Konrad Banaszek

Optimal Quantum Phase Estimation

By using a systematic optimization approach, we determine quantum states of light with definite photon number leading to the best possible precision in optical two-mode interferometry. Our treatment takes into account the experimentally relevant situation of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit, thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.

Fiber-assisted detection with photon number resolution

We report the development of a photon-number-resolving detector based on a fiber-optical setup and a pair of standard avalanche photodiodes. The detector is capable of resolving individual photon numbers and operates on the well-known principle by which a single-mode input state is split into a large number (eight) of output modes. We reconstruct the photon statistics of weak coherent input light from experimental data and show that there is a high probability of inferring the input photon number from a measurement of the number of detection events on a single run.

Efficient Conditional Preparation of High-Fidelity Single Photon States for Fiber-Optic Quantum Networks

A prerequisite for practical quantum information processing is an efficient source of high-fidelity single photons. We report single photon preparation with a conditional detection efficiency exceeding 51% and detection rate of up to 8.5 times 105 counts/[smiddotmW]

Experimental quantum-enhanced estimation of a lossy phase shift

Evidence that appropriately engineered quantum states outperform both standard and N00N states in the precision of phase estimation — even in the presence of losses and decoherence — is presented. The results show that the strategy for realizing the quantum enhancement of metrology is quite distinct from protecting quantum information encoded in light.

Quantum phase estimation with lossy interferometers

We give a detailed discussion of optimal quantum states for optical two-mode interferometry in the presence of photon losses. We derive analytical formulae for the precision of phase estimation obtainable using quantum states of light with a definite photon number and prove that maximization of the precision is a convex optimization problem. The corresponding optimal precision, i.e., the lowest possible uncertainty, is shown to beat the standard quantum limit thus outperforming classical interferometry. Furthermore, we discuss more general inputs: states with indefinite photon number and states with photons distributed between distinguishable time bins. We prove that neither of these is helpful in improving phase estimation precision.

Photon-number-resolving detection using time-multiplexing

A time-multiplexed detector capable of photon number resolution was constructed. The detector is analyzed theoretically and used to verify the photon statistics of weak coherent light. Conditional state preparation using the detector is explored

Pulsed squeezed light: Simultaneous squeezing of multiple modes

We analyze the spectral properties of squeezed light produced by means of pulsed, single-pass degenerate parametric down-conversion. The multimode output of this process can be decomposed into characteristic modes undergoing independent squeezing evolution akin to the Schmidt decomposition of the biphoton spectrum. The main features of this decomposition can be understood using a simple analytical model developed in the perturbative regime. In the strong pumping regime, for which the perturbative approach is not valid, we present a numerical analysis, specializing to the case of one-dimensional propagation in a beta-barium borate waveguide. Characterization of the squeezing modes provides us with an insight necessary for optimizing homodyne detection of squeezing. For a weak parametric process, efficient squeezing is found in a broad range of local oscillator modes, whereas the intense generation regime places much more stringent conditions on the local oscillator. We point out that without meeting these conditions, the detected squeezing can actually diminish with the increasing pumping strength, and we expose physical reasons behind this inefficiency.

Quantifying the non-Gaussian character of a quantum state by quantum relative entropy

We introduce a measure to quantify the non-Gaussian character of a quantum state: the quantum relative entropy between the state under examination and a reference Gaussian state. We analyze in detail the properties of our measure and illustrate its relationships with relevant quantities in quantum information such as the Holevo bound and the conditional entropy; in particular, a necessary condition for the Gaussian character of a quantum channel is also derived. The evolution of non-Gaussianity is analyzed for quantum states undergoing conditional Gaussification toward twin beams and de-Gaussification driven by Kerr interaction. Our analysis allows us to assess non-Gaussianity as a resource for quantum information and, in turn, to evaluate the performance of Gaussification and de-Gaussification protocols.

Photon counting with a loop detector

We propose a design for a photon-counting detector that is capable of resolving multiphoton events. The basic element of the setup is a fiber loop, which traps the input field with the help of a fast electro-optic switch. A single weakly coupled avalanche photodiode is used to detect small portions of the signal field extracted from the loop. We analyze the response of the loop detector to an arbitrary input field and discuss both the reconstruction of the photon-number distribution of an unknown field from the count statistics measured in the setup and the application of the detector in conditional-state preparation.

Fidelity of single qubit maps

We describe a simple way of characterizing the average fidelity between a unitary (or anti-unitary) operator and a general operation on a single qubit, which only involves calculating the fidelities for a few pure input states, and discuss possible applications to experimental techniques including nuclear magnetic resonance (NMR).