Related papers: Sample optimal Quantum identity testing via Pauli …
We study the question of closeness testing for two discrete distributions. More precisely, given samples from two distributions $p$ and $q$ over an $n$-element set, we wish to distinguish whether $p=q$ versus $p$ is at least $\eps$-far from…
We revisit the basic problem of quantum state certification: given copies of unknown mixed state $\rho\in\mathbb{C}^{d\times d}$ and the description of a mixed state $\sigma$, decide whether $\sigma = \rho$ or $\|\sigma -…
We consider the problem of testing distribution identity. Given a sequence of independent samples from an unknown distribution on a domain of size n, the goal is to check if the unknown distribution approximately equals a known distribution…
We analyse orthogonal bases in a composite $N\times N$ Hilbert space describing a bipartite quantum system and look for a basis with optimal single-sided mutual state distinguishability. This condition implies that in each subsystem the…
It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error $\epsilon$ in trace distance required…
The relative entropy between quantum states quantifies their distinguishability. The estimation of certain relative entropies has been investigated in the literature, e.g., the von Neumann relative entropy and sandwiched R\'enyi relative…
Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of…
Statistical verification of a quantum state aims to certify whether a given unknown state is close to the target state with confidence. So far, sample-optimal verification protocols based on local measurements have been found only for…
Recently, a technique known as quantum symmetry test has gained increasing attention for detecting bipartite entanglement in pure quantum states. In this work we show that, beyond qualitative detection, a family of well-defined measures of…
A discrimination problem consists of $N$ linearly independent pure quantum states $\Phi=\{\ket{\phi_i}\}$ and the corresponding occurrence probabilities $\eta=\{\eta_i\}$. To any such problem we associate, up to a permutation over the…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
Any rule for identifying a quantum system's state within a set of two non-orthogonal pure states by a single measurement is flawed. It has a non-zero probability of either yielding the wrong result or leaving the query undecided. This also…
Self-testing refers to the possibility of characterizing uniquely (up to local isometries) the state and measurements contained in quantum devices, based only on the observed input-output statistics. Already in the basic case of the…
We consider a fixed quantum measurement performed over $n$ identical copies of quantum states. Using a rigorous notion of distinguishability We consider a fixed quantum measurement performed over $n$ identical copies of quantum states.…
With the advance of quantum information technology, the question of how to most efficiently test quantum circuits is becoming of increasing relevance. Here we introduce the statistics of lengths of measurement sequences that allows one to…
Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on…
Verification is a task to check whether a given quantum state is close to an ideal state or not. In this paper, we show that a variety of many-qubit quantum states can be verified with only sequential single-qubit measurements of Pauli…
We study the power of local test for bipartite quantum states. Our central result is that, for properties of bipartite pure states, unitary invariance on one part implies an optimal (over all global testers) local tester acting only on the…
We consider a quantum version of the famous low-rank approximation problem. Specifically, we consider the distance $D(\rho,\sigma)$ between two normalized quantum states, $\rho$ and $\sigma$, where the rank of $\sigma$ is constrained to be…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…