Related papers: Invariants in Linear Optics
We give a necessary condition for photon state transformations in linear optical setups preserving the total number of photons. From an analysis of the algebra describing the quantum evolution, we find a conserved quantity that appears in…
Linear optical networks (LONs) with multi-photon inputs offer a powerful platform for advanced quantum technologies. However, the number of degrees of freedom of a LON is far fewer than the dimensionality of the multi-photon multi-mode Fock…
We study the evolution of the quantum state of $n$ photons in $m$ different modes when they go through a lossless linear optical system. We show that there are quantum evolution operators $U$ that cannot be built with linear optics alone…
Quantum linear optics without post-selection is not powerful enough to produce any quantum state from a given input state. This limits its utility since some applications require entangled resources that are difficult to prepare. Thus, we…
We demonstrate suppression and enhancement of spontaneous parametric down- conversion via quantum interference with two weak fields from a local oscillator (LO). Pairs of LO photons are observed to upconvert with high efficiency for…
A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…
We investigate which pure states of $n$ photons in $d$ modes can be transformed into each other via linear optics, without post-selection. In other words, we study the local unitary (LU) equivalence classes of symmetric many-qudit states.…
Loop invariants are software properties that hold before and after every iteration of a loop. As such, invariants provide inductive arguments that are key in automating the verification of program loops. The problem of generating loop…
We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes…
We provide a general approach for the analysis of optical state evolution under conditional measurement schemes, and identify the necessary and sufficient conditions for such schemes to simulate unitary evolution on the freely propagating…
Loop invariants are properties of a program loop that hold both before and after each iteration of the loop. They are often used to verify programs and ensure that algorithms consistently produce correct results during execution.…
Linear-Optical Passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
We analyze the problem of increasing the efficiency of single-photon sources or single-rail photonic qubits via linear optical processing and destructive conditional measurements. In contrast to previous work we allow for the use of…
Transformations achievable by linear optical components allow to generate the whole unitary group only when restricted to the one-photon subspace of a multimode Fock space. In this paper, we address the more general problem of encoding…
We establish a formal bridge between qubit-based and photonic quantum computing. We do this by defining a functor from the ZX calculus to linear optical circuits. In the process we provide a compositional theory of quantum linear optics…
We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents. In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to…
Determining an unknown quantum state from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in quantum science. Here we study the number of measurement bases needed to fully characterize an arbitrary…
Previous formulations of transformation optics have generally been restricted to transformations from relatively simple initial media, such as the vacuum, because of limitations due to their non-covariance. I show that a completely…
The general transformation of the product of coherent states $\prod_{i=1}^N|\alpha_i>$ to the output state $\prod_{i=1}^M|\beta_i>$ ($N=M$ or $N\neq M$), which is realizable with linear optical circuit, is characterized with a linear map…