Related papers: Instance-Optimal Quantum State Certification with …
Quantum state tomography (QST) aims at estimating a quantum state from averaged quantum measurements made on copies of the state. Most quantum algorithms rely on QST at some point and it is a well explored topic in the literature, mostly…
One of the most fundamental problems in distribution testing is the identity testing problem: given samples $x_1,\ldots,x_s$, the goal is to determine whether the samples are drawn from a target distribution $\mathcal{D}$. When…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…
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…
The emergence of quantum devices has raised a significant issue: how to certify the quantum properties of a device without placing trust in it. To characterise quantum states and measurements in a device-independent way, up to some degree…
This paper discusses properties of quantum fingerprinting with shared entanglement. Under certain restriction of final measurement, a relation is given between unitary operations of two parties. Then, by reducing to spherical coding…
We study quantum state testing where the goal is to test whether $\rho=\rho_0\in\mathbb{C}^{d\times d}$ or $\|\rho-\rho_0\|_1>\varepsilon$, given $n$ copies of $\rho$ and a known state description $\rho_0$. In practice, not all measurements…
So far, certifying quantum devices from their input-output statistics, under minimal assumptions, required the preparation of specific pure quantum states. Recently, Xu et al. [Phys. Rev. Lett. 132, 140201 (2024)] have demonstrated that…
We study the distinguishability of bipartite quantum states by Positive Operator-Valued Measures with positive partial transpose (PPT POVMs). The contributions of this paper include: (1). We give a negative answer to an open problem of [M.…
In this work, we present a practical and efficient framework for verifying entangled states when only a tomographically incomplete measurement setting is available-specifically, when access to observables is severely limited. We show how…
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting…
We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the…
One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for…
In recent times, device-independent certification of quantum states has been one of the intensively studied areas in quantum information. However, all such schemes utilise projective measurements which are practically difficult to generate.…
Optimal quantum cloning is the process of making one or more copies of an arbitrary unknown input quantum state with the highest possible fidelity. All reported demonstrations of quantum cloning have so far been limited to copying…
Quantum learning from state samples is often benchmarked in a fixed-budget paradigm, relating error to a prescribed number of copies. We instead adopt a stopping-time viewpoint: in minimal-feedback learning, the learning completion can be…
Bell inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description.…
Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies. Here, we introduce a generalized framework to directly certify maximal…
Quantum state tomography (QST) is an essential tool for characterizing an unknown quantum state. Recently, QST has been performed for entangled qudits based on orbital angular momentum, time-energy uncertainty, and frequency bins. Here, we…
Entanglement is an important resource that allows quantum technologies to go beyond the classically possible. There are many ways quantum systems can be entangled, ranging from the archetypal two-qubit case to more exotic scenarios of…