’ measurement results except in the amplitude-damping noise.

Bounds for fidelity of semiclassical Lagrangian states in Kähler quantization

We define mixed states associated with submanifolds with probability densities in quantizable closed Kähler manifolds. Then, we address the problem of comparing two such states via their fidelity. First, we estimate the sub-fidelity and super-fidelity of two such states, giving lower and upper bounds for their fidelity, when the underlying submanifolds are two Lagrangian submanifolds intersecting transversally at a finite number of points, in the semiclassical limit. Second, we investigate a family of examples on the sphere, for which we manage to obtain a better upper bound for the fidelity. We conclude by stating a conjecture regarding the fidelity in the general case.

Demonstration of Topological Robustness of Anyonic Braiding Statistics with a Superconducting Quantum Circuit.

Anyons are quasiparticles occurring in two dimensions, whose topological properties are believed to be robust against local perturbations and may hold promise for fault tolerant quantum computing. Here we present an experiment of demonstrating the path independent nature of anyonic braiding statistics with a superconducting quantum circuit, which represents a 7-qubit version of the toric code model. We dynamically create the ground state of the model, achieving a state fidelity of 0.688±0.015 as verified by quantum state tomography. Anyonic excitations and braiding operations are subsequently implemented with single-qubit rotations. The braiding robustness is witnessed by looping an anyonic excitation around another one along two distinct, but topologically equivalent paths: Both reveal the nontrivial π-phase shift, the hallmark of Abelian 1/2 anyons, with a phase accuracy of ∼99% in the Ramsey-type interference measurement.

Efficient quantum circuit for singular-value thresholding

Singular value thresholding (SVT) operation is a fundamental core module in many mathematical models in computer vision and machine learning, particularly for many nuclear norm minimizing-based problems. We presented a quantum SVT (QSVT) algorithm which was used as a subroutine to address an image classification problem. This algorithm runs in $O\left[\log\left(pq\right)\right]$, an exponential speed improvement over the classical algorithm which runs in $O\left[poly\left(pq\right)\right]$. In this study, we investigate this algorithm and design a scalable quantum circuit for QSVT. In the circuit design, we introduce an adjustable parameter $\alpha$ to ensure the high probability of obtaining the final result and the high fidelity of actual and ideal final states. We also show that the value of $\alpha$ can be computed ahead of implementing the quantum circuit when the inputs of the QSVT algorithm, i.e. matrix ${\bf{A}}$ and constant $\tau$, are given. In addition, we propose a small-scale quantum circuit for QSVT. We numerically simulate and demonstrate the performance of this circuit, verifying its capability to solve the intended SVT. The quantum circuit for QSVT implies a tempting possibility for experimental realization on a quantum computer.

Bounds on Information Combining With Quantum Side Information

"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in classical information theory, particularly in coding and Shannon theory; entropy power inequalities are special instances of them. The arguably most elementary kind of information combining is the addition of two binary random variables (a CNOT gate), and the resulting quantities play an important role in Belief propagation and Polar coding. We investigate this problem in the setting where quantum side information is available, which has been recognized as a hard setting for entropy power inequalities. Our main technical result is a non-trivial, and close to optimal, lower bound on the combined entropy, which can be seen as an almost optimal "quantum Mrs. Gerber's Lemma". Our proof uses three main ingredients: (1) a new bound on the concavity of von Neumann entropy, which is tight in the regime of low pairwise state fidelities; (2) the quantitative improvement of strong subadditivity due to Fawzi-Renner, in which we manage to handle the minimization over recovery maps; (3) recent duality results on classical-quantum-channels due to Renes et al. We furthermore present conjectures on the optimal lower and upper bounds under quantum side information, supported by interesting analytical observations and strong numerical evidence. We finally apply our bounds to Polar coding for binary-input classical-quantum channels, and show the following three results: (A) Even non-stationary channels polarize under the polar transform. (B) The blocklength required to approach the symmetric capacity scales at most sub-exponentially in the gap to capacity. (C) Under the aforementioned lower bound conjecture, a blocklength polynomial in the gap suffices.

NOON state of Bose atoms in the double-well potential via an excited-state quantum phase transition

We suggest a simple scheme for creating a NOON state of repulsively interacting Bose atoms in the double-well potential. The protocol consists of two steps. First, by setting atom-atom interactions to zero, the system is driven to the upper excited state. Second, the interactions is slowly increased and, simultaneously, the inter-well tunneling is decreased to zero. We analyze fidelity of the final state to the NOON state depending on the number of atoms, ramp rate, and fluctuations of the system parameters. It is shown that for a given fidelity the ramp rate scales algebraically with the number of atoms.

18-Qubit Entanglement with Six Photons' Three Degrees of Freedom.

Full control of multiple degrees of freedom of multiple particles represents a fundamental ability for quantum information processing. We experimentally demonstrate an 18-qubit Greenberger-Horne-Zeilinger entanglement by simultaneous exploiting three different degrees of freedom of six photons, including their paths, polarization, and orbital angular momentum. We develop high-stability interferometers for reversible quantum logic operations between the photons' different degrees of freedom with precision and efficiencies close to unity, enabling simultaneous readout of 2^{18}=262 144 outcome combinations of the 18-qubit state. A state fidelity of 0.708±0.016 is measured, confirming the genuine entanglement of all 18 qubits.