Related papers: Quantum chi-squared tomography and mutual informat…
We show new lower bounds on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer large sets of counting queries. A counting query on a database $D \in (\{0,1\}^d)^n$ has the form "What…
Dicke states are typical examples of quantum states with genuine multipartite entanglement. They are valuable resources in many quantum information processing tasks, including multiparty quantum communication and quantum metrology. Phased…
We explore potential quantum speedups for the fundamental problem of testing the properties of closeness and $k$-wise uniformity of probability distributions. Closeness testing is the problem of distinguishing whether two $n$-dimensional…
We propose a randomized algorithm with query access that given a graph $G$ with arboricity $\alpha$, and average degree $d$, makes $\widetilde{O}\left(\frac{\alpha}{\varepsilon^2d}\right)$ \texttt{Degree} and…
We present new algorithms for estimating and testing \emph{collision probability}, a fundamental measure of the spread of a discrete distribution that is widely used in many scientific fields. We describe an algorithm that satisfies…
We study the problem of testing identity of a collection of unknown quantum states given sample access to this collection, each state appearing with some known probability. We show that for a collection of $d$-dimensional quantum states of…
We study the fundamental limits on the reliable storage of quantum information in lattices of qubits by deriving tradeoff bounds for approximate quantum error correcting codes. We introduce a notion of local approximate correctability and…
Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…
We prove a lower bound on the number of copies needed to test the property of a multipartite quantum state being product across some bipartition (i.e. not genuinely multipartite entangled), given the promise that the input state either has…
In this note, we develop a bounded-error quantum algorithm that makes $\tilde O(n^{1/4}\varepsilon^{-1/2})$ queries to a Boolean function $f$, accepts a monotone function, and rejects a function that is $\varepsilon$-far from being…
Reconfigurable devices which can implement arbitrary unitary operations are crucial for photonic quantum computation, optical neural networks, and boson sampling. Here, we address the problem of, using multiport interferometers,…
Quantum devices for generating entangled states have been extensively studied and widely used. As so, it becomes necessary to verify that these devices truly work reliably and efficiently as they are specified. Here, we experimentally…
We study quantum soft covering and privacy amplification against quantum side information. The former task aims to approximate a quantum state by sampling from a prior distribution and querying a quantum channel. The latter task aims to…
We provide the first non-trivial lower bounds for single-qubit tomography algorithms and show that at least ${\Omega}\left(\frac{10^N}{\sqrt{N} \varepsilon^2}\right)$ copies are required to learn an $N$-qubit state…
As a measure of the 'closeness' of two quantum states, fidelity plays a fundamental role in quantum information theory. Fidelity estimation protocols try to strike a balance between information gleaned from an experiment, and the efficiency…
Extensive quantum error correction is necessary in order to perform a useful computation on a noisy quantum computer. Moreover, quantum error correction must be implemented based on imperfect parity check measurements that may return…
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…
The fidelity estimation between two quantum states is crucial for quantum computation and information science. However, an efficacious method for this, especially for mixed states and higher-dimensional density matrices, remains elusive.…
It has been known that all bipartite pure quantum states can be certified by quantum self-testing, i.e., any such states can be pinned down completely based on the statistics produced by local quantum measurements. A notable feature of…
We consider the task of quantum state certification: given a description of a hypothesis state $\sigma$ and multiple copies of an unknown state $\rho$, a tester aims to determine whether the two states are equal or $\epsilon$-far in trace…