Related papers: Operational distance and fidelity for quantum chan…
We study the complexity of testing properties of quantum channels. First, we show that testing identity to any channel $\mathcal N: \mathbb C^{d_{\mathrm{in}} \times d_{\mathrm{in}}} \to \mathbb C^{d_{\mathrm{out}} \times d_{\mathrm{out}}}$…
Random feature neural network approximations of the potential in Hamiltonian systems yield approximations of molecular dynamics correlation observables that have the expected error $\mathcal{O}\big((K^{-1}+J^{-1/2})^{\frac{1}{2}}\big)$, for…
We consider the problem of distinguishing, with minimum probability of error, two optical beam-splitter channels with unequal complex-valued reflectivities using general quantum probe states entangled over M signal and M' idler mode pairs…
In the present paper, the trace distance is exposed within the quantum operations formalism. The definition of the trace distance in terms of a maximum over all quantum operations is given. It is shown that for any pair of different states,…
We present a strategy to generate long-range entanglement in noisy quantum networks. We consider a cubic lattice whose bonds are partially entangled mixed states of two qubits, and where quantum operations can be applied perfectly at the…
In the theory of quantum transmission of information the concept of fidelity plays a fundamental role. An important class of channels, which can be experimentally realized in quantum optics, is that of Gaussian quantum channels. In this…
We consider several definitions of the quantum Wasserstein distance based on an optimization over general bipartite quantum states with given marginals. Then, we examine the quantities obtained after the optimization is carried out over…
Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication.…
The data processing inequality is the most basic requirement for any meaningful measure of information. It essentially states that distinguishability measures between states decrease if we apply a quantum channel and is the centerpiece of…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
The classical Hennessy-Milner theorem is an important tool in the analysis of concurrent processes; it guarantees that any two non-bisimilar states in finitely branching labelled transition systems can be distinguished by a modal formula.…
So far, there have been plenty of literatures on the metric in the space of probability distributions and quantum states. As for channels, however, only a little had been known. In this paper, we impose monotonicity by concatenation of…
Coherence and correlation are key features of the quantum system. Quantifying these quantities are astounding task in the framework of resource theory of quantum information processing. In this article, we identify an affinity-based metric…
In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
Under rather general assumptions about the properties of a noisy quantum channel, a first quantum protocol is proposed which allows to implement the secret bit commitment with the probability arbitrarily close to unity.
We present a simple, dimension-independent criterion which guarantees that some quantum channel $\Phi$ is divisible, i.e. that there exists a non-trivial factorization $\Phi=\Phi_1\Phi_2$. The idea is to first define an "elementary" channel…
The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…
Channel Charting is a dimensionality reduction technique that learns to reconstruct a low-dimensional, physically interpretable map of the radio environment by taking advantage of similarity relationships found in high-dimensional channel…
Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…