Related papers: Quantum Circuits, Feature Maps, and Expanded Pseud…
Efficient estimation of nonlinear functions of quantum states is crucial for various key tasks in quantum computing, such as entanglement spectroscopy, fidelity estimation, and feature analysis of quantum data. Conventional methods using…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
In this article, we present quantum algorithms for estimating von Neumann entropy and Renyi entropy, which are crucial physical and information-theoretical properties of a given quantum state $\rho$. Although there have been existing works…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
Evolution of charged quantum fields under the action of constant nonuniform electric fields is studied. To this end we construct a special generating functional for density operators of the quantum fields with different initial conditions.…
The entropy of a quantum system is a measure of its randomness, and has applications in measuring quantum entanglement. We study the problem of measuring the von Neumann entropy, $S(\rho)$, and R\'enyi entropy, $S_\alpha(\rho)$ of an…
Quantum informatic quantities such as entanglement entropy are useful in detecting quantum phase transitions. Recently, a new entanglement measure called pseudo-entropy was proposed which is a generalization of the more well-known…
In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the…
We propose a series of quantum algorithms for computing a wide range of quantum entropies and distances, including the von Neumann entropy, quantum R\'{e}nyi entropy, trace distance, and fidelity. The proposed algorithms significantly…
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling…
Regarding the strange properties of quantum entropy and entanglement, e.g., the negative quantum conditional entropy, we revisited the foundations of quantum entropy, namely, von Neumann entropy, and raised the new method of quantum…
We develop a graph-based method to study the entanglement entropy of Calderbank-Shor-Steane quantum codes. This method offers a straightforward interpretation for the entanglement entropy of quantum error correcting codes through…
Statistical correlations that can be generated across the nodes in a quantum network depend crucially on its topology. However, this topological information might not be known a priori, or it may need to be verified. In this paper, we…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
We develop a rigorous framework for quantifying quantum coherence in finite-dimensional systems by applying the Schur-Horn majorization theorem to relate eigenvalue distributions and diagonal entries of density matrices. Building on this…
Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of…
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…
In this thesis, we study aspects of entanglement theory of quantum field theories from an algebraic point of view. The main motivation is to gain insights about the general structure of the entanglement in QFT, towards a definition of an…
The aim of this work is to introduce the entanglement entropy of real and virtual excitations of fermion and photon fields. By rewriting the generating functional of quantum electrodynamics theory as an inner product between quantum…
The von Neumann and quantum R\'enyi entropies characterize fundamental properties of quantum systems and lead to theoretical and practical applications in many fields. Quantum algorithms for estimating quantum entropies, using a quantum…