Related papers: Two-Qubit Separability Probabilities: A Concise Fo…
I report the existence of exactly one non-trivial solution to the equation $i(A,B)+i(A,\neg B)+i(\neg A,B)+i(\neg A,\neg B)= 0$, where $i(A,B)=\log\frac{P(A\text{ and }B)}{P(A)P(B)}$, and $P(A)$ is the probability of the proposition $A$.…
The problems of Hadamard quantum coin flipping in n-trials and related generalized Fibonacci sequences of numbers were introduced in [1]. It was shown that for an arbitrary number of repeated consecutive states, probabilities are determined…
Quantum tomography is a widely applicable method for reconstructing unknown quantum states and processes. However, its applications in quantum technologies usually also require estimating the difference between prepared and target quantum…
We analytically derive the bit-string probability distributions of subsystems of random pure states and depolarized random states using the Dirichlet distribution. We identify the exact Beta distribution as the universal statistical law of…
Digital computers store information in the form of bits that can take on one of two values 0 and 1, while quantum computers are based on qubits that are described by a complex wavefunction, whose squared magnitude gives the probability of…
The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum…
We propose an algorithm which proves a given bipartite quantum state to be separable in a finite number of steps. Our approach is based on the search for a decomposition via a countable subset of product states, which is dense within all…
The quantum guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on…
We obtain a collection of necessary (sufficient) conditions for a bipartite system of qubits to be separable (entangled), which are based on the Landau-Pollak formulation of the uncertainty principle. These conditions are tested, and…
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…
As it is well known, every bipartite $2\otimes 2$ density matrix can be obtained from Bell decomposable states via local quantum operations and classical communications (LQCC). Using this fact, the Lewenstein-Sanpera decomposition of an…
In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra's classical reformulation…
We show that the bipartite separability of a pure qubit state hinges critically on the combinatorial structure of its computational-basis support. Using Boolean cube geometry, we introduce a taxonomy that distinguishes support-guaranteed…
We report the implementation of Grover's quantum search algorithm in the scalable system of trapped atomic ion quantum bits. Any one of four possible states of a two-qubit memory is marked, and following a single query of the search space,…
We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…
We analyze the set of two-qubit states from which a secret key can be extracted by single-copy measurements plus classical processing of the outcomes. We introduce a key distillation protocol and give the corresponding necessary and…
We distinguish six classes of families of locally equivalent states in a straightforward scheme for classifying all 2-q-bit states; four of the classes consist of two subclasses each. The simple criteria that we stated recently for checking…
Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings. The…
Given integers n $\geq$ m, let Sep(n,m) be the set of separable states on the Hilbert space $\mathbb{C}^n \otimes \mathbb{C}^m$. It is well-known that for (n,m)=(3,2) the set of separable states has a simple description using semidefinite…
In this paper, the binary random packing fraction of similar particles with size ratios ranging from unity to well over 2 is studied. The classic excluded volume model for spherocylinders and cylinders proposed by Onsager [1] is revisited…