Related papers: Measuring unitary invariants with the quantum swit…
We explore a very simple distribution of unitaries: random (binary) phase -- Hadamard -- random (binary) phase -- random computational-basis permutation. We show that this distribution is statistically indistinguishable from random Haar…
The evolution of a quantum system undergoing repeated indirect measurements naturally leads to a Markov chain on the set of states which is called a quantum trajectory. In this paper we consider a specific model of such a quantum trajectory…
The involutory birack counting invariant is an integer-valued invariant of unoriented tangles defined by counting homomorphisms from the fundamental involutory birack of the tangle to a finite involutory birack over a set of framings modulo…
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…
The concept of \textquotedblleft the permutationally invariant part of a density matrx\textquotedblright constitutes an important tool for entanglement characterization of multiqubit systems. In this paper, we first present $(k+1)$-partite…
This work analyses the performance of quantum circuits and general processes to transform $k$ uses of an arbitrary unitary operation $U$ into another unitary operation $f(U)$. When the desired function $f$ a homomorphism, i.e.,…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
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…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
Quantum state tomography suffers from the measurement effort increasing exponentially with the number of qubits. Here, we demonstrate permutationally invariant tomography for which, contrary to conventional tomography, all resources scale…
It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from…
In this article it will be presented the first attempt made in order to perform gauge invariant calculations of eigenstates of a quantum body in its condensed phase, the latter reacting to an external uniform magnetic field. The target is…
Based on the theory of quantum mechanics, intrinsic randomness in measurement distinguishes quantum effects from classical ones. From the perspective of states, this quantum feature can be summarized as coherence or superposition in a…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
We consider perturbative quantum field theory in the causal framework. Gauge invariance is, in this framework, an identity involving chronological products of the interaction Lagrangian; it express the fact that the scattering matrix must…
In this Chapter, we present some interesting properties of quantum walks on the line. We concentrate our attention in the emergence of invariance and provide some insights into the ultimate origin of the observed behavior. In the first part…
Investigating the role of causal order in quantum mechanics has recently revealed that the causal distribution of events may not be a-priori well-defined in quantum theory. While this has triggered a growing interest on the theoretical…
We introduce a measure of quantum correlations in the $N$-qubit quantum system which is invariant with respect to the $SU(2^N)$ group of transformations of this system. This measure is a modification of the quantum discord introduced…
We study the extent to which the outcomes of a quantum measurement can be manipulated by changing the state of the measurement apparatus. The measurement process is modeled as decoherence induced by the experimenter, to gain knowledge about…
We present two general methods to implement quantum circuits for the direct measuring of local unitary invariants on quantum computers. We work these out for important three-qubit invariants, and also demonstrate these on the IBM Quantum…