No Arabic abstract
No-go theorems assert that hidden-variable theories, subject to appropriate hypotheses, cannot reproduce the predictions of quantum theory. We examine two species of such theorems, value no-go theorems and expectation no-go theorems. The former assert that hidden-variables cannot match the predictions of quantum theory about the possible values resulting from measurements; the latter assert that hidden-variables cannot match the predictions of quantum theory about the expectation values of measurements. We sharpen the known results of both species, which allows us to clarify the similarities and differences between the two species. We also repair some flaws in existing definitions and proofs.
The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. It remains an open problem of finding general forbidden principles to unify these results. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed state in Hilbert space of finite dimension. Two general forms include the no-cloning theorem, the no-deleting theorem, and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may yield to fruitful results that are completely characterized with the linear independence of the input pure states. The generalized upper bounds for the success probability will be proved. Third, we generalize a recent superposing of unknown states with fixed overlaps when multiple copies of the input states are available.
We review model independent arguments showing that massless particles interacting with gravity in a Minkowski background space can have at most spin two. These arguments include a classic theorem due to Weinberg, as well as a more recent extension of the Weinberg-Witten theorem. A puzzle arising from an apparent counterexample to these theorems is examined and resolved.
The information encoded in a quantum system is generally spoiled by the influences of its environment, leading to a transition from pure to mixed states. Reducing the mixedness of a state is a fundamental step in the quest for a feasible implementation of quantum technologies. Here we show that it is impossible to transfer part of such mixedness to a trash system without losing some of the initial information. Such loss is lower-bounded by a value determined by the properties of the initial state to purify. We discuss this interesting phenomenon and its consequences for general quantum information theory, linking it to the information theoretical primitive embodied by the quantum state-merging protocol and to the behaviour of general quantum correlations.
The evaluation of expectation values $Trleft[rho Oright]$ for some pure state $rho$ and Hermitian operator $O$ is of central importance in a variety of quantum algorithms. Near optimal techniques developed in the past require a number of measurements $N$ approaching the Heisenberg limit $N=mathcal{O}left(1/epsilonright)$ as a function of target accuracy $epsilon$. The use of Quantum Phase Estimation requires however long circuit depths $C=mathcal{O}left(1/epsilonright)$ making their implementation difficult on near term noisy devices. The more direct strategy of Operator Averaging is usually preferred as it can be performed using $N=mathcal{O}left(1/epsilon^2right)$ measurements and no additional gates besides those needed for the state preparation. In this work we use a simple but realistic model to describe the bound state of a neutron and a proton (the deuteron) and show that the latter strategy can require an overly large number of measurement in order to achieve a reasonably small relative target accuracy $epsilon_r$. We propose to overcome this problem using a single step of QPE and classical post-processing. This approach leads to a circuit depth $C=mathcal{O}left(epsilon^muright)$ (with $mugeq0$) and to a number of measurements $N=mathcal{O}left(1/epsilon^{2+ u}right)$ for $0< uleq1$. We provide detailed descriptions of two implementations of our strategy for $ u=1$ and $ uapprox0.5$ and derive appropriate conditions that a particular problem instance has to satisfy in order for our method to provide an advantage.
Quantum mechanics, one of the keystones of modern physics, exhibits several peculiar properties, differentiating it from classical mechanics. One of the most intriguing is that variables might not have definite values. A complete quantum description provides only probabilities for obtaining various eigenvalues of a quantum variable. These and corresponding probabilities specify the expectation value of a physical observable, which is known to be a statistical property of an ensemble of quantum systems. In contrast to this paradigm, we demonstrate a unique method allowing to measure the expectation value of a physical variable on a single particle, namely, the polarisation of a single protected photon. This is the first realisation of quantum protective measurements.