Related papers: Optimal Qubit Purification and Unitary Schur Sampl…
Quantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum…
We develop a measurement-based protocol for simultaneously purifying arbitrary logical states in multiple quantum error correcting codes with unit fidelity and finite probability, starting from arbitrary thermal states of each code. The…
Purification of mixed states in Quantum Mechanics, by which we mean the transformation into pure states, has been viewed as an {\it Operation} in the sense of Kraus et al and explicit {\it Kraus Operators} \cite{kra1,kra2,kra3} have been…
Given an ensemble of mixed qubit states, it is possible to increase the purity of the constituent states using a procedure known as state purification. The reverse operation, which we refer to as dilution, reduces the level of purity…
Quantum state purification is crucial in quantum communication and computation, aiming to recover a purified state from multiple copies of an unknown noisy state. This work introduces a general state purification framework designed to…
A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However existing results suggest that such an enhancement is only possible when the measurement…
Quantum error mitigation is essential for computing on the noisy quantum computer with a limited number of qubits. In this paper, we propose a practical protocol of error mitigation by virtually purifying the quantum state without qubit…
Given multiple copies of a mixed quantum state with an unknown, nondegenerate principal eigenspace, quantum state purification is the task of recovering a quantum state that is closer to the principal eigenstate. A streaming protocol…
We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about number and positions of errors in the noisy ensemble in an explicit and controlled way,…
We study the estimation of the overlap between two unknown pure quantum states of a finite dimensional system, given $M$ and $N$ copies of each type. This is a fundamental primitive in quantum information processing that is commonly…
The quantum Schur transform maps the computational basis of a system of $n$ qudits onto a \textit{Schur basis}, which spans the minimal invariant subspaces of the representations of the unitary and the symmetric groups acting on the state…
We investigate the probabilistic cloning and purification of quantum states. The performance of these probabilistic operations is quantified by the average fidelity between the ideal and actual output states. We provide a simple formula for…
Quantum state purification is the functionality that, given multiple copies of an unknown state, outputs a state with increased purity. This will be an essential building block for near- and middle-term quantum ecosystems before the…
We propose a single auxiliary-assisted purification-based framework for quantum error correction, capable of correcting errors that drive a system from its ground-state subspace into excited-state sectors. The protocol consists of a joint…
In this paper we consider feedback control algorithms for the rapid purification of a bipartite state consisting of two qubits, when the observer has access to only one of the qubits. We show 1) that the algorithm that maximizes the average…
The precision and sensitivity achievable in quantum metrology are often compromised by the presence of noise. While quantum error correction has emerged as a promising strategy, it is ineffective in addressing noise that is…
Quantum state tomography (QST) is one of the fundamental problems in quantum information. Among various metrics, sample complexity is widely used to evaluate QST algorithms. While multi-copy measurements are known to achieve optimal sample…
The success of quantum information processing applications relies on accurate and efficient characterization of quantum states, especially nearly-pure states. In this work, we investigate a procedure for adaptive qubit state tomography…
Quantum state purification, a process that aims to recover a state closer to a system's principal eigenstate from multiple copies of an unknown noisy quantum state, is crucial for restoring noisy states to a more useful form in quantum…
Global unitary transformations (OPTSWAPS) that optimally increase the bias of any mixed computation qubit in a quantum system -- represented by a diagonal density matrix -- towards a particular state of the computational basis which, in…