Quantum Fidelity Research Articles

Underwater wireless optical communication employing polarization multiplexing modulation and photon counting detection.

Wireless optical communication is a crucial direction for improving the data transmission rate in underwater environments. In order to improve the communication performance over the water channel, this paper studies underwater wireless optical communication (UWOC) employing polarization multiplexing modulation and photon counting detection. The improvements in bit error rates and communication capacities are analyzed theoretically by constructing the communication model of polarization multiplexing modulation UWOC based on photon counting. Under specific conditions, the polarization maintenance characteristics of photons over water channels are demonstrated by measuring the Mueller matrix, the fidelity of quantum states, depolarization ratio, and calculating the ratios of ballistic photons. Based on these results, by designing and developing the experimental system of UWOC with the polarization multiplexing modulation and photon counting detection, the data transmission rates of 14.58Mbps and 7.29Mbps are realized over a water channel of 92 m by using polarization on-off keying multiplexing modulation and polarization 2-pulse-position multiplexing modulation, respectively.

Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Static aspects.

The basic Lipkin-Meshkov-Glick model displays a second-order ground-state quantum phase transition and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the Hamiltonian implies a second ESQPT of a different nature. We characterize this ESQPT using the mean field limit of the model. The alternative ESQPT, associated with the changes in the boundary of the finite Hilbert space of the system, can be properly described using the order parameter of the ground-state quantum phase transition, the energy gap between adjacent states, the participation ratio, and the quantum fidelity susceptibility.

Many-body Hilbert space scarring on a superconducting processor

Quantum many-body scarring (QMBS) -- a recently discovered form of weak ergodicity breaking in strongly-interacting quantum systems -- presents opportunities for mitigating thermalization-induced decoherence in quantum information processsing. However, the existing experimental realizations of QMBS are based on kinetically-constrained systems where an emergent dynamical symmetry "shields" such states from the thermalizing bulk of the spectrum. Here, we experimentally realize a distinct kind of QMBS phenomena by approximately decoupling a part of the many-body Hilbert space in the computational basis. Utilizing a programmable superconducting processor with 30 qubits and tunable couplings, we realize Hilbert space scarring in a non-constrained model in different geometries, including a linear chain as well as a quasi-one-dimensional comb geometry. By performing full quantum state tomography on 4-qubit subsystems, we provide strong evidence for QMBS states by measuring qubit population dynamics, quantum fidelity and entanglement entropy following a quench from initial product states. Our experimental findings broaden the realm of QMBS mechanisms and pave the way to exploiting correlations in QMBS states for applications in quantum information technology.

Realization of the Hadamard gate based on superposition of the composite solitons

In this article, we propose the implementation of quantum Hadamard gate through the superposition of composite solitons. Single qubit of the quantum state is defined by the components of the composite soliton which are the exact solution of the Manakov system. Through a rotation operation with an appropriate rotation angle, the Hadamard operation is realized on the single qubit, leading to the superposition state in which the measurement probability of individual qubits is half. Subsequently, repeating the similar Hadamard operation on the superposition state leads to the restoration of the original states of the qubit, as expected. Additionally, the measure of quantum fidelity of the qubit is expressed through the density operator matrix using Uhlmann-Jozsa fidelity. The versatility in the application of composite solitons to accomplish the quantum Hadamard operation through diverse physical systems is also demonstrated through suitable examples.

Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations

In certain regimes, the fidelity of quantum states will decay at a rate set by the classical Lyapunov exponent. This serves both as one of the most important examples of the quantum-classical correspondence principle and as an accurate test for the presence of chaos. While detecting this phenomenon is one of the first useful calculations that noisy quantum computers without error correction can perform [G. Benenti et al., Phys. Rev. E 65, 066205 (2001)], a thorough study of the quantum sawtooth map reveals that observing the Lyapunov regime is just beyond the reach of present-day devices. We prove that there are three bounds on the ability of any device to observe the Lyapunov regime and give the first quantitatively accurate description of these bounds: (1) the Fermi golden rule decay rate must be larger than the Lyapunov rate, (2) the quantum dynamics must be diffusive rather than localized, and (3) the initial decay rate must be slow enough for Lyapunov decay to be observable. This last bound, which has not been recognized previously, places a limit on the maximum amount of noise that can be tolerated. The theory implies that an absolute minimum of 6 qubits is required. Recent experiments on IBM-Q and IonQ imply that some combination of a noise reduction by up to 100× per gate and large increases in connectivity and gate parallelization are also necessary. Finally, scaling arguments are given that quantify the ability of future devices to observe the Lyapunov regime based on trade-offs between hardware architecture and performance.

Square-root measurements and degradation of the resource state in port-based teleportation scheme

Port-based teleportation (PBT) is a protocol of quantum teleportation in which a receiver does not have to apply correction to the transmitted state. In this protocol two spatially separated parties can teleport an unknown quantum state only by exploiting joint measurements on number of shared d-dimensional maximally entangled states (resource state) together with a state to be teleported and one way classical communication. In this paper we analyse for the first time the recycling protocol for the deterministic PBT beyond the qubit case. In the recycling protocol the main idea is to re-use the remaining resource state after one or many rounds of PBT for further processes of teleportation. The key property is to learn how much the underlying resource state degrades after every round of the teleportation process. We measure this by evaluating quantum fidelity between respective resource states. To do so we first present analysis of the square-root measurements used by the sender in PBT by exploiting the symmetries of the system. In particular, we show how to effectively evaluate their square-roots and composition. These findings allow us to present the explicit formula for the recycling fidelity involving only group-theoretic parameters describing irreducible representations in the Schur–Weyl duality. For the first time, we also analyse the degradation of the resource state for the optimal PBT scheme and show its degradation for all d ⩾ 2. In the both versions, the qubit case is discussed separately resulting in compact expression for fidelity, depending only on the number of shared entangled pairs.

Two measures elaborated for entangled states: Quantum entropy and fidelity using Schmidt coefficients of the reduced density matrix of full TRI

In the present study, we determined quantum entanglement in a full trapped ion (TRI)-coherent system and its dependence on the LambDicke parameter (LDP). We investigated the entanglement in view of two elaborated measurements of the family: entropy and fidelity. We selected three values of the deep LDP to demonstrate the benefits of these two critical measures. The findings obtained in this study showed that the maximum value of fidelity for entangled states is quantified approximately to be 0.35, and the long lifetime is also observed with entropy measurement. The findings suggest that three coupling parameters play a significant role in developing quantum entanglement.

Thermal topological phase transition in SnTe from ab initio calculations

One of the key issues in the physics of topological insulators is whether the topologically non-trivial properties survive at finite temperatures and, if so, whether they disappear only at the temperature of topological gap closing. Here, we study this problem, using quantum fidelity as a measure, by means of \emph{ab-initio} methods supplemented by an effective dissipative theory built on the top of the \emph{ab-initio} electron and phonon band structures. In the case of SnTe, the prototypical crystal topological insulator, we reveal the presence of a characteristic temperature, much lower than the gap-closing one, that marks a loss of coherence of the topological state. The transition is not present in a purely electronic system but it appears once we invoke coupling with a dissipative bosonic bath. Features in the dependence with temperature of the fidelity susceptibility can be related to changes in the band curvature, but signatures of a topological phase transition appear in the fidelity only though the non-adiabatic coupling with soft phonons. Our argument is valid for valley topological insulators, but in principle can be generalized to the broader class of topological insulators which host any symmetry-breaking boson.

Metric properties of alternative fidelities

On the space of mixed quantum states, several alternative fidelities have been proposed besides the standard Uhlmann-Jozsa fidelity. It has been known that several properties of the Uhlmann-Jozsa fidelity still hold true for these alternative fidelities. The aim of this paper is to give positive answers to some questions about the metric properties of functionals of alternative quantum fidelities raised by Y. C. Liang {\it et al.} in \cite{LYM}. Our method is to use the non-negativity of the Gram determinant of three vectors constructed from the quantum states to prove the triangle inequality for the modified Bures angle.

Quantum cost of dense coding and teleportation

The quantum cost is a key ingredient to evaluate the quality of quantum protocols from a practical viewpoint. We show that the quantum cost of d-dimensional dense coding protocol is equal to d+3 when transmitting the classical message (0,0), and that is equal to d+4 when transmitting other classical message. It appears linear growth with the dimension and thus makes sense for implementation. In contrast, the quantum cost of high-dimensional teleportation protocols is equal to 13, which is the maximum value of the cost for the two-dimensional case. As an application, we establish the relation between the quantum cost and fidelity of dense coding protocols in terms of four typical noise scenario.

Detection of Quantum Phase Boundary at Finite Temperatures in Integrable Spin Models.

Quantum phase transitions occur when quantum fluctuation destroys order at zero temperature. With an increase in temperature, normally the thermal fluctuation wipes out any signs of this transition. Here, we identify a physical quantity that shows nonanalytic behavior at finite temperatures, when an interaction parameter is quenched across the line of quantum phase transition. This quantity under consideration is the long time limit of a form of quantum fidelity. Our treatment is analytic for XY chain and 2D Kitaev model and is numerical for a 3D Hamiltonian applicable to Weyl semimetals.

Continuous variable quantum teleportation of a thermal state in a thermal environment

The analytical formula for the fidelity of teleportation from Alice to Bob of a thermal state used as an input state is derived using the characteristic function approach. As a resource state it is used a continuous-variable two-mode bosonic state shared between Alice and Bob and the system is placed in a contact with a general environment. The quantum fidelity depends on the average thermal photon number of the input sate and on the parameters of the resource state and environment. In order to evaluate the parameters required for a successful quantum teleportation of a thermal state we estimate the evolution of the entanglement and fidelity of teleportation in the case when Alice and Bob share an initial squeezed thermal state in contact with a thermal bath. We work in the framework of the theory of open quantum systems based on completely positive dynamical semigroups and we use the Gorini–Kossakowski–Lindblad–Sudarshan master equation in order to describe the evolution of the system. The conditions for a successful quantum teleportation are the fidelity of teleportation larger than the threshold value of the classical fidelity of teleportation and entanglement present in the resource state. In order to assure the fulfillment of these conditions it is necessary to select the time of teleportation and to adjust the parameters characterizing the system (squeezing between the modes of the resource state, their average numbers of thermal photons and frequencies), and the temperature of the thermal reservoir. It is shown that in similar physical conditions, the fidelity of teleportation of the thermal states is larger than that one for a coherent state.

Using a Deep Quantum Neural Network to Enhance the Fidelity of Quantum Convolutional Codes

The fidelity of quantum states is an important concept in quantum information. Improving quantum fidelity is very important for both quantum communication and quantum computation. In this paper, we use a quantum neural network (QNN) to enhance the fidelity of [6, 2, 2] quantum convolutional codes. Towards the circuit of quantum convolutional codes, the target quantum state |0⟩ or |1⟩ is turned into entangled quantum states, which can defend against quantum noise more effectively. As the quantum neural network works better for quantum states with low dimension, we divide the quantum circuits into two parts. Then we apply the quantum neural network to each part of the circuit. The results of the simulation show that the network performs well in enhancing the fidelity of the quantum states. Through the quantum neural network, the fidelity of the first part is enhanced from 95.2% to 99.99%, and the fidelity of the second part is enhanced from 93.88% to 94.57%.

Thermal Fisher information and entropy squeezing for superconducting qubits

We investigate the effects of temperature on quantum Fisher information (QFI), fidelity, and entropy squeezing in two interacting superconducting qubits (SCQs). We show how the variations in these quantum quantifiers may be controlled by carefully selecting the model's physical parameters (PPM). We obtain a trapping phenomena for Fisher information, allowing us to improve the QFI and retain the amount of information while also preserving it from information loss due to temperature impacts. We evaluate the fidelity of the SCQ to explain the dynamic aspects of the QFI in relation to the PPM. Furthermore, we examine the influence of the PPM on the variation in the squeezing entropy for SCQs. The results indicate how, in terms of quantum measurement theory, the system under consideration might be valuable in enabling the realization of experiments under optimal conditions.

Error metrics for partially coherent wave fields.

Lensless imaging methods that account for partial coherence have become very common in the past decade. However, there are no metrics in use for comparing partially coherent light fields, despite the widespread use of such metrics to compare fully coherent objects and wave fields. Here, we show how reformulating the mean squared error and Fourier ring correlation in terms of quantum state fidelity naturally generalizes them to partially coherent wave fields. These results fill an important gap in the lensless imaging literature and will enable quantitative assessments of the reliability and resolution of reconstructed partially coherent wave fields.

Pairwise quantum criteria and teleportation in a spin square complex

Thermal non-classical correlations quantified by concurrence entanglement, local quantum uncertainty, and quantum coherence in a four-qubit square chain are exactly examined. The influences of the Hamiltonian parameters on the mentioned pairwise quantum criteria and fidelity of teleportation are studied, and the most interesting findings are discussed in detail. It is found that the tuning anisotropy results in enhancing the thermal quantum correlations and coherence as well as average fidelity until achieving maximum values. We persuasively deduce that quantum coherence is a more efficient criterion than that of concurrence and local quantum uncertainty to detect the quantumness of a thermal state.

Anharmonicity-induced excited-state quantum phase transition in the symmetric phase of the two-dimensional limit of the vibron model

In most cases, excited state quantum phase transitions can be associated with the existence of critical points (local extrema or saddle points) in a system's classical limit energy functional. However, an excited-state quantum phase transition might also stem from the lowering of the asymptotic energy of the corresponding energy functional. One such example occurs in the 2D limit of the vibron model, once an anharmonic term in the form of a quadratic bosonic number operator is added to the Hamiltonian. The study of this case in the broken-symmetry phase was presented in Phys. Rev. A. 81 050101 (2010). In the present work, we delve further into the nature of this excited-state quantum phase transition and we characterize it in the, previously overlooked, symmetric phase of the model making use of quantities such as the effective frequency, the expected value of the quantum number operator, the participation ratio, the density of states, and the quantum fidelity susceptibility. In addition to this, we extend the usage of the quasilinearity parameter, introduced in molecular physics, to characterize the phases in the spectrum of the anharmonic 2D limit of the vibron model and a down-to-earth analysis has been included with the characterization of the critical energies for the linear isomers HCN/HNC.

Analytical and experimental study of center-line miscalibrations in Mølmer-Sørensen gates

A major challenge for the realization of useful universal quantum computers is achieving high fidelity two-qubit entangling gate operations. However, calibration errors can affect the quantum gate operations and limit their fidelity. To reduce such errors it is desirable to have an analytical understanding and quantitative predictions of the effects that miscalibrations of gate parameters have on the gate performance. In this work, we study a systematic perturbative expansion in miscalibrated parameters of the M\o{}lmer-S\o{}rensen entangling gate, which is widely used in trapped-ion quantum processors. Our analytical treatment particularly focuses on systematic center-line detuning miscalibrations. Via a unitary Magnus expansion, we compute the gate evolution operator, which allows us to obtain relevant key properties such as relative phases, electronic populations, quantum state purity and fidelities. These quantities, subsequently, are used to assess the performance of the gate using the fidelity of entangled states as performance metric. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor. The method and the results presented here can help design and calibrate high-fidelity gate operations of large-scale quantum computers.

Statistical Methods for Quantum State Verification and Fidelity Estimation

AbstractThe efficient and reliable certification of quantum states is essential for various quantum information processing tasks as well as for the general progress on the implementation of quantum technologies. In the last few years several methods have been introduced which use advanced statistical methods to certify quantum states in a resource‐efficient manner. In this article, a review of the recent progress in this field is presented. How the verification and fidelity estimation of a quantum state can be discussed in the language of hypothesis testing is explained first. Then, various strategies for the verification of entangled states with local measurements or measurements assisted by local operations and classical communication are explained in detail. Finally, several extensions of the problem, such as the certification of quantum channels and the verification of entanglement are discussed.

Visible-wavelength polarization-entangled photon source for quantum communication and imaging

We present a polarization-entangled photon pair source operating in the visible light range around 532 nm. Employing a collinear crossed-crystal scheme with type-I degenerate phase matching in barium borate (BBO), our source achieves a brightness of 9.5 k pairs/s/mW and a quantum state fidelity of 98.3%, making it a candidate for integration in microscopes and make use of the advantages of mid-visible optimized single-photon detection technologies. In order to study potential applications, we present a trade-off between source brightness and polarization entanglement visibility and propose use cases for different filtering configurations of the source, capable of a brightness up to 1.23 M pairs/s/mW.