Related papers: Quantum Potato Chips
A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres--Horodecki positive partial transpose…
We start with the simplest quantum system (a two-level system, i.e., a qubit) and discuss a one-to-one mapping of the quantum state in a two-dimensional Hilbert space to a vector in an eight dimensional probability space (probability…
We express the matrix elements of the density matrix of the qutrit state in terms of probabilities associated with artificial qubit states. We show that the quantum statistics of qubit states and observables is formally equivalent to the…
Using the tomographic probability representation of qudit states and the inverse spin-portrait method, we suggest a bijective map of the qudit density operator onto a single probability distribution. Within the framework of the approach…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
We examine the geometric structure of qutrit state space by identifying the outcome probabilities of symmetric informationally complete (SIC) measurements with quantum states. We categorize the infinitely many qutrit SICs into eight SIC…
The quantum state of a $d$-dimensional system can be represented by the $d^2$ probabilities corresponding to a SIC-POVM, and then this distribution of probability can be represented by a vector of $\R^{d^2-1}$ in a simplex, we will call…
The determination of the density matrix of an ensemble of identically prepared quantum systems by performing a series of measurements, known as quantum tomography, is minimal when the number of outcomes is minimal. The most accurate minimal…
Quantum state tomography is the experimental procedure of determining an unknown state. It is not only essential for the verification of resources and processors of quantum information but is also important in its own right with regard to…
We present, and analyze thoroughly, a highly symmetric and efficient scheme for the determination of a single-qubit state, such as the polarization properties of photons emitted by a single-photon source. In our scheme there are only four…
We present a surprisingly simple three-dimensional Bloch sphere representation of a qutrit, i.e., a single three-level quantum system. We start with a symmetric state of a two-qubit system and relate it to the spin-1 representation. Using…
The geometry of the Quantum State Space, described by Bloch vectors, is a very intricate one. A deeper understanding of this geometry could lead to the solution of some difficult problems in Quantum Foundations and Quantum Information such…
The novel experimental realization of three-state optical quantum systems is presented. We use the polarization state of biphotons,propagating in single frequency- and spatial mode, to generate an arbitrary qutrits. In particular the…
A possibility of describing two-level atom states in terms of positive probability distributions (analog to the symplectic tomography scheme) is considered. As a result the basis of the irreducible representation of a rotation group can be…
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 framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups…
Bell state measurements, in which two quantum bits are projected onto a maximally entangled state, are an essential component of quantum information science. We propose and experimentally demonstrate the projection of two quantum systems…
We compute the probability that a bipartite quantum state is separable by Monte Carlo sampling. This is carried out for rebits, qubits and quaterbits. We sampled $5\times 10^{11}$ points for each of these three cases. The results strongly…
An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state.…
Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure…