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We present a procedure inspired by dense coding, which enables a highly efficient transmission of information of a continuous nature. The procedure requires the sender and the recipient to share a maximally entangled state. We deal with the…
We show that the lower bound for the optimal directional discrepancy with respect to the class of rectangles in $\mathbb{R}^2$ rotated in a restricted interval of directions $[-\theta, \theta]$ with $\theta < \frac{\pi}{4}$ is of the order…
We give a first physical model for the quantum measurement of the spin direction. It is an Arthurs-Kelly model that involves a kind of magnetic-dipole interaction of the spin with three modes of radiation. We show that in a limit of…
We calculate the relative entropy of entanglement for rotationally invariant states of spin-1/2 and arbitrary spin-$j$ particles or of spin-1 particle and spin-$j$ particle with integer $j$. A lower bound of relative entropy of entanglement…
Molecular nanostructures are promising building blocks for future quantum technologies, provided methods of harnessing their multiple degrees of freedom can be identified and implemented. Due to low decoherence rates nuclear spins are…
Control pulses that nominally optimize fidelity are sensitive to routine hardware drift and modeling errors. Robust quantum optimal control seeks error-insensitive control pulses that maintain fidelity thresholds and obey hardware…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
Quantum particles, such as spins, can be used for communicating spatial directions to observers who share no common coordinate frame. We show that if the emitter's signals are the orbit of a group, then the optimal detection method may not…
Maximal entanglement and Schmidt number play an important role in various quantum information tasks. In this paper, it is shown that a local channel preserves maximal entanglement state(MES) or preserves pure states with Schmidt number…
We discuss the communication complexity of establishing a shared reference frame, in particular examining the case of aligning spatial axes via the exchange of spin-1/2 particles. Unlike previous work we allow for multiple rounds of…
We study magnetometry of gradients and homogeneous background fields along the three orthogonal directions using two spatially separated spin ensembles. We derive trade-off relations for the achievable estimation precision of these…
Marginal optima are minima or maxima of a function with many nearly flat directions. In settings with many competing optima, marginal ones tend to attract algorithms and physical dynamics. Often, the important family of marginal attractors…
We investigate the problem of communicating three parameters in the absence of shared reference frame. We explore two methods in which the relative angles of spins are used to encode the parameters. In the first method we use three spins…
We define the perspective of any quantum reference frame (QRF) and construct reversible transformations between different perspectives. This extends the framework of [arXiv:2110.13199] to non-ideal QRFs with finite resources such as energy…
The concept of entanglement, in which coherent quantum states become inextricably correlated, has evolved from one of the most startling and controversial outcomes of quantum mechanics to the enabling principle of emerging technologies such…
As we typically teach in an introductory mechanics course, choosing a "good" reference frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely…
A simple formula is derived for the maximum squeezing rate which occurs at the initial stages of the squeezing process: the rate only depends on the second partial derivatives of a classical Hamiltonian. Rules for optimum rotation of the…
Under the spin-position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra, substitutes the vector-matrix spin model built on the Pauli spin operator. The standard quantum operator-state…
We determine the complete set of generalized spin squeezing inequalities. These are entanglement criteria that can be used for the experimental detection of entanglement in a system of spin-1/2 particles in which the spins cannot be…
Entanglement can improve the measurement precision of quantum sensors beyond the shot noise limit. Neutral atoms, the basis of some of the most precise and accurate optical clocks and interferometers, do not naturally exhibit all-to-all…