Related papers: Schmidt representation of 3-qubits with real ampli…

We present a family of three-qubit quantum states with a basic local hidden variable model. Any von Neumann measurement can be described by a local model for these states. We show that some of these states are genuine three-partite…

We show, within the circuit model, how any quantum computation can be efficiently performed using states with only real amplitudes (a result known within the Quantum Turing Machine model). This allows us to identify a 2-qubit (in fact…

We develop a new method of representation of quantum states in terms of the displaced number states. We call it representation, where is an amplitude of the base displaced states. In particular, representation was obtained for set of the…

Any 8-qubit graph state belongs to one of the 101 equivalence classes under local unitary operations within the Clifford group. For each of these classes we obtain a representative which requires the minimum number of controlled-Z gates for…

We report an exhaustive numerical analysis of violations of local realism by two qutrits in all possible pure entangled states. In Bell type experiments we allow any pairs of local unitary U(3) transformations to define the measurement…

We initially consider a quantum system consisting of two qubits, which can be in one of two nonorthogonal states, \Psi_0 or \Psi_1. We distribute the qubits to two parties, Alice and Bob. They each measure their qubit and then compare their…

In this short note we show two completely opposite methods of constructing entangled states. Given a bipartite state $\gamma\in M_k\otimes M_k$, define $\gamma_S=(Id+F)\gamma (Id+F)$, $\gamma_A=(Id-F)\gamma(Id-F)$, where $F\in M_k\otimes…

We experimentally explore the state space of three qubits on an NMR quantum information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form…

We present a deterministic framework for preparing an arbitrary three-qubit pure state. To leverage entanglement structure in the state-preparation task, we classify three-qubit pure states into five types with respect to a $1|2$…

The dimensionality of entanglement, quantified by the Schmidt number, is a valuable resource for a wide range of quantum information processing tasks. In this work, we introduce the notion of the absolute Schmidt number, referring to states…

We provide new examples of pure entangled systems related to cluster state quantum computation that can be efficiently simulated classically. In cluster state quantum computation input qubits are initialised in the `equator' of the Bloch…

By building on the work in Kuzmak & Tkachuk, "Preparation of quantum states of two spin-$\frac{1}{2}$ particles in the form of the Schmidt decomposition", Physics Letters A, {\bf 378}, pp1469-1474, which outlined the control of the degree…

While all quantum algorithms can be expressed in terms of single-qubit and two-qubit gates, more expressive gate sets can help reduce the algorithmic depth. This is important in the presence of gate errors, especially those due to…

Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…

We study the local distinguishability of general multi-qubit states and show that local projective measurements and classical communication are as powerful as the most general local measurements and classical communication. Remarkably, this…

We introduce the notion of a Schmidt number of a bipartite density matrix, characterizing the minimum Schmidt rank of the pure states that are needed to construct the density matrix. We prove that Schmidt number is nonincreasing under local…

The amount of entanglement that exists in a parametric down-converted state is investigated in terms of all the degrees of freedom of the state. We quantify the amount of entanglement by the Schmidt number of the state, represented as a…

We discuss three important classes of three-qubit entangled states and their encoding into quantum gates, finite groups and Lie algebras. States of the GHZ and W-type correspond to pure tripartite and bipartite entanglement, respectively.…

Entangled states with a positive partial transpose (so-called PPT states) are central to many interesting problems in quantum theory. On one hand, they are considered to be weakly entangled, since no pure state entanglement can be distilled…

We describe an algorithm for converting one bipartite quantum state into another using only local operations and classical communication, which is much simpler than the original algorithm given by Nielsen [Phys. Rev. Lett. 83, 436 (1999)].…