Related papers: Redheffer: Trig to Quantum Error Bounds
In Diophantine approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that…
Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin--Knill theorem,…
Quantum autoencoders allow for reducing the amount of resources in a quantum computation by mapping the original Hilbert space onto a reduced space with the relevant information. Recently, it was proposed to employ approximate quantum…
We provide a tight asymptotic characterization of the error exponent for classical-quantum channel coding assisted by activated non-signaling correlations. Namely, we find that the optimal exponent--also called reliability function--is…
Decoherence and gate errors severely limit the capabilities of state-of-the-art quantum computers. This work introduces a strategy for reference-state error mitigation (REM) of quantum chemistry that can be straightforwardly implemented on…
Quantum phase estimation (QPE) serves as a building block of many different quantum algorithms and finds important applications in computational chemistry problems. Despite the rapid development of quantum hardware, experimental…
We consider the one helper source coding problem posed and investigated by Ahlswede, K\"orner and Wyner. In this system, the error probability of decoding goes to one as the source block length $n$ goes to infinity. This implies that we…
We use the effective potential method of quantum field theory to obtain the quantum corrections to the zero temperature phase diagram of systems with competing order parameters. We are particularly interested in two different scenarios:…
Fast quantum data transmission faces several shortcomings such as the indistinguishability of some partly overlapping signals, the channel noises, and so on. Based on the encoded quantum data transmission protocol, an unconventional scheme…
Noise in quantum hardware remains the biggest roadblock for the implementation of quantum computers. To fight the noise in the practical application of near-term quantum computers, instead of relying on quantum error correction which…
One of the fundamental challenges in enabling fault-tolerant quantum computation is realising fast enough quantum decoders. We present a new two-stage decoder that accelerates the decoding cycle and boosts accuracy. In the first stage, a…
Enhancing the lifetime of qubits with quantum code-based memories on different quantum hardware is a significant step towards fault-tolerant quantum computing. We theoretically show that the break-even point, i.e., preserving arbitrary…
We show that the construction of the linear interferometer in the Supplemental Material of arXiv:1909.09581 is flawed, leading to a generally suboptimal solution. We then provide the correct derivation of the optimal interferometric…
The correction of errors is of fundamental importance for the development of contemporary computing devices and of robust communication protocols. In this paper we propose a scheme for the implementation of the three-qubit quantum…
By probabilistic means, the concept of contextuality is extended so that it can be used in non-ideal situations. An inequality is presented, which at least in principle enables a test to discard non-contextual hidden-variable models at low…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
Using the theorem of residues Chiarella and Reichel derived a series that can be represented in terms of the complex error function (CEF). Here we show a simple derivation of this CEF series by Fourier expansion of the exponential function…
More than ten years ago a first step towards quantum error correction (QEC) was implemented [Phys. Rev. Lett. 81, 2152 (1998)]. The work showed there was sufficient control in nuclear magnetic resonance (NMR) to implement QEC, and…
Quantum metrology aims to exploit quantum phenomena to overcome classical limitations in the estimation of relevant parameters. We consider a probe undergoing a phase shift $\varphi$ whose generator is randomly sampled according to a…
Quantitative measures are introduced for the indistinguishability $U$ of two quantum states in a given measurement and the amount of interference $I$ observable in this measurement. It is shown that these measures obey an inequality $U\geq…