Related papers: Numerical ranges of Bargmann invariants
Quantum states defined over a parameter space form a Grassmann manifold. To capture the geometry of the associated gauge structure, gauge-invariant quantities are essential. We employ the projector of a multilevel system to quantify the…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
We prove that the results of a finite set of general quantum measurements on an arbitrary dimensional quantum system can be simulated using a polynomial (in measurements) number of hidden-variable states. In the limit of infinitely many…
In its standard formulation, quantum mechanics presents a very serious inconvenience: given a quantum system, there is no possibility at all to unambiguously (causally) connect a particular feature of its final state with some specific…
We introduce a novel strategy, based on the use of modular variables, to encode and deterministically process quantum information using states described by continuous variables. Our formalism leads to a general recipe to adapt existing…
The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on…
We introduce two new sets of invariant functions of quark mass matrices, which express the constraints on these mass matrices due to knowledge of the quark mixing matrix. These invariants provide a very simple method to test candidate forms…
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of…
Debugging quantum states transformations is an important task of modern quantum computing. The use of quantum tomography for these purposes significantly expands the range of possibilities. However, the presence of preparation and…
Quantum information theory is used to analize various non-linear operations on quantum states. The universal disentanglement machine is shown to be impossible, and partial (negative) results are obtained in the state-dependent case. The…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…
In theories like SM or MSSM with a complex gauge group structure the complete set of Feynman diagrams contributed to a particular physics process can be splited to exact gauge invariant subsets. Arguments and examples given in the review…
The gauge theory for random spin systems is extended to quantum spin glasses to derive a number of exact and/or rigorous results. The transverse Ising model and the quantum gauge glass are shown to be gauge invariant. For these models, an…
In this paper the problem of the gauge in a bound state calculation is discussed. In particular, in order to verify the gauge invariance in the energy levels expansion, some set of gauge invariant contributions are given.
The geometric phase can act as a signature for critical regions of interacting spin chains in the limit where the corresponding circuit in parameter space is shrunk to a point and the number of spins is extended to infinity; for finite…
The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential…
Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In these notes, we consider two…
Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact…
Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments, such as maximum likelihood estimation, lack a well-justified error analysis.…
Non-Gaussian bosonic states are ubiquitous in interacting light--matter systems, many-body platforms, and relativistic quantum field settings, but their quantitative characterization is hindered by the infinite-dimensional Hilbert space and…