Using the Bloch-Messiah reduction we show that squeezing is an ``irreducible'' resource which remains invariant under transformations by linear optical elements. In particular, this gives a decomposition of any optical circuit with linear input-output relations into a linear multiport interferometer followed by a unique set of single-mode squeezers and then another multiport interferometer. Using this decomposition we derive a no-go theorem for creating superpositions of macroscopically distinct states from single-photon detection. Further, we demonstrate the equivalence between several schemes for randomly creating polarization-entangled states. Finally, we derive minimal quantum optical circuits for ideal quantum nondemolition coupling of quadrature-phase amplitudes.
Using the Bloch-Messiah reduction we show that squeezing is an ``irreducible'' resource which remains invariant under transformations by linear optical elements. In particular, this gives a decomposition of any optical circuit with linear input-output relations into a linear multiport interferometer followed by a unique set of single-mode squeezers and then another multiport interferometer. Using this decomposition we derive a no-go theorem for creating superpositions of macroscopically distinct states from single-photon detection. Further, we demonstrate the equivalence between several schemes for randomly creating polarization-entangled states. Finally, we derive minimal quantum optical circuits for ideal quantum nondemolition coupling of quadrature-phase amplitudes.
The linear optical creation of Gaussian cluster states, a potential resource for universal quantum computation, is investigated. First, using Bloch-Messiah reduction, we show how to achieve canonical cluster-state generation, otherwise based on pairwise acting quantum nondemolition gates, by off-line squeezers and beam splitters. Moreover, we find that, in terms of squeezing resources, the canonical states are rather wasteful. Hence we propose a systematic way to create a whole family of cluster-type states, including potentially cheaper states. Any given cluster (or graph) state can be realized this way. As an example, we consider a protocol in which a single-mode quantum state propagates through a multiple-rail cluster. Such a redundant encoding may reduce errors due to finite squeezing.
Methods to decompose nonlinear optical transformation vary from setting to setting, leading to apparent differences in the treatments used to model photon pair sources, compared to those used to model degenerate down-conversion processes. The Bloch-Messiah reduction of Gaussian processes to single-mode squeezers and passive (linear) unitaries appears juxtaposed against the practicalities of the Schmidt-decomposition for photon pair sources into two-mode squeezers and passive unitaries. Here, we present a general framework which unifies these forms as well as elucidating more general structure in multimode Gaussian transformations. The decomposition is achieved by introducing additional constraints into the Bloch-Messiah reduction used to diagonalise Gaussian processes, these constraints motivated by physical constraints following from the inequivalence of different physical degrees of freedom in a system, ie. the temporal-spectral degrees of freedom vs different spatial modes in a transformation. The result is the emergence of the two-mode squeezing picture from the reduction, as well as the potential to generalise these constraints to accommodate spectral imperfections in a source generating 3-mode continuous variable GHZ-like states. Furthermore, we consider the practical scenario in which a transformation aims to generate a multiphoton entangled state, whereby spatial modes provide desirable degrees of freedom, whilst undesired spectral mode structure contributes noise, and show that this spectral impurity can be efficiently modeled by finding an optimal low dimensional bases for its simulation.
Optical quantum-nondemolition devices can provide essential tools for quantum information processing. Here, we describe several optical interferometers that signal the presence of a single photon in a particular input state without destroying it. We discuss both entanglement-assisted and nonentanglement-assisted interferometers, with ideal and realistic detectors. We found that the existing detectors with 88% quantum efficiency and single-photon resolution can yield output fidelities of up to 89%, depending on the input state. Furthermore, we construct expanded protocols to perform quantum-nondemolition detections of single photons that leave the polarization invariant. For detectors with 88% efficiency, we found polarization-preserving output fidelities of up to 98.5%.
Linear canonical transformations of bosonic modes correspond to Gaussian unitaries, which comprise passive linear-optical transformations as effected by a multiport passive interferometer and active Bogoliubov transformations as effected by a nonlinear amplification medium. As a consequence of the Bloch-Messiah theorem, any Gaussian unitary can be decomposed into a passive interferometer followed by a layer of single-mode squeezers and another passive interferometer. Here, it is shown how to circumvent the need for active transformations. Namely, we provide a technique to simulate sampling from the joint input and output distributions of any Gaussian circuit with passive interferometry only, provided two-mode squeezed vacuum states are available as a prior resource. At the heart of the procedure, we exploit the fact that a beam splitter under partial time reversal simulates a two-mode squeezer, which gives access to an arbitrary Gaussian circuit without any nonlinear optical medium. This yields, in particular, a procedure for simulating with linear optics an extended boson sampling experiment, where photons jointly propagate through an arbitrary multimode Gaussian circuit followed by the detection of output photon patterns.
A non-trace-preserving map describing a probabilistic but heralded noiseless linear amplifier has recently been proposed and experimentally demonstrated. Here, we exhibit another remarkable feature of this peculiar transformation, namely its ability to serve as a universal single-mode squeezer regardless of the quadrature that is initially squeezed. Hence, it acts as a heralded phase-insensitive optical squeezer, conserving the signal-to-noise ratio just as a phase-sensitive optical amplifier but for all quadratures at the same time, which may offer interesting perspectives in quantum optical communications. Although this ability to squeeze all quadratures seemingly opens a way to instantaneous signaling by circumventing the quantum no-cloning theorem, we explain the subtle mechanism by which such a causality violation is forbidden, even on an heralded basis.
We propose and experimentally realize a novel versatile protocol that allows the quantum state engineering of heralded optical coherent-state superpositions. This scheme relies on a two-mode squeezed state, linear mixing, and a n-photon detection. It is optimally using expensive non-Gaussian resources to build up only the key non-Gaussian part of the targeted state. In the experimental case of a two-photon detection based on high-efficiency superconducting nanowire single-photon detectors, the freely propagating state exhibits a 67% fidelity with a squeezed even coherent-state superposition with a size |α|(2)=3. The demonstrated procedure and the achieved rate will facilitate the use of such superpositions in subsequent protocols, including fundamental tests and optical hybrid quantum information implementations.