Related papers: Using Disentangled States and Algorithmic Informat…
In this short communication it is proposed the general form of a n-qubit disentangled state as a irreducible sentence, in the sense explained by the algorithmic information theory, whose length increases in a non-polynomial way when the…
In this short communication it is discussed the relation between disentangled states and algorithmic information theory aiming to construct an irreducible sentence whose length increases in a non-polynomial way when the number of qubits…
This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
Classifying states as entangled or separable is a highly challenging task, while it is also one of the foundations of quantum information processing theory. This task is higly nontrivial even for relatively simple cases, such as two-qutrit…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
We use some general results regarding positive maps to exhibit examples of non-decomposable maps and 2^N x 2^N, N >= 2, bound entangled states, e.g. non distillable bipartite states of N + N qubits.
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
We develop a novel method in classifying the multipartite entanglement state of $2\times N\times N$ under stochastic local operation and classical communication. In this method, all inequivalent classes of true entangled state can be…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
The majorization relation has been shown to be useful in classifying which transformations of jointly held quantum states are possible using local operations and classical communication. In some cases, a direct transformation between two…
The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that…
We analyse the entanglement of the antisymmetric state in dimension d x d and present two main results. First, we show that the amount of secrecy that can be extracted from the state is low, more precisely, the distillable key is bounded by…
A problem about how to transport profitably a group of cars leads us to study the set $T$ formed by the integers $n$ such that the system of inequalities, with non-negative integer coefficients, $$a_1x_1 +\cdots+ a_px_p + \alpha \leq n \leq…
The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the…
The series solution of the behavior of a finite number of physical bodies and Chaitin's Omega number share quasi-algorithmic expressions; yet both lack a computable radius of convergence.
We show that any pseudoentangled state ensemble with a gap of $t$ bits of entropy requires $\Omega(t)$ non-Clifford gates to prepare. This bound is tight up to polylogarithmic factors if linear-time quantum-secure pseudorandom functions…
In the presence of a globally conserved charge $N$, a natural question is whether a given separable state can be separated into charge-conserving components. We dub this problem the Symmetric Separability Problem (SSP). On random states,…
The utilization of a $d$-level partially entangled state, shared by two parties wishing to communicate classical information without errors over a noiseless quantum channel, is discussed. We analytically construct deterministic dense coding…