Increasing efficiency of a linear-optical quantum gate using an electronic feed forward

We have successfully used a fast electronic feed forward to increase the success probability of a linear optical implementation of a programmable phase gate from 25% to its theoretical limit of 50%. The feed forward applies a conditional unitary operation which changes the incorrect output states of the data qubit to the correct ones. The gate itself rotates an arbitrary quantum state of the data qubit around the z-axis of the Bloch sphere with the angle of rotation being fully determined by the state of the program qubit. The gate implementation is based on fiber optics components. Qubits are encoded into spatial modes of single photons. The signal from the feed-forward detector is led directly to a phase modulator using only a passive voltage divider. We have verified the increase of the success probability and characterized the gate operation by means of quantum process tomography. We have demonstrated that the use of the feed forward does not affect either the process fidelity or the output-state fidelities

The algebra of adjacency patterns: Rees matrix semigroups with reversion

We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by so-called adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties of the variety generated by adjacency semigroups that are regular unary semigroups is essentially the same as the lattice of universal Horn classes of reflexive directed graphs. A number of examples follow, including a limit variety of regular unary semigroups and finite unary semigroups with NP-hard variety membership problems.Comment: 30 pages, 9 figure

Deterministic superresolution with coherent states at the shot noise limit

Interference of light fields plays an important role in various high-precision measurement schemes. It has been shown that super resolving phase measurements beyond the standard coherent state limit can be obtained either by using maximally entangled multi-particle states of light or using complex detection approaches. Here we show that super resolving phase measurements at the shot noise limit can be achieved without resorting to non-classical optical states or to low-efficiency detection processes. Using robust coherent states of light, high-efficiency homodyne detection and a deterministic binarization processing technique, we show a narrowing of the interference fringes that scales with 1/Sqrt{N} where N is the mean number of photons of the coherent state. Experimentally we demonstrate a 12-fold narrowing at the shot noise limit.Comment: 5 pages, 3 figure

A classification of bisymmetric polynomial functions over integral domains of characteristic zero

We describe the class of n-variable polynomial functions that satisfy Acz\'el's bisymmetry property over an arbitrary integral domain of characteristic zero with identity

Optimal discrimination of mixed quantum states involving inconclusive results

We propose a generalized discrimination scheme for mixed quantum states. In the present scenario we allow for certain fixed fraction of inconclusive results and we maximize the success rate of the quantum-state discrimination. This protocol interpolates between the Ivanovic-Dieks-Peres scheme and the Helstrom one. We formulate the extremal equations for the optimal positive operator valued measure describing the discrimination device and establish a criterion for its optimality. We also devise a numerical method for efficient solving of these extremal equations.Comment: 5 pages, 1 figur

Reconstruction of superoperators from incomplete measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[rho_j ] that originate from a set of four linearly independent test states j (j = 1, 2, 3, 4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator rho = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.Comment: 13 pages, 6 figure