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The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…
Non-orthogonal quantum states pose a fundamental challenge in quantum information processing, as they cannot be distinguished with absolute certainty. Conventionally, the focus has been on minimizing error probability in quantum state…
We study the distinguishability of quantum states under local operations with classical communication (LOCC), separable, and positive-partial-transpose (PPT) measurements, focusing on locally diagonal orthogonally invariant (LDOI) states --…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
There are two notions of approximate Birkhoff-James orthogonality in a normed space. We characterize both the notions of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on a normed space. A complete…
We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors…
By using the method of orthogonal polynomials we analyze the statistical properties of complex eigenvalues of random matrices describing a crossover from Hermitian matrices characterized by the Wigner- Dyson statistics of real eigenvalues…
In this paper, the distinguishability of multipartite geometrically uniform quantum states obtained from a single reference state is studied in the symmetric subspace. We specially focus our attention on the unitary transformation in a way…
In this work we study a version of the general question of how well a Haar distributed orthogonal matrix can be approximated by a random gaussian matrix. Here, we consider a gaussian random matrix $Y_n$ of order $n$ and apply to it the…
The ability to decompose a signal in an orthonormal basis (a set of orthogonal components, each normalized to have unit length) using a fast numerical procedure rests at the heart of many signal processing methods and applications. The…
We study quantum phase transitions by measuring the bond energy, the number density, and the half-chain entanglement entropy in the one-dimensional ionic Hubbard model. By performing the infinite density matrix renormalization group with…
[This is the unpublished supplemental information from 1989 to the paper: J.M. Deutsch, "Quantum statistical mechanics in a closed system." Phys. Rev. A, 43(4), 2046 (1991).] A closed quantum mechanical system does not necessarily give time…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as…
We report on a systematic implementation of su(2) invariance for matrix product states (MPS) with concrete computations cast in a diagrammatic language. As an application we present a variational MPS study of $su(2)$ invariant quantum spin…
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New…
We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of generators of a Lie algebra. The number of terms in the product depends on the structure factors. When the generators have large norm…
In the study of quantum computation, data is represented in terms of linear operators which form a generalized model of probability, and computations are most commonly described as products of unitary transformations, which are the…
We consider the problem of learning $N$ identical copies of an unknown $n$-qubit quantum graph state with product measurements. These graph states have corresponding graphs where every vertex has exactly $d$ neighboring vertices. Here, we…
A new method for simulation of a binary homogeneous Markov process using a quantum computer was proposed. This new method allows using the distinguished properties of the quantum mechanical systems -- superposition, entanglement and…