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We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time…
We develop an intuitive geometric picture of quantum states, define a particular state distance, and derive a quantum speed limit (QSL) for open systems. Our QSL is attainable because any initial state can be driven to a final state by the…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
A version of quantum orbit method is presented for real forms of equal rank of quantum complex simple groups. A quantum moment map is constructed, based on the canonical isomorphism between a quantum Heisenberg algebra and an algebra of…
The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been…
Quantum states of motion are critical components in the second quantum revolution. We investigate the generation and control of non-Gaussian motional states in a tripartite hybrid quantum system consisting of a collection of qubits coupled…
Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation…
It has been a long-standing debate that why quantum mechanics uses complex numbers but not only real numbers. To address this topic, in recent years, the imaginarity theory has been developed in the way of quantum resource theory. However,…
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…
The measurement of quantum signals that traveled through long distances is of fundamental and technological interest. We present quantum-limited coherent measurements of optical signals, sent from a satellite in geostationary Earth orbit to…
Integrated optics allow the generation and control of increasingly complex photonic states on chip based architectures. Here, we implement two entangled qutrits - a 9-dimensional quantum system - and demonstrate an exceptionally high degree…
We derive an explicit expressions for geometric description of state manifold obtained from evolution governed by a three parameter family of Hamiltonians covering most cases related to real interacting two-qubit systems. We discuss types…
In Hilbert space, the geometry of the quantum state is identified by the quantum geometric tensor (QGT), whose imaginary part is the Berry curvature and real part is the quantum metric tensor. Here, we propose and experimentally implement a…
The geometry of quantum states is well-established as a basis for understanding the response of electronic systems to static electromagnetic fields, as exemplified by the theory of the quantum and anomalous Hall effects. However, it has…
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing…
We show that optomechanical systems in the quantum regime can be used to demonstrate EPR-type quantum entanglement between the optical field and the mechanical oscillator, via quantum-state steering. Namely, the conditional quantum state of…
Although the study of ultracold quantum gases trapped by light is a prominent direction of modern research, the quantum properties of light were widely neglected in this field. Quantum optics with quantum gases closes this gap and addresses…
Quantum state tomography is an important tool for quantum communication, computation, metrology, and simulation. Efficient quantum state tomography on a high dimensional quantum system is still a challenging problem. Here, we propose a…
We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…