Related papers: Rotational covariance restricts available quantum …
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements.…
In the absence of external relata, internal quantum reference frames (QRFs) appear widely in the literature on quantum gravity, gauge theories and quantum foundations. Here, we extend the perspective-neutral approach to QRF covariance to…
A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
We introduce an operational and statistically meaningful measure, the quantum tomographic transfer function, that possesses important physical invariance properties for judging whether a given informationally complete quantum measurement…
Genuinely quantum states of a harmonic oscillator may be distinguished from their classical counterparts by the Glauber-Sudarshan P-representation -- a state lacking a positive P-function is said to be nonclassical. In this paper, we…
We study a quantum theory based on two assumptions: In the intrinsic frame of reference of an isolated, macroscopic system, (i) the system has no global motion and is not entangled with any other system, (ii) time evolution of statevectors…
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to…
We develop an operational framework, combining relativistic quantum measurement theory with quantum reference frames (QRFs), in which local measurements of a quantum field on a background with symmetries are performed relative to a QRF.…
The lack of information obtained from informationally incomplete quantum measurements can prevent the detection of quantum resources, such as optical nonclassicality. We develop a technique that overcomes this limitation for single-mode…
Functions which are covariant or invariant under the transformations of a compact linear group $G$ acting in a euclidean space $\real^n$, can be profitably studied as functions defined in the orbit space of the group. The orbit space is the…
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…
An experiment is performed to reconstruct an unknown photonic quantum state with a limited amount of copies. A semi-quantum reinforcement learning approach is employed to adapt one qubit state, an "agent," to an unknown quantum state, an…
A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…
We study the quantization of many-body systems in two dimensions in rotating coordinate frames using a gauge invariant formulation of the dynamics. We consider reference frames defined by linear and quadratic gauge conditions. In both cases…
Quantum field theory (QFT) on non-stationary spacetimes is well understood from the side of the algebra of observables. The state space, however, is largely unexplored, due to the non-existence of distinguished states (vacuum, scattering…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
Measuring quantum observables by grouping terms that can be rotated to sums of only products of Pauli $\hat z$ operators (Ising form) is proven to be efficient in near term quantum computing algorithms. This approach requires extra unitary…
Resource theory of imaginarity provides a useful framework to understand the role of complex numbers, which are essential in the formulation of quantum mechanics, in a mathematically rigorous way. In the first part of this article, we study…