Related papers: Optimal tradeoffs for estimating Pauli observables
A new qubit tomography protocol is introduced, based on a continuous positive operator valued measure, which is supported by the set of pure states, and equivariant under the symmetry group SO(3,R) of the qubit state space. Thus the sample…
Pauli Check Sandwiching (PCS) is an error detection scheme that protects quantum circuits by inserting pairs of parity checks and discarding runs that signal errors. However, each additional check introduces noise and exponentially…
We develop a practical quantum tomography protocol and implement measurements of pure states of ququarts realized with polarization states of photon pairs (biphotons). The method is based on an optimal choice of the measuring scheme's…
A fundamental task in quantum information science is to measure nonlinear functionals of quantum states, such as $\mathrm{Tr}(\rho^k O)$. Intuitively, one expects that computing a $k$-th order quantity generally requires $O(k)$ copies of…
We introduce and investigate a data access model (approximate sample and query) that is satisfiable by the preparation and measurement of block encoded states, as well as in contexts such as classical quantum circuit simulation or Pauli…
BosonSampling is a problem where a quantum computer offers a provable speedup over classical computers. Its main feature is that it can be solved with current linear optics technology, without the need for a full quantum computer. In this…
A quantum copying machine producing two (in general non-identical) copies of an arbitrary input state of a two-dimensional Hilbert space (qubit) is studied using a quality measure based on distinguishability of states, rather than fidelity.…
Lowering the resource overhead needed to achieve fault-tolerant quantum computation is crucial to building scalable quantum computers. We show that adapting conventional maximum likelihood (ML) decoders to a small subset of efficiently…
We present a lower bound for Pauli Manipulation Detection (PMD) codes, a class of quantum codes that detect every Pauli error with high probability. Our lower bound reveals the first trade-off between the error parameter and the coding…
Although the realization of useful quantum computers poses significant challenges, swift progress in emerging quantum technologies is making this goal realistically approachable. In this context, one of the essential resources is quantum…
The accuracy of any physical scheme used to estimate the parameter describing the strength of a single qubit Pauli channel can be quantified using standard techniques from quantum estimation theory. It is known that the optimal estimation…
We initiate the study of sample-optimal quantum state tomography with minimal disturbance to the samples. Can we efficiently learn a precise description of a quantum state through sequential measurements of samples while at the same time…
We show that $n = \Omega(rd/\varepsilon^2)$ copies are necessary to learn a rank $r$ mixed state $\rho \in \mathbb{C}^{d \times d}$ up to error $\varepsilon$ in trace distance. This matches the upper bound of $n = O(rd/\varepsilon^2)$ from…
A fundamental challenge in multiparameter quantum estimation arises from the incompatibility of optimal measurements for different parameters, leading to intricate precision trade-offs that obscure the understanding of ultimate quantum…
Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be…
Quantum state tomography is essential for characterizing quantum systems, but it becomes infeasible for large systems due to exponential resource scaling. Overlapping tomography addresses this challenge by reconstructing all $k$-body…
We study the problem of finding a (pure) product state with optimal fidelity to an unknown $n$-qubit quantum state $\rho$, given copies of $\rho$. This is a basic instance of a fundamental question in quantum learning: is it possible to…
The Pauli channel is a fundamental model of noise in quantum systems, motivating the task of Pauli error estimation. We present an algorithm that builds on the reduction to Population Recovery introduced in [FO21]. Addressing an open…
Advances in quantum technology require scalable techniques to efficiently extract information from a quantum system, such as expectation values of observables or its entropy. Traditional tomography is limited to a handful of qubits and…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…