Related papers: A Discrete Phase-Space Calculus for Quantum Spins …
The most irreducible way to represent information is a sequence of two symbols. In this paper, we construct quantum states using this basic building block. Specifically, we show that the probabilities that arise in quantum theory can be…
State reconstruction for quantum spins is reviewed. Emphasis is on non-tomographic approaches which are based on measurements performed with a Stern-Gerlach apparatus. Two consequences of successfully implemented state reconstruction are…
As a toy model for the microscopic description of matter in de Sitter space, we consider a Hamiltonian acting on the spin-j representation of SU(2). This is a model with a finite-dimensional Hilbert space, from which quasinormal modes…
We generalize the Majorana stellar representation of spin-$s$ pure states to mixed states, and in general to any hermitian operator, defining a bijective correspondence between three spaces: the spin density-matrices, a projective space of…
Consider a spin s prepared in a pure state. It is shown that, generically, the moduli of the (2s+1) spin components along three directions in space determine the state unambiguously. These probabilities are accessible experimentally by…
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
Completely positive quantum operations are frequently discussed in the contexts of statistical mechanics and quantum information. They are customarily given by maps forming positive operator-values measures. To intuitively understand…
We propose a mechanism to describe how a physical quantity, which initially can take continuous values, is restricted within some discrete values after a measurement. As an example of the present theory, in which interplay between coherence…
The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…
Quantum states are described by wave functions whose phases cannot be directly measured, but which play a vital role in quantum effects such as interference and entanglement. The loss of the relative phase information, termed decoherence,…
We show how group symmetries can be used to reconstruct quantum states. In our scheme for SU(1,1) states, the input field passes through a non-degenerate parametric amplifier and one measures the probability of finding the output state with…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
The possibility of using strongly and continuously interacting spins for quantum computation has recently been discussed. Here we present a simple optical scheme that achieves this goal while avoiding the drawbacks of earlier proposals. We…
We discuss how to recognize the constellations seen in the Majorana representation of quantum states. Then we give explicit formulas for the metric and symplectic form on SU(2) orbits containing general number states. Their metric and…
We present detailed discussions on a new approach we proposed in a previous paper to numerically study quantum spin systems. This method, which we will call re-structuring method hereafter, is based on rearrangement of intermediate states…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phase-space techniques are known, however a thorough…
We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems.…
It is proposed to map the quantum information qubit not to individual spin 1/2 states, but to the collective spin states being eigenfunctions of the Hamiltonian including spin-spin interactions, which may be not small. Such an approach…
We propose a quantum feedback scheme for producing deterministically reproducible spin squeezing. The results of a continuous nondemolition atom number measurement are fed back to control the quantum state of the sample. For large samples…