Related papers: Second-order asymptotics for quantum hypothesis te…
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…
Quantum mechanics implies that not all physical properties can be simultaneously well defined, such as the momentum and position due to Heisenberg uncertainty principle. Some alternative theories have been explored, notably the…
A theory of quantum measurement was introduced some time ago that was based on the notion of the so-called separation status. This separation status had a spatial, local character, so that the theory worked only in special cases.…
This is an English translation of the manuscript which appeared in Surikaiseki Kenkyusho Kokyuroku No. 1055 (1998). The asymptotic efficiency of statistical estimate of unknown quantum states is discussed, both in adaptive and collective…
In this paper, we show that $\Theta(\mathrm{poly}(n)\cdot\frac{4^n}{\epsilon^2})$ is the sample complexity of testing whether two $n$-qubit quantum states $\rho$ and $\sigma$ are identical or $\epsilon$-far in trace distance using…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
A general scenario for an $N$-sequential conclusive state discrimination introduced recently in Loubenets and Namkung [arXiv:2102.04747] can provide a multipartite quantum communication realizable in the presence of a noise. In the present…
A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. However, it is possible to exclude a subset of non-orthogonal states without error in certain…
The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum…
Quantum steering is an asymmetric correlation which occupies a place between entanglement and Bell nonlocality. In the paradigmatic scenario involving the protagonists Alice and Bob, the entangled state shared between them, is said to be…
We study the error exponents in quantum hypothesis testing between two sets of quantum states, extending the analysis beyond the independent and identically distributed case to encompass composite correlated hypotheses. In particular, we…
We define a quantum learning task called agnostic tomography, where given copies of an arbitrary state $\rho$ and a class of quantum states $\mathcal{C}$, the goal is to output a succinct description of a state that approximates $\rho$ at…
The principle of microscopic reversibility lies at the core of fluctuation theorems, which have extended our understanding of the second law of thermodynamics to the statistical level. In the quantum regime, however, this elementary…
We propose to use quantum information notions to characterize thermally induced melting of nonperturbative bound states at high temperatures. We apply tensor networks to investigate this idea in static and dynamical settings within the…
Quantum hypothesis testing (QHT) has been traditionally studied from the information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of samples of an unknown…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
In this paper, we consider the problem of discriminating quantum states by local operations and classical communication (LOCC) when an arbitrarily small amount of error is permitted. This paradigm is known as asymptotic state…
We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we…
The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states provided that…
Nonlocality lies at the core of quantum mechanics from both a fundamental and applicative point of view. It is typically revealed by a Bell test, that is by violation of a Bell inequality, whose success depends both on the state of the…