Related papers: Sample-optimal tomography of quantum states
Quantum state and process tomography are typically analyzed under the assumption that devices emit independent and identically distributed (i.i.d.) states or channels. In realistic experiments, however, noise, drift, feedback, or…
While quantum state tomography (QST) remains the gold standard for benchmarking and verifying quantum devices, it requires an exponentially large number of measurements and classical computational resources for generic quantum many-body…
We consider the problem of testing whether an unknown $n$-qubit quantum state $|\psi\rangle$ is a stabilizer state, with only single-copy access. We give an algorithm solving this problem using $O(n)$ copies, and conversely prove that…
Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication…
It is now experimentally possible to entangle thousands of qubits, and efficiently measure each qubit in parallel in a distinct basis. To fully characterize an unknown entangled state of $n$ qubits, one requires an exponential number of…
We study the sample complexity of shadow tomography in the high-precision regime under realistic measurement constraints. Given an unknown $d$-dimensional quantum state $\rho$ and a known set of observables $\{O_i\}_{i=1}^m$, the goal is to…
Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme's validity via the probability that…
Quantum state learning is a fundamental problem in physics and computer science. As near-term quantum devices are error-prone, it is important to design error-resistant algorithms. Apart from device errors, other unexpected factors could…
Quantum state estimation is important for various quantum information processes, including quantum communications, computation, and metrology, which require the characterization of quantum states for evaluation and optimization. We present…
We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular,…
The reconstruction of quantum states from experimental measurements, often achieved using quantum state tomography (QST), is crucial for the verification and benchmarking of quantum devices. However, performing QST for a generic…
We revisit the problem of Pauli shadow tomography: given copies of an unknown $n$-qubit quantum state $\rho$, estimate $\text{tr}(P\rho)$ for some set of Pauli operators $P$ to within additive error $\epsilon$. This has been a popular…
Assessing the quality of an ensemble of noisy entangled states is a central task in quantum information processing. Usually this is done by measuring and hence destroying multiple copies, from which state tomography or fidelity estimation…
Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this…
We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. This structured discrimination problems allow for a novel scheme that provides a certified level of error, that is,…
Quantum state tomography is the task of inferring the state of a quantum system by appropriate measurements. Since the frequency distributions of the outcomes of any finite number of measurements will generally deviate from their asymptotic…
Quantum state tomography is the standard tool in current experiments for verifying that a state prepared in the lab is close to an ideal target state, but up to now there were no rigorous methods for evaluating the precision of the state…
We provide more sample-efficient versions of some basic routines in quantum data analysis, along with simpler proofs. Particularly, we give a quantum "Threshold Search" algorithm that requires only $O((\log^2 m)/\epsilon^2)$ samples of a…