相关论文: Resource-efficient algorithm for estimating the tr…
In quantum information, trace distance is a basic metric of distinguishability between quantum states. However, there is no known efficient approach to estimate the value of trace distance in general. In this paper, we propose efficient…
In the quantum state tomography problem, one wishes to estimate an unknown $d$-dimensional mixed quantum state $\rho$, given few copies. We show that $O(d/\epsilon)$ copies suffice to obtain an estimate $\hat{\rho}$ that satisfies…
We consider a fundamental task in quantum information theory, estimating the values of $\operatorname{tr}(O\rho)$, $\operatorname{tr}(O\rho^2)$, ..., $\operatorname{tr}(O\rho^k)$ for an observable $O$ and a quantum state $\rho$. We show…
As often emerges in various basic quantum properties such as R\'enyi and Tsallis entropies, the trace of quantum state powers $\text{tr}(\rho^q)$ has attracted a lot of attention. The recent work of Liu and Wang (SODA 2025) showed that,…
We investigate the computational complexity of estimating the trace of quantum state powers $\text{tr}(\rho^q)$ for an $n$-qubit mixed quantum state $\rho$, given its state-preparation circuit of size $\text{poly}(n)$. This quantity is…
We describe algorithms to obtain an approximate classical description of a $d$-dimensional quantum state when given access to a unitary (and its inverse) that prepares it. For pure states we characterize the query complexity for…
Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or…
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…
In the fields of quantum mechanics and quantum information science, the traces of reduced density matrix powers play a crucial role in the study of quantum systems and have numerous important applications. In this paper, we propose a…
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…
Estimating nonlinear properties such as R\'enyi entropies and observable-weighted moments serves as a central strategy for spectrum spectroscopy, which is fundamental to property prediction and analysis in quantum information science,…
Demonstration of quantum advantage remains challenging due to the increased overhead of controlling large quantum systems. While significant effort has been devoted to qubit-based devices, qudits ($d$-level systems) offer potential…
How many copies of a mixed state $\rho \in \mathbb{C}^{d \times d}$ are needed to learn its spectrum? To date, the best known algorithms for spectrum estimation require as many copies as full state tomography, suggesting the possibility…
In the problem of quantum state tomography, one is given $n$ copies of an unknown rank-$r$ mixed state $\rho \in \mathbb{C}^{d \times d}$ and asked to produce an estimator of $\rho$. In this work, we present the debiased Keyl's algorithm,…
Measuring the distinguishability between quantum states is a basic problem in quantum information theory. In this paper, we develop optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure…
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…
We propose a series of quantum algorithms for computing a wide range of quantum entropies and distances, including the von Neumann entropy, quantum R\'{e}nyi entropy, trace distance, and fidelity. The proposed algorithms significantly…
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…
In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that…
When it comes to discriminating between two quantum states, trace distance is one of the well-known metrics used in quantum computation and quantum information theory. While there are several quantum algorithms for calculating the trace…