Related papers: Efficient algorithm for fidelity estimation of two…
Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…
Quantum fidelity between two density matrices, $F(\rho_1,\rho_2)$ is usually defined as the trace of the operator ${\cal F}=\sqrt{\sqrt{\rho_1} \rho_2 \sqrt{\rho_1}}$. We study the logarithmic spectrum of this operator, which we denote by…
We show that $\Omega(rd/\epsilon)$ copies of an unknown rank-$r$, dimension-$d$ quantum mixed state are necessary in order to learn a classical description with $1 - \epsilon$ fidelity. This improves upon the tomography lower bounds…
We present a general theoretical formalism to compute the fidelity of transformations of unknown quantum states. We then focus on the case of Gaussian transformations of continuous variable quantum systems, where, for the case of a Gaussian…
When a system undergoes a quantum phase transition, the ground-state wave-function shows a change of nature, which can be monitored using the fidelity concept. We introduce two Quantum Monte Carlo schemes that allow the computation of…
The measures of distances between points in a Hilbert space are one of the basic theoretical concepts used to characterize properties of a quantum system with respect to some etalon state. These are not only used in studying fidelity of…
The problem of the quantitative degradation of the performance of a quantum computer due to noisy unitary gates (imperfect external control) is studied. It is shown that quite general conclusions on the evolution of the fidelity can be…
Practical quantum state tomography is usually performed by carrying out repeated measurements on many copies of a given state. The accuracy of the reconstruction depends strongly on the dimensionality of the system and the number of copies…
We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity…
Quantum state tomography, which aims to find the best description of a quantum state -- the density matrix, is an essential building block in quantum computation and communication. Standard techniques for state tomography are incapable of…
We present optimal measuring strategies for the estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general…
Universal quantum computation using optical coherent states is studied. A teleportation scheme for a coherent-state qubit is developed and applied to gate operations. This scheme is shown to be robust to detection inefficiency.
Quantum systems have entered a competitive regime where classical computers must make approximations to represent highly entangled quantum states. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and…
We consider a single copy of a mixed state of two qubits and show how its fidelity or maximal singlet fraction is related to the entanglement measures concurrence and negativity. We characterize the extreme points of the convex set of…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
To gain an advantage, quantum technologies utilize phenomena particular to quantum mechanics. Two such phenomena are squeezing and entanglement. Having generated states that exhibit these features, verification of their generation with…
While quantum algorithms for simulation exhibit better asymptotic scaling than their classical counterparts, they currently cannot be implemented on real-world devices. Instead, chemists and computer scientists rely on costly classical…
We extend to finite temperature the fidelity approach to quantum phase transitions (QPTs). This is done by resorting to the notion of mixed-state fidelity that allows one to compare two density matrices corresponding to two different…