Related papers: Average fidelity between random quantum states
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
Quantum tomography is a widely applicable method for reconstructing unknown quantum states and processes. However, its applications in quantum technologies usually also require estimating the difference between prepared and target quantum…
Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization for state reconstruction, we…
We propose a quantum tomography scheme for pure qudit systems which adopts random base measurements and generative learning methods, along with a built-in fidelity estimation approach to assess the reliability of the tomographic states. We…
In almost all quantum applications, one of the key steps is to verify that the fidelity of the prepared quantum state meets expectations. In this Letter, we propose a new approach solving this problem using machine-learning techniques.…
The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical…
We report on experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in Hilbert space is far less complex than…
The transfer of quantum information between different locations is key to many quantum information processing tasks. Whereas, the transfer of a single qubit state has been extensively investigated, the transfer of a many-body system…
Estimation of quantum states is one of the most important steps in any quantum information processing experiment. A naive reconstruction of the density matrix from experimental measurements can often give density matrices which are not…
We study the problem of quantum-state tomography under the assumption that the state of the system is close to pure. In this context, an efficient measurements that one typically formulates uniquely identify a pure state from within the set…
We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of…
Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and…
In quantum information geometry, the curvature of von-Neumann entropy and relative entropy induce a natural metric on the space of mixed quantum states. Here we use this information metric to construct a random matrix ensemble for states…
We consider the quantum expectation value \mathcal{A}=\<\psi|A|\psi\> of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all…
Matrix product states, a key ingredient of numerical algorithms widely employed in the simulation of quantum spin chains, provide an intriguing tool for quantum phase transition engineering. At critical values of the control parameters on…
We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact…
We describe a simple way of characterizing the average fidelity between a unitary (or anti-unitary) operator and a general operation on a single qubit, which only involves calculating the fidelities for a few pure input states, and discuss…
Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…
A quantum ensemble $\{(p_x, \rho_x)\}$ is a set of quantum states each occurring randomly with a given probability. Quantum ensembles are necessary to describe situations with incomplete a priori information, such as the output of a…
We introduce and investigate a distance-type measure of non-Gaussianity based on the quantum fidelity. This new measure can readily be evaluated for all pure states and mixed states that are diagonal in the Fock basis. In particular, for an…