Related papers: A note on the state-space realizations equivalence
NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has…
We solve the problem of achieving the optimal physical approximation of the transposition for pure states of arbitrary quantum systems for finite and infinite dimensions. A unitary realization is also given for any finite dimension, which…
In this paper, the reachability of dimension-bounded linear systems is investigated.Since state dimensions of dimension-bounded linear systems vary with time, the expression of state dimension at each time is provided.A method for judging…
We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word.
There is a direct correspondence between two-particle, entangled quantum states, for example, Bell states, and the relative values of the component one-particle states. This leads to a new rationale for quantum computing which makes use of…
A more conventional realization of a symmetry which had been proposed towards the solution of cosmological constant problem is considered. In this study the multiplication of the coordinates by the imaginary number $i$ in the literature is…
We unify two recent results concerning equilibration in quantum theory. We first generalise a proof of Reimann [PRL 101,190403 (2008)], that the expectation value of 'realistic' quantum observables will equilibrate under very general…
The realizability problem is a well-known problem in the analysis of complex systems, which can be modeled as an infinite-dimensional moment problem. More precisely, as a truncated $K-$moment problem where $K$ is the space of all possible…
Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phase-space techniques are known, however a thorough…
The starting point of this work is a framework allowing to model systems with dynamic process creation, equipped with a procedure to detect symmetric executions (ie., which differ only by the identities of processes). This allows to reduce…
We derive a necessary condition for the existence of a completely-positive, linear, trace-preserving map which deterministically transforms one finite set of pure quantum states into another. This condition is also sufficient for…
In this paper, we present experimental algorithms for solving the dualization problem. We present the results of extensive experimentation comparing the execution time of various algorithms.
In this work, we extend the concept of Robinson spaces to asymmetric dissimilarities, enhancing their applicability in representing and analyzing complex data. Within this generalized framework, we introduce two different problems that…
We generalize the concept of synchronizing words for finite automata, which map all states of the automata to the same state, to deterministic visibly push-down automata. Here, a synchronizing word w does not only map all states to the same…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
Necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under Local Unitary (LU) operations are derived. First, an easily computable standard form for multipartite states is introduced. Two generic…
We propose a notion of state distinguishability that does not refer to probabilities, but rather to the ability of a set of states to serve as programs for a desired set of gates. Using this notion, we reconstruct the structural features of…
We establish a connection between optimal quantum cloning and optimal state estimation for d-dimensional quantum systems. In this way we derive an upper limit on the fidelity of state estimation for d-dimensional pure quantum states and,…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
We give necessary and sufficient conditions for the set of Neumark projections of a countable set of phase space observable to constitute a resolution of the identity, and we give a criteria for a phase space observable to be…