Related papers: Learning Pure Quantum States in Any Dimension (Alm…
The goal of qubit purification is to combine multiple noisy copies of an unknown pure quantum state to obtain one or more copies that are closer to the pure state. We show that a simple protocol based solely on random SWAP tests achieves…
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…
The Bloch Sphere visualization of the possible states of a single qubit has proved a useful pedagogical and conceptual tool as a one-to-one map between qubit states and points in a 3-D space. However, understanding many important concepts…
Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography…
Adaptive measurements were recently shown to significantly improve the performance of quantum state tomography. Utilizing information about the system for the on-line choice of optimal measurements allows to reach the ultimate bounds of…
Distinguishing different quantum states is a fundamental task having practical applications for information processing. Despite the efforts devoted so far, however, strategies for optimal discrimination are known only for specific examples.…
A fundamental task in photonics is to characterise an unknown optical process, defined by properties such as birefringence, spectral response, thickness and flatness. Amongst many ways to achieve this, single-photon probes can be used in a…
A longstanding belief in quantum tomography is that estimating a mixed state is far harder than estimating a pure state. This is borne out in the mathematics, where mixed state algorithms have always required more sophisticated techniques…
A long-standing problem in quantum physics is to determine the minimal number of measurement bases required for the complete characterization of unknown quantum states, a question of particular relevance to high-dimensional quantum…
Starting from a simple estimation problem, here we propose a general approach for decoding quantum measurements from the perspective of information extraction. By virtue of the estimation fidelity only, we provide surprisingly simple…
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 present the optimal scheme for estimating a pure qubit state by means of local measurements on N identical copies. We give explicit examples for low N. For large N, we show that the fidelity saturates the collective measurement bound up…
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…
Quantum tomography is a crucial tool for characterizing quantum states and devices and estimating nonlinear properties of the systems. Performing full quantum state tomography on an $N_\mathrm{q}$ qubit system requires an exponentially…
The characterization of continuous-variable quantum states is crucial for applications in quantum communication, sensing, simulation and computing. However, a full characterization of multimode quantum states requires a number of…
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…
Quantum state tomography seeks to reconstruct an unknown state from measurement statistics. A finite measurement (POVM) is \emph{pure-state informationally complete} (PSI-Complete) if the outcome probabilities determine any pure state up to…
We present an effective measurement scheme for the solid-state qubits that does {\bf not} introduce extra decoherence to the qubits until the measurement is switched on by a resonant pulse. The resonant pulse then maximally entangles the…
We use a meta-learning neural-network approach to analyse data from a measured quantum state. Once our neural network has been trained it can be used to efficiently sample measurements of the state in measurement bases not contained in the…
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…