Related papers: Product testing with single-copy measurements
Quantities invariant under local unitary transformations are of natural interest in the study of entanglement. This paper deduces and studies a particularly simple quantity that is constructed from a combination of two standard permutations…
A new variant of the Compressed Sensing problem is investigated when the number of measurements corrupted by errors is upper bounded by some value l but there are no more restrictions on errors. We prove that in this case it is enough to…
We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…
We study quantum hypothesis testing between orthogonal states under restricted local measurements in the many-copy scenario. For testing arbitrary multipartite entangled pure state against its orthogonal complement state via the local…
Quantum state tomography is the problem of estimating a given quantum state. Usually, it is required to run the quantum experiment - state preparation, state evolution, measurement - several times to be able to estimate the output quantum…
The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup…
The characterization of high-dimensional entanglement plays a crucial role in the field of quantum information science. Conventional entanglement criteria measuring coherent superpositions of multiple basis states face experimental…
Broad claims about whether adaptivity helps in quantum state tomography can be misleading unless the state family, measurement architecture, and error metric are specified carefully. We study a restricted but physically important regime:…
We present observable lower bounds for several bipartite entanglement measures including entanglement of formation, geometric measure of entanglement, concurrence, convex-roof extended negativity, and G-concurrence. The lower bounds…
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…
Given $n$ copies of an unknown quantum state $\rho\in\mathbb{C}^{d\times d}$, quantum state certification is the task of determining whether $\rho=\rho_0$ or $\|\rho-\rho_0\|_1>\varepsilon$, where $\rho_0$ is a known reference state. We…
State tomography on qubit pairs is routinely carried out by measuring the two qubits separately, while one expects a higher efficiency from tomography with highly symmetric joint measurements of both qubits. Our numerical study of simulated…
We analyze the distinguishability norm on the states of a multi-partite system, defined by local measurements. Concretely, we show that the norm associated to a tensor product of sufficiently symmetric measurements is essentially equivalent…
Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
Self-testing is a method to certify quantum states and measurements in a device-independent way. The device-independent certification of quantum properties is purely based on input-output measurement statistics of the involved devices with…
We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space can exceed the observed dimensionality. In particular, we consider multiview mixtures, spherical…
We show that combining randomized measurement protocols with importance sampling allows for characterizing entanglement in significantly larger quantum systems and in a more efficient way than in previous work. A drastic reduction of…
In this paper, we introduce a class of highly entangled real quantum states that cannot be approximated by circuits with $\log$-many non-Clifford gates and prove that Bell sampling enables efficient cross-device verification (or distributed…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…