Quantum state testing beyond the polarizing regime and quantum triangular discrimination

The complexity class Quantum Statistical Zero-Knowledge ($\mathsf{QSZK}$) captures computational difficulties of the time-bounded quantum state testing problem with respect to the trace distance, known as the Quantum State Distinguishability Problem (QSDP) introduced by Watrous (FOCS 2002). However, QSDP is in $\mathsf{QSZK}$ merely within the constant polarizing regime, similar to its classical counterpart shown by Sahai and Vadhan (JACM 2003) due to the polarization lemma (error reduction for SDP). Recently, Berman, Degwekar, Rothblum, and Vasudevan (TCC 2019) extended the $\mathsf{SZK}$ containment for SDP beyond the polarizing regime via the time-bounded distribution testing problems with respect to the triangular discrimination and the Jensen-Shannon divergence. Our work introduces proper quantum analogs for these problems by defining quantum counterparts for triangular discrimination. We investigate whether the quantum analogs behave similarly to their classical counterparts and examine the limitations of existing approaches to polarization regarding quantum distances. These new $\mathsf{QSZK}$-complete problems improve $\mathsf{QSZK}$ containments for QSDP beyond the polarizing regime and establish a simple $\mathsf{QSZK}$-hardness for the quantum entropy difference problem (QEDP) defined by Ben-Aroya, Schwartz, and Ta-Shma (ToC 2010). Furthermore, we prove that QSDP with some exponentially small errors is in $\mathsf{PP}$, while the same problem without error is in $\mathsf{NQP}$.Comment: 31 pages. v3: added a simple QSZK-hardness proof for QEDP, updated a correct version of Theorem 5.1(2), and improved presentation. v2: minor change

Cold heteromolecular dipolar collisions

We present the first experimental observation of cold collisions between two different species of neutral polar molecules, each prepared in a single internal quantum state. Combining for the first time the techniques of Stark deceleration, magnetic trapping, and cryogenic buffer gas cooling allows the enhancement of molecular interaction time by 10$^5$. This has enabled an absolute measurement of the total trap loss cross sections between OH and ND$_3$ at a mean collision energy of 3.6 cm$^{-1}$ (5 K). Due to the dipolar interaction, the total cross section increases upon application of an external polarizing electric field. Cross sections computed from \emph{ab initio} potential energy surfaces are in excellent agreement with the measured value at zero external electric field. The theory presented here represents the first such analysis of collisions between a $^2\Pi$ radical and a closed-shell polyatomic molecule.Comment: 7 pages, 5 figure

Cold heteromolecular dipolar collisions

We present the first experimental observation of cold collisions between two different species of neutral polar molecules, each prepared in a single internal quantum state. Combining for the first time the techniques of Stark deceleration, magnetic trapping, and cryogenic buffer gas cooling allows the enhancement of molecular interaction time by 10$^5$. This has enabled an absolute measurement of the total trap loss cross sections between OH and ND$_3$ at a mean collision energy of 3.6 cm$^{-1}$ (5 K). Due to the dipolar interaction, the total cross section increases upon application of an external polarizing electric field. Cross sections computed from \emph{ab initio} potential energy surfaces are in excellent agreement with the measured value at zero external electric field. The theory presented here represents the first such analysis of collisions between a $^2\Pi$ radical and a closed-shell polyatomic molecule.Comment: 7 pages, 5 figure

Reversible compression of an optical piston through Kramers dynamics

We study the reversible crossover between stable and bistable phases of an over-damped Brownian bead inside an optical piston. The interaction potentials are solved developing a method based on Kramers' theory that exploits the statistical properties of the stochastic motion of the bead. We evaluate precisely the energy balance of the crossover. We show that the deformation of the optical potentials induced by the compression of the piston is related to a production of heat which measures the non-adiabatic character of the crossover. This reveals how specific thermodynamic processes can be designed and controlled with a high level of precision by tailoring the optical landscapes of the piston.Comment: 9 pages, 9 figure

Photonic qubits, qutrits and ququads accurately prepared and delivered on demand

Reliable encoding of information in quantum systems is crucial to all approaches to quantum information processing or communication. This applies in particular to photons used in linear optics quantum computing (LOQC), which is scalable provided a deterministic single-photon emission and preparation is available. Here, we show that narrowband photons deterministically emitted from an atom-cavity system fulfill these requirements. Within their 500 ns coherence time, we demonstrate a subdivision into d time bins of various amplitudes and phases, which we use for encoding arbitrary qu-d-its. The latter is done deterministically with a fidelity >95% for qubits, verified using a newly developed time-resolved quantum-homodyne method.Comment: 5 pages, 4 figure

Strong Optomechanical Squeezing of Light

We create squeezed light by exploiting the quantum nature of the mechanical interaction between laser light and a membrane mechanical resonator embedded in an optical cavity. The radiation pressure shot noise (fluctuating optical force from quantum laser amplitude noise) induces resonator motion well above that of thermally driven motion. This motion imprints a phase shift on the laser light, hence correlating the amplitude and phase noise, a consequence of which is optical squeezing. We experimentally demonstrate strong and continuous optomechanical squeezing of 1.7 +/- 0.2 dB below the shot noise level. The peak level of squeezing measured near the mechanical resonance is well described by a model whose parameters are independently calibrated and that includes thermal motion of the membrane with no other classical noise sources.Comment: 12 pages, 8 figure

Properties of a Variable-delay Polarization Modulator

We investigate the polarization modulation properties of a variable-delay polarization modulator (VPM). The VPM modulates polarization via a variable separation between a polarizing grid and a parallel mirror. We find that in the limit where the wavelength is much larger than the diameter of the metal wires that comprise the grid, the phase delay derived from the geometric separation between the mirror and the grid is sufficient to characterize the device. However, outside of this range, additional parameters describing the polarizing grid geometry must be included to fully characterize the modulator response. In this paper, we report test results of a VPM at wavelengths of 350 microns and 3 mm. Electromagnetic simulations of wire grid polarizers were performed and are summarized using a simple circuit model that incorporates the loss and polarization properties of the device.Comment: 25 pages, 10 figures, accepted by Applied Optic