Related papers: Randomization theorems for quantum channels

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…

Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We…

We complete the proof of conjecture, which allows to complete the derivation of the random coding bound for the reliability function in quantum channel in the case of arbitrary signal states

Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic…

To identify which principles characterize quantum correlations, it is essential to understand in which sense this set of correlations differs from that of almost quantum correlations. We solve this problem by invoking the so-called…

Randomized benchmarking (RB) is the gold standard for experimentally evaluating the quality of quantum operations. The current framework for RB is centered on groups and their representations, but this can be problematic. For example,…

Similarities between quantum systems and analogous systems for classical waves have been used to great effect in the physics community, be it to gain an intuition for quantum systems or to anticipate novel phenomena in classical waves. This…

Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0>…

A theorem of Blackwell about comparison between information structures in classical statistics is given an analogue in the quantum probabilistic setup. The theorem provides an operational interpretation for trace-preserving completely…

When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a…

We consider a pair of causally independent processes, modelled as the tensor product of two channels, acting on a possibly correlated input to produce random outputs X and Y. We show that, assuming the processes produce a sufficient amount…

A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…

This paper develops the resource theory of asymmetric distinguishability for quantum channels, generalizing the related resource theory for states [arXiv:1010.1030; arXiv:1905.11629]. The key constituents of the channel resource theory are…

Given $n$ copies of an unknown quantum state $\rho\in\mathbb{C}^{d\times d}$, quantum state certification is the task of determining whether $\rho=\rho_0$ or $\|\rho-\rho_0\|_1>\varepsilon$, where $\rho_0$ is a known reference state. We…

We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible…

Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…

In the context of quantum information theory, "quantization" of various mathematical and computational constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of…

According to the so-called ``Quantum Darwinist'' approach, the emergence of ``classical islands'' from a quantum background is assumed to obey a (selection) principle of maximal information. We illustrate this idea by considering the…

Quantum key distribution is widely thought to offer unconditional security in communication between two users. Unfortunately, a widely accepted proof of its security in the presence of source, device and channel noises has been missing.…

Randomized protocols are procedures that incorporate probabilistic choices during their execution and they play a central role in quantum algorithms, spanning Hamiltonian simulation, noise mitigation, and measurement tasks. In practical…