Related papers: Improved Lower Bounds for Learning Quantum Channel…
Consider quantum channels with input dimension $d_1$, output dimension $d_2$ and Kraus rank at most $r$. Any such channel must satisfy the constraint $rd_2\geq d_1$, and the parameter regime $rd_2=d_1$ is called the boundary regime. In this…
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 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…
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 study the complexity of testing properties of quantum channels. First, we show that testing identity to any channel $\mathcal N: \mathbb C^{d_{\mathrm{in}} \times d_{\mathrm{in}}} \to \mathbb C^{d_{\mathrm{out}} \times d_{\mathrm{out}}}$…
Understanding the noise affecting a quantum device is of fundamental importance for scaling quantum technologies. A particularly important class of noise models is that of Pauli channels, as randomized compiling techniques can effectively…
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 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…
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…
We study distributed similarity estimation of quantum channels (DSEC), a primitive for cross-platform verification where two remote quantum devices are compared by estimating the inner product of their Choi states. We show that the optimal…
How many black-box queries to a quantum channel are needed to learn its full classical description? This question lies at the heart of quantum channel tomography (also known as quantum process tomography), a fundamental task in the…
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…
The recently introduced random purification channel, which converts $n$ copies of an arbitrary mixed quantum state into $n$ copies of the same uniformly random purification, has emerged as a powerful tool in quantum information theory.…
We consider the problem of learning low-degree quantum objects up to $\varepsilon$-error in $\ell_2$-distance. We show the following results: $(i)$ unknown $n$-qubit degree-$d$ (in the Pauli basis) quantum channels and unitaries can be…
The tight, in a sense, lower estimates of diamond-norm distance from a given quantum channel to the sets of degradable, antidegradable and entanglement-breaking channels are obtained via the tight continuity bounds for quantum mutual…
How many copies of a quantum process are necessary and sufficient to construct an approximate classical description of it? We extend the result of Surawy-Stepney, Kahn, Kueng, and Guta (2022) to show that…
Degradable quantum channels are an important class of completely positive trace-preserving maps. Among other properties, they offer a single-letter formula for the quantum and the private classical capacity and are characterized by the fact…
Estimating the unitarity of an unknown quantum channel $\mathcal{E}$ provides information on how much it is unitary, which is a basic and important problem in quantum device certification and benchmarking. Unitarity estimation can be…
We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise. For a wide range of codes we analytically compute the effective logical channel that results when…
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…