Related papers: Quantum Channel Testing in Average-Case Distance
Certifying the correct functioning of a unitary channel is a critical step toward reliable quantum information processing. In this work, we investigate the query complexity of the unitary channel certification task: testing whether a given…
Quantum process tomography, the task of estimating an unknown quantum channel, is a central problem in quantum information theory. A long-standing open question is to determine the optimal number of uses of an unknown channel required to…
We introduce distance measures between quantum states, measurements, and channels based on their statistical distinguishability in generic experiments. Specifically, we analyze the average Total Variation Distance (TVD) between output…
Amplitude damping (AD) channels are good models for many physical scenarios, and so the development of protocols to discriminate between them is an important task in quantum information science. It is therefore important to bound the…
We prove that learning an unknown quantum channel with input dimension $d_A$, output dimension $d_B$, and Choi rank $r$ to diamond distance $\varepsilon$ requires $ \Omega\!\left( \frac{d_A d_B r}{\varepsilon \log(d_B r / \varepsilon)}…
For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two…
For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two…
In this work, we perform an in-depth study of recently introduced average-case quantum distances. The average-case distances approximate the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in…
Quantum state and process tomography are typically analyzed under the assumption that devices emit independent and identically distributed (i.i.d.) states or channels. In realistic experiments, however, noise, drift, feedback, or…
We consider process tomography for unitary quantum channels. Given access to an unknown unitary channel acting on a $\textsf{d}$-dimensional qudit, we aim to output a classical description of a unitary that is $\varepsilon$-close to the…
Checking whether two quantum circuits are approximately equivalent is a common task in quantum computing. We consider a closely related identity check problem: given a quantum circuit $U$, one has to estimate the diamond-norm distance…
In the problem of quantum channel certification, we have black box access to a quantum process and would like to decide if this process matches some predefined specification or is $\varepsilon$-far from this specification. The objective is…
Fault-tolerant quantum computation requires non-destructive quantum measurements with classical feed-forward. Many experimental groups are actively working towards implementing such capabilities and so they need to be accurately evaluated.…
We study the estimation of an unknown quantum channel $\mathcal{E}$ with input dimension $d_1$, output dimension $d_2$ and Kraus rank at most $r$. We establish a connection between the query complexities in two models: (i) access to…
We consider the problem of quantum channel certification to unitary, where one is given access to an unknown $d$-dimensional channel $\mathcal{E}$, and wants to test whether $\mathcal{E}$ is equal to a target unitary channel or is…
In this work we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant…
The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one…
The classical randomization criterion is an important result of statistical decision theory. Recently, a quantum analogue has been proposed, giving equivalent conditions for two sets of quantum states, ensuring existence of a quantum…
The diamond norm measures the distance between two quantum channels. From an operational vewpoint, this norm measures how well we can distinguish between two channels by applying them to input states of arbitrarily large dimensions. In this…
The data-processing inequality ensures quantum channels reduce state distinguishability, with contraction coefficients quantifying optimal bounds. However, these can be overly optimistic and not representative of the usual behavior. We…