Related papers: Adventures in Invariant Theory
Recently a new formulation of quantum mechanics has been introduced, based on signed classical field-less particles interacting with an external field by means of only creation and annihilation events. In this paper, we extend this novel…
The thesis showcases the importance of tomograms in quantifying nonclassical effects such as wavepacket revivals, squeezing, and quantum entanglement in continuous-variable, hybrid quantum, and qubit systems. This approach avoids…
Proposed is an alternative method for permutational sampling in quantum gases using the path integral formulation of statistical mechanics. It is shown that in principle we are able to use two operators which enable us to construct a Markov…
First, we show how the quantum circuits for generating and measuring multi-party entanglement of qubits can be translated to continuous quantum variables. We derive sufficient inseparability criteria for $N$-party continuous-variable states…
Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the…
How can we quantify the entanglement in a quantum state, if only the expectation value of a single observable is given? This question is of great interest for the analysis of entanglement in experiments, since in many multiparticle…
The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…
Measurements are essential for the processing and protection of information in quantum computers. They can also induce long-range entanglement between unmeasured qubits. However, when post-measurement states depend on many non-deterministic…
We introduce novel schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in [Phys. Rev. Lett. 98, 220503 (2007), quant-ph/0609149]. Our method makes use of…
We demonstrate that temporal observables, which are sensitive to a system's history (as opposed to its state), implicate entangled histories. We exemplify protocols for measuring such observables, and algorithms for predicting the…
We present in this paper a new technique for generating polynomial invariants, divided in two independent parts : a procedure that reduces polynomial assignments composed loops analysis to linear loops under certain hypotheses and a…
Problem of classification of all the set of entangled states is considered. Invariance of entangled states relative to transformations from a group of symmetry of qubit space leads to classification of all states of the system through…
The study of representations invariant to common transformations of the data is important to learning. Most techniques have focused on local approximate invariance implemented within expensive optimization frameworks lacking explicit…
Due to \v{C}encov's theorem, there exists a unique family of invariant symmetric $(0,2)$-tensor fields on the space of positive probability measures on a set of $n$-points indexed by $n\in \mathbb{N}$ under Markov embeddings. We deform…
In this lectures I explain a connection between geometric invariant theory and entanglement, and give a number of examples how this approach works.
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
We present local invariants of multi-partite pure or mixed states, which can be easily calculated and have a straight-forward physical meaning. As an application, we derive a new entanglement criterion for arbitrary mixed states of $n$…
We present a mathematical construction of new quantum information measures that generalize the notion of logarithmic negativity. Our approach is based on formal group theory. We shall prove that this family of generalized negativity…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
Asymptotic properties of Markov Processes, such as steady state probabilities or hazard rate for absorbing states can be efficiently calculated by means of linear algebra even for large-scale problems. This paper discusses the methods for…