Time fractional evolution of a single quantum state and entangled state

There exists an interesting relationship between entanglement and the time evolution of composite quantum systems: quantum entanglement enhances the ‘speed’ of evolution of certain quantum states, as measured by the time needed to reach an orthogonal state. Previous research done on this subject has been focused upon comparing extreme cases (highly entangled states versus separable states) or upon bi-partite systems. In the present contribution we explore the aforementioned connection (between entanglement and time evolution) in the cases of two-qubits and N-qubits systems, taking into account states of intermediate entanglement. In particular, we investigate a family of energetically symmetric states of low entanglement that saturate the quantum speed bound. We show that, as the number of qubits increases, very little entanglement is needed to reach the quantum speed limit.

According to the orthodox interpretation of quantum physics, wave-particle duality (WPD) is the intrinsic property of all massive microscopic particles. All gedanken or realistic experiments based on atom interferometers (AI) have so far upheld the principle of WPD, either by the mechanism of the Heisenberg’s position-momentum uncertainty relation or by quantum entanglement. In this paper, we propose and make a systematic quantum mechanical analysis of several schemes of weak-measurement atom interferometer (WM-AI) and compare them with the historical schemes of strong-measurement atom interferometer (SM-AI), such as Einstein’s recoiling slit and Feynman’s light microscope. As the critical part of these WM-AI setups, a weak-measurement path detector (WM-PD) deliberately interacting with the atomic internal electronic quantum states is designed and used to probe the which-path information of the atom, while only inducing negligible perturbation of the atomic center-of-mass motion. Another instrument that is used to directly interact with the atomic center-of-mass while being insensitive to the internal electronic quantum states is used to monitor the atomic center-of-mass interference pattern. Two typical schemes of WM-PD are considered. The first is the micromaser-cavity path detector, which allows us to probe the spontaneously emitted microwave photon from the incoming Rydberg atom in its excited electronic state and record unanimously the which-path information of the atom. The second is the optical-lattice Bragg-grating path detector, which can split the incoming atom beam into two different directions as determined by the internal electronic state and thus encode the which-path information of the atom into the internal states of the atom. We have used standard quantum mechanics to analyze the evolution of the atomic center-of-mass and internal electronic state wave function by directly solving Schrödinger’s equation for the composite atom-electron-photon system in these WM-AIs . We have also compared our analysis with the theoretical and experimental studies that have been presented in the previous literature. The results show that the two sets of instruments can work separately, collectively, and without mutual exclusion to enable simultaneous observation of both wave and particle nature of the atoms to a much higher level than the historical SM-AIs, while avoiding degradation from Heisenberg’s uncertainty relation and quantum entanglement. We have further investigated the space–time evolution of the internal electronic quantum state, as well as the combined atom–detector system and identified the microscopic origin and role of quantum entanglement, as emphasized in numerous previous studies. Based on these physics insights and theoretical analyses, we have proposed several new WM-AI schemes that can help to elucidate the puzzling physics of the WPD of the atoms. The principle of WM-AI scheme and quantum mechanical analyses made in this work can be directly extended to examine the principle of WPD for other massive particles.

Different mathematics forms of entangled state can judge prepared many particles is if entangled. Entangled state is a key role of quantum information technology. The more entangled states are generated, the better performances are presented. In order to make it more convenient to generate entangled state or judge the state prepared is entangled, we investigate three-qubit GHZ state and expand recurrence relation based on an expand recurrence relation of multi-qubit state. Furthermore, new forms of maximally five and seven-qubit entangled states are reconstructed via three-qubit GHZ state. These new forms stand for universal law of n-qubit and [Formula: see text]-qubit can have direct application in quantum entangle state generation and quantum communications.

Multiparticle entanglement enables quantum simulations, quantum computing, and quantum-enhanced metrology. Yet, there are few methods to produce and measure such entanglement while maintaining single-qubit resolution as the number of qubits is scaled up. Using atom chips and fiber-optical cavities, we have developed a method based on nondestructive collective measurement and conditional evolution to create symmetric entangled states and perform their tomography. We demonstrate creation and analysis of entangled states with mean atom numbers up to 41 and experimentally prove multiparticle entanglement. Our method is independent of atom number and should allow generalization to other entangled states and other physical implementations, including circuit quantum electrodynamics.

Controlling the evolution of photonic quantum states is crucial for most quantum information processing and metrology tasks. Due to its importance, many mechanisms of quantum state evolution have been tested in detail and are well understood; however, the fundamental phase anomaly of evolving waves, called the Gouy phase, has had a limited number of studies in the context of elementary quantum states of light, especially in the case of photon number states. Here we outline a simple method for calculating the quantum state evolution upon propagation and demonstrate experimentally how this quantum Gouy phase affects two-photon quantum states. Our results show that the increased phase sensitivity of multi-photon states also extends to this fundamental phase anomaly and has to be taken into account to fully understand the state evolution. We further demonstrate how the Gouy phase can be used as a tool for manipulating quantum states of any bosonic system in future quantum technologies, outline a possible application in quantum-enhanced sensing, and dispel a common misconception attributing the increased phase sensitivity of multi-photon quantum states solely to an effective de Broglie wavelength.

The detection of microwave states is complicated by strong thermal noise, which is inevitably introduced by linear amplifiers. We show how to extract from measured data normally or anti-normally ordered moments of photon creation and annihilation operators, the set of which contains complete information on the quantum state of an electromagnetic field. Equations for the evolution of the quantum state are derived in terms of moments. Using this approach, we consider in detail issues of decoherence and thermalization of microwave quantum states. Results are illustrated using the examples of Fock, coherent, squeezed, thermal, and even and odd coherent states (Schrodinger cat states).

The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation, and measurement of two-level quantum states is well understood, the same is not true in higher dimensions. Here we present the experimental generation of a complete set of Bell states in a four-dimensional Hilbert space, comprising of 16 orthogonal entangled Bell-like states encoded in the orbital angular momentum of photons. The states are created by the application of generalized high-dimensional Pauli gates on an initial entangled state. Our results pave the way for the application of high-dimensional quantum states in complex quantum protocols such as quantum dense coding.

Quantum gyroscopes have the advantages of high precision and drift-free, and are extensively applied in high accuracy spacecraft attitude control, but it is extremely sensitive to quantum noise, zero-bias drift and nonlinear errors under complex space conditions, which directly affect the accuracy of attitude solving. According to the well-established quantum gyro error models, including the random walk model and Markov error modeling, We propose a multi-channel error physics model, which integrates the non-Gaussian error modeling, multi-scale quantum state perturbation analysis and sensor-environment interaction coupling mechanism (MCEAM-AKF). In this section we use the error propagation equation to obtain the response matrix as influenced by noise under the evolution of quantum state, not only the noise responses of device linear part but also the nonlinear terms of state transition, which is the internal state decoherence phenomenon of the device. Then a model and augmented state based adaptive Kalman filter algorithm is designed, which integrates the time-varying error covariance estimation mechanism and the multi-layer scale observation update strategy and achieves the real-time dynamic correction of the attitude angle output error. Furthermore, external reference sources (e.g., star sensors) for closed-loop joint calibration accordingly to the movements to enhance the anti-interference ability and fast convergence performance are introduced in the model. Simulation results demonstrate that the average attitude angle error of MCEAM-AKF model can be decreased by $38.2 \%$ for different orbit and disturbance scenarios.

For a fundamental understanding of quantum mechanics, superposition and entanglement of quantum states are essential issues. These phenomena are explained by means of examples including the scattering of two identical particles. Special focus is on the quantum mechanical measurement process and on the disappearance of double slit interferences by gaining “Which Way” information. Using the density matrix formalism, open quantum systems and dephasing of coherent quantum states are discussed. This includes a short consideration of Schrödinger’s cat paradox. Important applications in the field of quantum information are presented, in particular the realization of a quantum bit by semiconductor quantum dots.KeywordsDensity MatrixReduce Density MatrixSuperposition StateSpin OrientationDouble Slit ExperimentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We consider a variation of the multi-party communication complexity scenario where the parties are supplied with an extra resource: particles<br />in an entangled quantum state. We show that, although a prior<br />quantum entanglement cannot be used to simulate a communication channel, it can reduce the communication complexity of functions in<br />some cases. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function's input), a prior quantum entanglement enables them to learn the value of the<br />function with only three bits of communication occurring among the parties, whereas, without quantum entanglement, four bits of communication are necessary. We also show that, for a particular two-party probabilistic communication complexity problem, quantum entanglement<br />results in less communication than is required with only classical<br />random correlations (instead of quantum entanglement). These results are a noteworthy contrast to the well-known fact that quantum entanglement cannot be used to actually simulate communication among<br />remote parties.

Deterministic sources of high-fidelity entangled qubit pairs encoded in the dual-rail photonic basis, i.e., presence of a single photon in one of two orthogonal modes, are a key enabling technology of many applications of quantum information processing, including high-rate, high-fidelity quantum communications over long distances. The most popular and mature sources of such photonic entanglement, e.g., those that leverage spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing, generate an entangled (so-called continuous-variable) quantum state that contains contributions from high-order photon terms that lie outside the span of the dual-rail basis, which is detrimental to most applications. One often uses low pump power to mitigate the effects of those high-order terms. However, that reduces the pair generation rate, and the source becomes inherently probabilistic. We investigate a cascaded source that performs a linear-optical entanglement swap between two SPDC sources, to generate a heralded photonic entangled state that has a higher fidelity (to the ideal Bell state) compared to a free-running SPDC source. Furthermore, with the Bell swap providing a heralding trigger, we show how to build a multiplexed source, which despite reasonable switching losses and detector loss and noise, yields a fidelity versus success probability trade-off of a high-efficiency source of high-fidelity dual-rail photonic entanglement. We find, however, that there is a threshold of $1.5$ dB of loss per switch, beyond which multiplexing hurts the fidelity versus success probability trade-off.

Entanglement is closely related to some fundamental features of the dynamics of composite quantum systems: quantum entanglement enhances the “speed” of evolution of certain quantum states, as measured by the time required to reach an orthogonal state. The concept of “speed” of quantum evolution constitutes an important ingredient in any attempt to determine the fundamental limits that basic physical laws impose on how fast a physical system can process or transmit information. Here we explore the relationship between entanglement and the speed of quantum evolution in the context of the quantum brachistochrone problem. Given an initial and a final state of a composite system we consider the amount of entanglement associated with the brachistochrone evolution between those states, showing that entanglement is an essential resource to achieve the alluded time-optimal quantum evolution.

In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theorry of axion field arising from Type IIB string theory compactified to four dimensions. We compute the expression for the power spectrum of vacuum fluctuation in three different approaches, namely (1) field operator expansion (FOE) technique with the quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed quantum state and (3) the method of non-entangled state (NES). For massless axion field, in all these three formalism, we reproduce, at the leading order, the exact scale invariant power spectrum which is well known in the literature. We observe that due to quantum entanglement, the sub-leading terms for these thee formalisms are different. Thus, such correction terms break the degeneracy among the analysis of the FOE, RDM and NES formalisms in the super-horizon limit. On the other hand, for massive axion field we get a slight deviation from scale invariance and exactly quantify the spectral tilt of the power spectrum in small scales. Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the result of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of the de Sitter space. Most importantly, in near future if experiments probe for early universe phenomena, one can detect such small quantum effects. In such a scenario, it is possible to test the implications of quantum entanglement in primordial cosmology.

During de Sitter inflation massless particles of minimally coupled scalar fields acquire a mass and a decay width thereby becoming quasiparticles. For bare massless particles nonperturbative infrared radiative corrections lead to a self-consistent generation of mass, for a quartic self-interaction $M\ensuremath{\propto}{\ensuremath{\lambda}}^{1/4}H$, and for a cubic self-interaction the mass is induced by the formation of a nonperturbative condensate leading to $M\ensuremath{\propto}{\ensuremath{\lambda}}^{1/3}{H}^{2/3}$. These radiatively generated masses restore de Sitter invariance and result in anomalous scaling dimensions of superhorizon fluctuations. We introduce a generalization of the nonperturbative Wigner-Weisskopf method to obtain the time evolution of quantum states that include the self-consistent generation of mass and regulate the infrared behavior. The infrared divergences are manifest as poles in $\ensuremath{\Delta}={M}^{2}/3{H}^{2}$ in the single particle self-energies, leading to a rearrangement of the perturbative series nonanalytic in the couplings. A set of simple rules that yield the leading order infrared contributions to the decay width are obtained and implemented. The lack of kinematic thresholds entail that all particle states acquire a decay width, dominated by the emission and absorption of superhorizon quanta $\ensuremath{\propto}(\ensuremath{\lambda}/H{)}^{4/3}[H/{k}_{ph}(\ensuremath{\eta}){]}^{6}$; $\ensuremath{\lambda}[H/{k}_{ph}(\ensuremath{\eta}){]}^{6}$ for cubic and quartic couplings respectively to leading order in $M/H$. The decay of single particle quantum states hastens as their wave vectors cross the Hubble radius and their width is related to the highly squeezed limit of the bi- or trispectrum of scalar fluctuations respectively.

We theoretically study the reversible process of quantum entanglement state by means of weak measurement and corresponding reversible operation. We present a protocol of the reversion operation in two bodies based on the theory of reversion of single photon and then expend it in quantum communication channels. The theoretical results demonstrate that the protocol does not break the information transmission after a weak measurement and a reversible measurement with the subsequent process in the transmission path. It can reverse the perturbed entanglement intensity evolution to its original state. Under the condition of different weak measurement intensity the protocol can reverse the perturbed quantum entanglement system perfectly. In the process we can get the classical information described by information gain from the quantum system through weak measurement operation. On the other hand, in order to realize complete reversibility, the classical information of the quantum entanglement system must obey a limited range we present in this paper in the reverse process.