Critical fluctuations in an optical parametric oscillator: when light behaves like magnetism

We study the nondegenerate optical parametric oscillator in a planar interferometer near threshold, where critical phenomena are expected. These phenomena are associated with nonequilibrium quantum dynamics that are known to lead to quadrature entanglement and squeezing in the oscillator field modes. We obtain a universal form for the equation describing this system, which allows a comparison with other phase transitions. We find that the unsqueezed quadratures of this system correspond to a two-dimensional XY-type model with a tricritical Lifshitz point. This leaves open the possibility of a controlled experimental investigation into this unusual class of statistical models. We evaluate the correlations of the unsqueezed quadrature using both an exact numerical simulation and a Gaussian approximation, and obtain an accurate numerical calculation of the non-Gaussian correlations.Comment: Title changed. New figures adde

Probabilistic quantum phase-space simulation of Bell violations and their dynamical evolution

Quantum simulations of Bell inequality violations are numerically obtained using probabilistic phase space methods, namely the positive P-representation. In this approach the moments of quantum observables are evaluated as moments of variables that have values outside the normal eigenvalue range. There is thus a parallel with quantum weak measurements and weak values. Nevertheless, the representation is exactly equivalent to quantum mechanics. A number of states violating Bell inequalities are sampled, demonstrating that these quantum paradoxes can be treated with probabilistic methods. We treat quantum dynamics by simulating the time evolution of the Bell state formed via parametric down-conversion, and discuss multi-mode generalizations

Probabilistic simulation of mesoscopic "Schr\"odinger cat" states

We carry out probabilistic phase-space sampling of mesoscopic Schr\"odinger cat quantum states, demonstrating multipartite Bell violations for up to 60 qubits. We use states similar to those generated in photonic and ion-trap experiments. These results show that mesoscopic quantum superpositions are directly accessible to probabilistic sampling, and we analyze the properties of sampling errors. We also demonstrate dynamical simulation of super-decoherence in ion traps. Our computer simulations can be either exponentially faster or slower than experiment, depending on the correlations measured

Quantum probabilistic sampling of multipartite 60-qubit Bell inequality violations

We show that violation of genuine multipartite Bell inequalities can be obtained with sampled, probabilistic phase space methods. These genuine Bell violations cannot be replicated if any part of the system is described by a local hidden variable theory. The Bell violations are simulated probabilistically using quantum phase-space representations. We treat mesoscopically large Greenberger-Horne-Zeilinger (GHZ) states having up to 60 qubits, using both a multipartite SU(2) Q-representation and the positive P-representation. Surprisingly, we find that sampling with phase-space distributions can be exponentially faster than experiment. This is due to the classical parallelism inherent in the simulation of quantum measurements using phase-space methods. Our probabilistic sampling method predicts a contradiction with local realism of "Schr\"odinger-cat" states that can be realized as a GHZ spin state, either in ion traps or with photonic qubits. We also present a quantum simulation of the observed super-decoherence of the ion-trap "cat" state, using a phenomenological noise model

Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering

We investigate the resources needed for secure teleportation of coherent states. We extend continuous variable teleportation to include quantum teleamplification protocols that allow nonunity classical gains and a preamplification or postattenuation of the coherent state. We show that, for arbitrary Gaussian protocols and a significant class of Gaussian resources, two-way steering is required to achieve a teleportation fidelity beyond the no-cloning threshold. This provides an operational connection between Gaussian steerability and secure teleportation. We present practical recipes suggesting that heralded noiseless preamplification may enable high-fidelity heralded teleportation, using minimally entangled yet steerable resources

Linear entropy in quantum phase space

We calculate the quantum Renyi entropy in a phase space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner product divergences. The preferred method is to use generalized Gaussian phase space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.Comment: 12 pages, 3 figures. To be published in Phys. Rev.