Decoherence Properties Research Articles

Ill-posedness for the Half wave Schrödinger equation

We study the Cauchy problem for the half wave Schrödinger equation introduced by Xu [9]. There are some well-posedness results for the equation, however there is no ill-posedness result. We focus on the scale critical space and obtain the ill-posedness in the super-critical or at the critical space under certain condition. The proofs in the super-critical space are based on the argument established by Christ, Colliander and Tao [4]. More precisely, we analyze dispersionless equation with smooth initial data, namely the Schwartz function and it is locally well-posed in some weighted Sobolev space. We construct the solution for the half wave Schrödinger equation by using the solution for the dispersionless equation and we can exploit the norm inflation or the decoherence properties. For the critical space, we use the standing wave solution, which was proved the existence by Bahri, Ibrahim and Kikuchi [1].

Environment Decoherence of Quantum Exclusion Semigroups in Terms of Quantum Bernoulli Noises

In this paper, we study the environment induced decoherence of quantum exclusion semigroups constructed by quantum Bernoulli noises. We first study the structure of the decoherence-free algebra and discuss some of its properties, and give the conditions for its possible mutual inclusions with the set of fixed points. Then we describe the structure of the set of fixed points and use the new results obtained here to discuss the environment induced decoherence properties of the semigroup.

Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits

In this paper we study the entanglement in symmetric N-quDit systems. In particular we use generalizations to U(D) of spin U(2) coherent states (CSs) and their projections on definite parity (multicomponent Schrödinger cat) states and we analyse their reduced density matrices when tracing out M < N quDits. The eigenvalues (or Schmidt coefficients) of these reduced density matrices are completely characterized, allowing to prove a theorem for the decomposition of a N-quDit Schrödinger cat state with a given parity into a sum over all possible parities of tensor products of Schrödinger cat states of N − M and M particles. Diverse asymptotic properties of the Schmidt eigenvalues are studied and, in particular, for the (rescaled) double thermodynamic limit ( fixed), we reproduce and generalize to quDits known results for photon loss of parity adapted CSs of the harmonic oscillator, thus providing an unified Schmidt decomposition for both multi-quDits and (multi-mode) photons. These results allow to determine the entanglement properties of these states and also their decoherence properties under quDit loss, where we demonstrate the robustness of these states.

Enhancement of mechanical entanglement and asymmetric steering with coherent feedback

We propose a scheme to enhance entanglement and asymmetric steering between two mechanical oscillators in an optomechanical system with coherent feedback control. In the system, an optical cavity interacts with two mechanical oscillators and an auxiliary cavity whose output field is fed back into the input port of the optical cavity via a feedback loop. Due to the coherence between the auxiliary cavity and feedback, we derive the effective decay rate and a nonzero frequency shift of the optical cavity. Consequently, the induced beam-splitter-type and parametric-type interactions between the two mechanical oscillators are modulated, which leads to the enhancement of entanglement and the generation of asymmetric steering even if the two mechanical oscillators possess identical decoherence properties. And the direction of asymmetric steering can be controlled by tuning the jumping phase between two cavities and optimizing the ratio of drive asymmetry. In contrast to the method of adding losses or noises to one subsystem at the cost of reducing steerability, this scheme provides an active way to achieve enhanced asymmetric steering. Furthermore, the steady-state and dynamical entanglement and asymmetric steering can be generated in the unresolved-sideband regime, which is friendly for experimental implementation.

Qubit and bit-based quantum hybrid secret key generation

For the generation of a hybrid secret key, hardly any quantum algorithms integrating computed qubits and decrypted bits have yet been developed. Integrating computed qubits and decrypted bits in a predetermined order is difficult for a combiner component. The underlying problems of the study are the design of a quantum circuit, an algorithm, base state polarizer setup, and the concatenation of decrypted bits and computed qubits. By combining either rectilinear, orthogonal (superposition), or both states with decrypted bits, we have investigated three different possibilities for the quantum hybrid protocol. We investigated errors in each case and compared them with regard to decoherence and other quantum mechanics properties by taking into consideration the effectiveness of base states during transmission time across an untrusted channel. Furthermore, we addressed the key size, base state errors, design complexity, and security in a reasonable manner for identifying solutions and compared our results to earlier proposed quantum protocols. Finally, our suggested key protocol is more effective than that of earlier proposed protocols.Graphical Abstract Combining randomly generated bits and qubits a predetermined order to create a hybrid key. In comparison to the earlier suggested classical and quantum cryptography, its size, structure, and mathematical calculations are relatively significant and effective

Quantizing Lévy flights

The Caldeira-Leggett model of quantum Brownian motion is generalized using a generic velocity-dependent coupling. That leads to the description of a set of models able to capture Markovian and non-Markovian versions of Brownian and L\'evy statistics, depending on the functional form of the coupling and on the spectral function of the reservoir. One specific coupling force is found that establishes a connection with L\'evy statistics of cold atoms in \textit{Sisyphus} laser cooling. In the low-velocity limit, this also gives rise to additional inertia of the Brownian particle, reproducing the Abraham-Lorentz equation from first principles for a superohmic bath. Through path-integral quantization in Euclidean time, the environment is integrated out, leaving a set of non-local effective actions. These results further serve as starting points for several numerical calculations, particularly decoherence properties of non-ohmic baths.

Quantifying quantum coherence of optical cat states

The optical cat state plays an essential role in quantum computation and quantum metrology. Here, we experimentally quantify quantum coherence of an optical cat state by means of relative entropy and the l 1 norm of coherence in a Fock basis based on the prepared optical cat state at the rubidium D1 line. By transmitting the optical cat state through a lossy channel, we also demonstrate the robustness of quantum coherence of the optical cat state in the presence of loss, which is different from the decoherence properties of fidelity and Wigner function negativity of the optical cat state. Our results confirm that quantum coherence of optical cat states is robust against loss and pave the way for the application of optical cat states.

Phonon-induced relaxation and decoherence times of the hybrid qubit in silicon quantum dots

We study theoretically the phonon-induced relaxation and decoherence processes in the hybrid qubit in silicon. Hybrid qubit behaves as a charge qubit when the detuning is close to zero and as spin qubit for large detuning values. It is realized starting from an electrostatically defined double quantum dot where three electrons are confined and manipulated through only electrical tuning. By employing a three-level effective model for the qubit and describing the environment bath as a series of harmonic oscillators in the thermal equilibrium states, we extract the relaxation and decoherence times as a function of the bath spectral density and of the bath temperature using the Bloch-Redfield theory. For Si quantum dots the energy dispersion is strongly affected by the physics of the valley, i.e. the conduction band minima, so we also included the contribution of the valley excitations in our analysis. Our results offer fundamental information on the system decoherence properties when the unavoidable interaction with the environment is included and temperature effects are considered.

Manipulation and enhancement of asymmetric steering via interference effects induced by closed-loop coupling

We present a phase control method for a general three-mode system with closed-loop coupling that drives the system into an entangled steady state and produces directional steering between two completely symmetric modes via quantum interference effects. In the scheme, two modes are coupled with each other both by a direct binary interaction and by an indirect interaction through a third intermediate damping mode, creating interference effects determined by the relative phase between the two physical interaction paths. By calculating the populations and correlations of the two modes, we show that, depending on the phase, two modes can be prepared into an entangled steady state with asymmetric and directional steering even if they possess completely symmetric decoherence properties. Meanwhile, entanglement and steering can be significantly enhanced due to constructive interference and thus are more robust to thermal noises. This provides an active method to manipulate the asymmetry of steering instead of adding asymmetric losses or noises to subsystems at the cost of reducing steerability. Moreover, we show that the interference effects can also enhance and control the correlations between other pairs of modes in the loop with opposite phase-dependent behavior, indicating monogamy constraints for distributing correlations among multiple parties. The present model could be applied in cavity optomechanical systems or in antiferromagnets where all components can mutually interact.

Decoherence dynamics of qubits coupled to systems at quantum transitions

We study the decoherence properties of a two-level (qubit) system homogeneously coupled to an environmental many-body system at a quantum transition, considering both continuous and first-order quantum transitions. In particular, we consider a $d$-dimensional quantum Ising model as environment system. We study the dynamic of the qubit decoherence along the global quantum evolution starting from pure states of the qubit and the ground state of the environment system. This issue is discussed within dynamic finite-size scaling frameworks. We analyze the dynamic finite-size scaling of appropriate qubit-decoherence functions. At continuous quantum transitions, they develop power laws of the size of the environment system, with a substantial enhancement of the growth rate of the qubit decoherence with respect to the case in which the environment system is in normal noncritical conditions. The enhancement of the qubit decoherence growth rate appears much larger at first-order quantum transitions, leading to exponential laws when increasing the size of the environment system.

Unconditional Steady-State Entanglement in Macroscopic Hybrid Systems by Coherent Noise Cancellation.

The generation of entanglement between disparate physical objects is a key ingredient in the field of quantum technologies, since they can have different functionalities in a quantum network. Here we propose and analyze a generic approach to steady-state entanglement generation between two oscillators with different temperatures and decoherence properties coupled in cascade to a common unidirectional light field. The scheme is based on a combination of coherent noise cancellation and dynamical cooling techniques for two oscillators with effective masses of opposite signs, such as quasispin and motional degrees of freedom, respectively. The interference effect provided by the cascaded setup can be tuned to implement additional noise cancellation leading to improved entanglement even in the presence of a hot thermal environment. The unconditional entanglement generation is advantageous since it provides a ready-to-use quantum resource. Remarkably, by comparing to the conditional entanglement achievable in the dynamically stable regime, we find our unconditional scheme to deliver a virtually identical performance when operated optimally.

Experimental simulation of a decohering Schrödinger’s cat state in wave optics

The study of decoherence properties improves our understanding of the fundamental principles of quantum mechanics and advances the study of quantum information processing. Herein, we report a wave-optical experiment that can simulate the decoherence process of a Schrodinger’s cat state (SCS) by photon loss. The method is based on an analogy between image rotation in wave optics and a beam splitter in quantum optics. Experimental results show that the SCS rapidly decays into a statistical mixture of two Gaussian states with approximately 10% photon loss. This behavior can be well described within the framework of quantum optics.

Coarse-grained representation of the quasi adiabatic propagator path integral for the treatment of non-Markovian long-time bath memory.

The description of non-Markovian effects imposed by low frequency bath modes poses a persistent challenge for path integral based approaches like the iterative quasi-adiabatic propagator path integral (iQUAPI) method. We present a novel approximate method, termed mask assisted coarse graining of influence coefficients (MACGIC)-iQUAPI, that offers appealing computational savings due to substantial reduction of considered path segments for propagation. The method relies on an efficient path segment merging procedure via an intermediate coarse grained representation of Feynman-Vernon influence coefficients that exploits physical properties of system decoherence. The MACGIC-iQUAPI method allows us to access the regime of biological significant long-time bath memory on the order of hundred propagation time steps while retaining convergence to iQUAPI results. Numerical performance is demonstrated for a set of benchmark problems that cover bath assisted long range electron transfer, the transition from coherent to incoherent dynamics in a prototypical molecular dimer and excitation energy transfer in a 24-state model of the Fenna-Matthews-Olson trimer complex where in all cases excellent agreement with numerically exact reference data is obtained.

Experimental study of entanglement evolution in the presence of bit-flip and phase-shift noises

Because of its important role both in fundamental theory and applications in quantum information, evolution of entanglement in a quantum system under decoherence has attracted wide attention in recent years. In this paper, we experimentally generate a high-fidelity maximum entangled two-qubit state and present an experimental study of the decoherence properties of entangled pair of qubits at collective (non-collective) bit-flip and phase-shift noises. The results shown that entanglement decreasing depends on the type of the noises (collective or non-collective and bit-flip or phase-shift) and the number of qubits which are subject to the noise. When two qubits are depolarized passing through non-collective noisy channel, the decay rate is larger than that depicted for the collective noise. When two qubits passing through depolarized noisy channel, the decay rate is larger than that depicted for one qubit.

Kinetics of Interactions of Matter, Antimatter and Radiation Consistent with Antisymmetric (CPT-Invariant) Thermodynamics

This work investigates the influence of directional properties of decoherence on kinetics rate equations. The physical reality is understood as a chain of unitary and decoherence events. The former are quantum-deterministic, while the latter introduce uncertainty and increase entropy. For interactions of matter and antimatter, two approaches are considered: symmetric decoherence, which corresponds to conventional symmetric (CP-invariant) thermodynamics, and antisymmetric decoherence, which corresponds to antisymmetric (CPT-invariant) thermodynamics. Radiation, in its interactions with matter and antimatter, is shown to be decoherence-neutral. The symmetric and antisymmetric assumptions result in different interactions of radiation with matter and antimatter. The theoretical predictions for these differences are testable by comparing absorption (emission) of light by thermodynamic systems made of matter and antimatter. Canonical typicality for quantum mixtures is briefly discussed in Appendix A.

Electron–phonon interaction in quantum transport through quantum dots and molecular systems

The quantum transport and effects of decoherence properties are studied in quantum dots systems and finite homogeneous chains of aromatic molecules connected to two semi-infinite leads. We study these systems based on the tight-binding approach through Green's function technique within a real space renormalization and polaron transformation schemes. In particular, we calculate the transmission probability following the Landauer–Büttiker formalism, the I−V characteristics and the noise power of current fluctuations taken into account the decoherence. Our results may explain the inelastic effects through nanoscopic systems.

Decoherence of the hybrid qubit in a double quantum dot

We study decoherence of the hybrid qubit in a double quantum dot system which exhibits the longest decoherence time in the large bias region rather than at the avoided crossing conventionally considered the sweet spot for decoherence performance. Using a three-level model, we analyze how the characteristics of the spectrum of the system dictate its decoherence properties, and confirm our conclusions quantitatively by calculating the decoherence performance of the system and comparing the results with experimental data.

Noise Effects on Entangled Coherent State Generated via Atom-Field Interaction and Beam Splitter

In this paper, we introduce a controllable method for producing two and three-mode entangled coherent states (ECS's) using atom-field interaction in cavity QED and beam splitter. The generated states play central roles in linear optics, quantum computation and teleportation. We especially focus on qubit, qutrit and qufit like ECS's and investigate their entanglement by concurrence measure. Moreover, we illustrate decoherence properties of ECS's due to noisy channels, using negativity measure. At the end the effect of noise on monogamy inequality is discussed.

Entanglement dynamics in the presence of controlled unital noise.

Quantum entanglement is notorious for being a very fragile resource. Significant efforts have been put into the study of entanglement degradation in the presence of a realistic noisy environment. Here, we present a theoretical and an experimental study of the decoherence properties of entangled pairs of qubits. The entanglement dynamics of maximally entangled qubit pairs is shown to be related in a simple way to the noise representation in the Bloch sphere picture. We derive the entanglement level in the case when both qubits of a Bell state are transmitted through any arbitrary unital Pauli channel, and compare it to the case when the channel is applied only to one of the qubits. The dynamics of both cases was verified experimentally using an all-optical setup. We further investigated the evolution of partially entangled initial states. Different dynamics was observed for initial mixed and pure states of the same entanglement level.

Quantum interference measurement of spin interactions in a bio-organic/semiconductor device structure.

Quantum interference is used to measure the spin interactions between an InAs surface electron system and the iron center in the biomolecule hemin in nanometer proximity in a bio-organic/semiconductor device structure. The interference quantifies the influence of hemin on the spin decoherence properties of the surface electrons. The decoherence times of the electrons serve to characterize the biomolecule, in an electronic complement to the use of spin decoherence times in magnetic resonance. Hemin, prototypical for the heme group in hemoglobin, is used to demonstrate the method, as a representative biomolecule where the spin state of a metal ion affects biological functions. The electronic determination of spin decoherence properties relies on the quantum correction of antilocalization, a result of quantum interference in the electron system. Spin-flip scattering is found to increase with temperature due to hemin, signifying a spin exchange between the iron center and the electrons, thus implying interactions between a biomolecule and a solid-state system in the hemin/InAs hybrid structure. The results also indicate the feasibility of artificial bioinspired materials using tunable carrier systems to mediate interactions between biological entities.