Related papers: On the complexity of approximating the diamond nor…
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 diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of quantum operations. Based on the theory of…
We provide an alternative proof of \class{QIP}=\class{PSPACE} to the recent breakthrough result. Unlike solving some semidefinite programs that captures the computational power of quantum interactive proofs, our method starts with one…
The theory of Quantum Darwinism aims to explain how our objective classical reality arises from the quantum world, by analysing the distribution of information about a quantum system that is accessible to multiple observers, who probe the…
The diamond norm plays an important role in quantum information and operator theory. Recently, it has also been proposed as a regularizer for low-rank matrix recovery. The norm constants that bound the diamond norm in terms of the nuclear…
Although quantum channels underlie the dynamics of quantum states, maps which are not physical channels -- that is, not completely positive -- can often be encountered in settings such as entanglement detection, non-Markovian quantum…
The present paper studies an operator norm that captures the distinguishability of quantum strategies in the same sense that the trace norm captures the distinguishability of quantum states or the diamond norm captures the…
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 advantage that quantum systems provide for certain quantum information processing tasks over their classical counterparts can be quantified within the general framework of resource theories. Certain distance functions between quantum…
Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum(NISQ) computing. However, bounding errors in quantum programs is a grand challenge, because the effects of quantum errors…
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…
The manipulation of quantum states through linear maps beyond quantum operations has many important applications in various areas of quantum information processing. Current methods simulate unphysical maps by sampling physical operations…
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.…
In recent years, machine and quantum learning have gained considerable momentum sustained by growth in computational power and data availability and have shown exceptional aptness for solving recognition- and classification-type problems,…
We study the complexity of testing properties of quantum channels. First, we show that testing identity to any channel $\mathcal N: \mathbb C^{d_{\mathrm{in}} \times d_{\mathrm{in}}} \to \mathbb C^{d_{\mathrm{out}} \times d_{\mathrm{out}}}$…
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…
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…
Quantum computing is an attractive and multidisciplinary field, which became a focus for experimental and theoretical research during last decade. Among other systems, like ions in traps or superconducting circuits, solid-states based…
We consider the family of energy-constrained diamond norms on the set of Hermitian-preserving linear maps (superoperators) between Banach spaces of trace class operators. We prove that any norm from this family generates the strong…