Related papers: Optimal quantum (tensor product) expanders from un…
We consider the general problem of the optimal transformation of N uses of (possibly different) unitary channels to a single use of another unitary channel in any finite dimension. We show how the optimal transformation can be fully…
The impressive pace of advance of quantum technology calls for robust and scalable techniques for the characterization and validation of quantum hardware. Quantum process tomography, the reconstruction of an unknown quantum channel from…
A fundamental question asks how uniformly finite sets of pure quantum states can be distributed in a Hilbert space. The Welch bounds address this question, and are saturated by $k$-designs, i.e. sets of states reproducing the $k$-th Haar…
We study the super dense coding capacity in the presence of quantum channels with correlated noise. We investigate both the cases of unitary and non-unitary encoding. Pauli channels for arbitrary dimensions are treated explicitly. The super…
We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on…
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly off-the-diagonal and $L^q$-sparse operators with an…
We give an efficient algorithm that transforms any bounded degree expander graph into another that achieves almost optimal (namely, near-quadratic, $d \leq 1/\lambda^{2+o(1)}$) trade-off between (any desired) spectral expansion $\lambda$…
In this article we consider flagged extensions of convex combination of quantum channels, and find general sufficient conditions for the degradability of the flagged extension. An immediate application is a bound on the quantum $Q$ and…
The capacity to randomly pick a unitary across the whole unitary group is a powerful tool across physics and quantum information. A unitary $t$-design is designed to tackle this challenge in an efficient way, yet constructions to date rely…
In this work, we prove a one-shot random coding bound for classical-quantum channel coding, a problem conjectured by Burnashev and Holevo in 1998. By choosing the optimal input distribution, the bound implies the optimal error exponent…
In this paper, we present a condition for the zero-error capacity of quantum channels. To achieve this result we first prove that the eigenvectors (or eigenstates) common to the Kraus operators representing the quantum channel are fixed…
Let $U_d$ be a unitary operator representing an arbitrary $d$-dimensional unitary quantum operation. This work presents optimal quantum circuits for transforming a number $k$ of calls of $U_d$ into its complex conjugate $\bar{U_d}$. Our…
Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically,…
We study the limiting spectral distribution of quantum channels whose Kraus operators are sampled as $n\times n$ random Hermitian matrices satisfying certain assumptions. We show that when the Kraus rank goes to infinity with n, the…
We introduce sequential and parallel decoders for quantum Tanner codes. When the Tanner code construction is applied to a sufficiently expanding square complex with robust local codes, we obtain a family of asymptotically good quantum…
We present a constructive control scheme for solving quantum state engineering problems based on a parametrization of the state vector in terms of complex hyperspherical coordinates. Unlike many control schemes based on factorization of…
Quantum generative models may achieve an advantage on quantum devices by their inherent probabilistic nature and efficient sampling strategies. However, current approaches mostly rely on general-purpose circuits, such as the hardware…
The characterization of quantum processes is a key tool in quantum information processing tasks for several reasons: on one hand, it allows to acknowledge errors in the implementations of quantum algorithms; on the other, it allows to…