Entanglement Dynamics of Multipartite Systems Under Decoherencefrom a Spin Environment

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 adiabatic theorem and "shortcuts to adiabaticity" for the adiabatic\ndynamics of time-dependent decoherence-free subspaces are explored in this\npaper. Starting from the definition of the dynamical stable decoherence-free\nsubspaces, we show that, under a compact adiabatic condition, the quantum state\nfollows time-dependent decoherence-free subspaces (the adiabatic decoherence\nfree subspaces) into the target subspace with extremely high purity, even\nthough the dynamics of the quantum system may be non-adiabatic. The adiabatic\ncondition mentioned in the adiabatic theorem is very similar with the adiabatic\ncondition for closed quantum systems, except that the operators required to be\n"slowness" is on the Lindblad operators. We also show that the adiabatic\ndecoherence-free subspaces program depends on the existence of instantaneous\ndecoherence-free subspaces, which requires that the Hamiltonian of open quantum\nsystems has to be engineered according to the incoherent control program.\nBesides, "the shortcuts to adiabaticity" for the adiabatic decoherence-free\nsubspaces program is also presented based on the transitionless quantum driving\nmethod. Finally, we provide an example of physical systems that support our\nprograms. Our approach employs Markovian master equations and applies primarily\nto finite-dimensional quantum systems.\n

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).

We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of position and its measurement in the sense of a weak measurement (positive operator-valued measure), we find two equivalent pictures in a position representation: a constrained local description in position containing additional degrees of freedom and an unconstrained nonlocal description in terms of the position without any other degrees of freedom. Both these descriptions have a corresponding classical theory which shows that the concept of extended, structured objects emerges quite naturally and unavoidably there. It is explicitly demonstrated that the conserved energy and angular momentum contain corrections to those of a point particle. We argue that these notions also extend naturally to the quantum level. The local description is found to be the most convenient as it manifestly displays additional information about the structure of quantum states that is more subtly encoded in the nonlocal, unconstrained description. Subsequently, we use this picture to discuss the free particle and harmonic oscillator as examples.

Time fractional evolution of a single quantum state and entangled state

In general, implementing a multi-logical-qubit gate by manipulating quantum states in a decoherence-free subspace (DFS) becomes more complex and difficult when increasing the number of logical qubits. In this work, we propose an idea to realize quantum gates by manipulating quantum states outside their DFS but having the states of the logical qubits remain in their DFS before and after the gate operation. This proposal has the following features: (i) because the states are manipulated outside the DFS, the multiqubit gate implementation can be simplified when compared to realizing a multiqubit gate via manipulating quantum states within the DFS, which usually requires unitary operations over a large DFS, and (ii) because the states of the logical qubits return to the DFS after the gate operation, the errors caused by decoherence during the gate operation are not accumulated for a long-running calculation, and the states of the logical qubits are immune to decoherence when they are stored. Based on this proposal, we then present a way for realizing a multi-target-qubit controlled-not gate using logical qubits encoded in a decoherence-free subspace against collective dephasing. This gate is realized by employing qutrits (three-level quantum systems) placed in a cavity or coupled to a resonator. This proposal has the following advantages: (i) the states of the logical qubits return to their DFS after the gate operation; (ii) the gate can be implemented with only a few basic operations; (iii) the gate operation time is independent of the number of logical qubits; (iv) this gate can be deterministically implemented because no measurement is needed; (v) the intermediate higher-energy level for all qutrits is not occupied during the entire operation, thus decoherence from this level is greatly suppressed; (vi) this proposal is universal and can be applied to realize the proposed gate using natural atoms or artificial atoms (e.g., quantum dots, nitrogen-vacancy centers, and various superconducting qutrits, etc.) placed in a cavity or coupled to a resonator. As an application, we also show how to apply this gate to create a Greenberger-Horne-Zeilinger (GHZ) entangled state of multiple logical qubits encoded in DFS, and further investigate the experimental feasibility for creating the GHZ state of three logical qubits in the DFS, by using six superconducting transmon qutrits coupled to a one-dimensional coplanar waveguide resonator.

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.

The degree conjecture for bipartite quantum states which are normalized graph Laplacians was first put forward by Braunstein et al. [Phys. Rev. A 73 (2006) 012320]. The degree criterion, which is equivalent to PPT criterion, is simpler and more efficient to detect the separability of quantum states associated with graphs. Hassan et al. settled the degree conjecture for the separability of multipartite quantum states in [J. Math. Phys. 49 (2008) 0121105]. It is proved that the conjecture is true for pure multipartite quantum states. However, the degree condition is only necessary for separability of a class of quantum mixed states. It does not apply to all mixed states. In this paper, we show that the degree conjecture holds for the mixed quantum states of nearest point graph. As a byproduct, the degree criterion is necessary and sufficient for multipartite separability of [Formula: see text]-qubit quantum states associated with graphs.

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.

In this paper, we propose a protocol to deterministically teleportan unknown mixed state of qubit by utilizing a maximally bipartiteentangled state of qubits as quantum channel. If a non-maximallyentangled bipartite pure state is employed as quantum channel, theunknown mixed quantum state of qubit can be teleported with1−(1−C2)1/2 probability, where C is the concurrence of thequantum channel. The protocol can also be generalized to teleport amixed state of qudit or a multipartite mixed state. More importantpurpose is that, on the basis of the protocol, the teleportation ofan arbitrary multipartite (pure or mixed) quantum state can bedecomposed into the teleportation of each subsystem by employingseparate entangled states as quantum channels. In the case ofdeterministic teleportation, Bob only needs to perform unitarytransformations on his single particles in order to recover theinitial teleported multipartite quantum state.

We consider two related problems of extracting correlation from a given multipartite mixed quantum state: the first is the distillation of a conference key when the state is shared between a number of legal players and an eavesdropper; the eavesdropper, apart from starting off with this quantum side information, also observes the public communication between the players. The second is the distillation of Greenberger-Horne-Zeilinger (GHZ) states by means of LOCC from the given mixed state. These problem settings extend our previous paper [FS & AW, IEEE Trans. Inf. Theory 68(2):976-988, 2022], and we generalise its results: using a quantum version of the task of communication for omniscience, we derive a novel lower bound on the distillable secret key from any multipartite quantum state by means of a so-called non-interacting communication protocol. Secondly, by making the secret key distillation protocol coherent, we derive novel lower bounds on the distillation rate of GHZ states. Full details in the long version [1].

Describing the dynamics of strong-laser driven open quantum systems is a very challenging task that requires the solution of highly involved equations of motion. While machine learning techniques are being applied with some success to simulate the time evolution of individual quantum states, their use to approximate time-dependent operators (that can evolve various states) remains largely unexplored. In this work, we develop driven (NQP), a universal neural network framework that solves driven-dissipative quantum dynamics by approximating propagators rather than wave functions or density matrices. NQP can handle arbitrary initial quantum states, adapt to various external fields, and simulate long-time dynamics, even when trained on far shorter time windows. Furthermore, by appropriately configuring the external fields, our trained NQP can be transferred to systems governed by different Hamiltonians. We demonstrate the effectiveness of our approach by studying the spin-boson and the three-state transition Gamma models.

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.

We consider a partial trace transformation which maps a multipartite quantum state to collection of local density matrices. We call this collection a mean field state. For the Hilbert spaces $(\CC^2)^{\otimes n}$ and $\CC^2\otimes\CC^2\otimes\CC^4$ the necessary and sufficient conditions under which a mean field state is compatible with at least one multipartite pure state are found. Compatibility of mean field states with more general classes of multipartite quantum states is discussed.

Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify arbitrary multipartite pure quantum states using adaptive local projective measurements. Moreover, we establish a universal upper bound on the sample complexity that is independent of the local dimensions. Numerical calculations further indicate that Haar-random pure states can be verified with a constant sample cost, irrespective of the qudit number and local dimensions, even in the adversarial scenario in which the source cannot be trusted. As alternatives, we provide several simpler variants that can achieve similar high efficiencies without using Schmidt decomposition. The simplest variant consists of only two distinct tests.