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Register a new userTight upper bound for the maximal expectation value of the Mermin operators
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The violation of the Mermin inequality (MI) for multipartite quantum states guarantees the existence of nonlocality between either few or all parties. The detection of optimal MI violation is fundamentally important, but current methods only involve numerical optimizations, thus hard to find even for three-qubit states. In this paper, we provide a simple and elegant analytical method to achieve the upper bound of Mermin operator for arbitrary three-qubit states. Also, the necessary and sufficient conditions for the tightness of the bound for some class of tri-partite states has been stated. Finally, we suggest an extension of this result for up to n qubits.
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Nonlocal quantum correlations among the quantum subsystems play essential roles in quantum science. The violation of the Svetlichny inequality provides sufficient conditions of genuine tripartite nonlocality. We provide tight upper bounds on the maximal quantum value of the Svetlichny operators under local filtering operations, and present a qualitative analytical analysis on the hidden genuine nonlocality for three-qubit systems. We investigate in detail two classes of three-qubit states whose hidden genuine nonlocalities can be revealed by local filtering.
Entangled coherent states for multiple bosonic modes, also referred to as multimode cat states, not only are of fundamental interest, but also have practical applications. The nonclassical correlation among these modes is well characterized by the violation of the Mermin-Klyshko inequality. We here study Mermin-Klyshko inequality violations for such multi-mode entangled states with rotated quantum-number parity operators. Our results show that the Mermin-Klyshko signal obtained with these operators can approach the maximal value even when the average quantum number in each mode is only 1, and the inequality violation exponentially increases with the number of entangled modes. The correlations among the rotated parities of the entangled bosonic modes are in distinct contrast with those among the displaced parities, with which a nearly maximal Mermin-Klyshko inequality violation requires the size of the cat state to be increased by about 15 times.
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.
We study the fully entangled fraction of quantum states. An upper bound is obtained for arbitrary dimensional bipartite systems. This bound is shown to be exact for the case of two-qubit systems. An inequality related the fully entangled fraction of two qubits in a three-qubit mixed state has been also presented.
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