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B. H. Liu

Publications and source records attributed to B. H. Liu.

10 recordsLinked to original sources
arXiv2008

Permutation asymmetry inducing entanglement between degrees of freedom in multiphoton states

We describe and examine entanglement between different degrees of freedom in multiphoton states based on the permutation properties. From the state description, the entanglement comes from the permutation asymmetry. According to the different permutation properties, the multiphoton states can be divided into several parts. It will help to deal with the multiphoton interference, which can be used as the measurement of the entanglement.

quant-ph↗
arXiv2008

Entanglement and interference between different degrees of freedom of photons states

In this paper, photonic entanglement and interference are described and analyzed with the language of quantum information process. Correspondingly, a photon state involving several degrees of freedom is represented in a new expression based on the permutation symmetry of bosons. In this expression, each degree of freedom of a single photon is regarded as a qubit and operations on photons as qubit gates. The two-photon Hong-Ou-Mandel interference is well interpreted with it. Moreover, the analysis reveals the entanglement between different degrees of freedom in a four-photon state from parametric down conversion, even if there is no entanglement between them in the two-photon state. The entanglement will decrease the state purity and photon interference visibility in the experiments on a four-photon polarization state.

quant-ph↗
arXiv2007

Experimental Measurement of Multi-dimensional Entanglement via Equivalent Symmetric Projection

We construct a linear optics measurement process to determine the entanglement measure, named \emph{I-concurrence}, of a set of $4 \times 4$ dimensional two-photon entangled pure states produced in the optical parametric down conversion process. In our experiment, an \emph{equivalent} symmetric projection for the two-fold copy of single subsystem (presented by L. Aolita and F. Mintert, Phys. Rev. Lett. \textbf{97}, 050501 (2006)) can be realized by observing the one-side two-photon coincidence without any triggering detection on the other subsystem. Here, for the first time, we realize the measurement for entanglement contained in bi-photon pure states by taking advantage of the indistinguishability and the bunching effect of photons. Our method can determine the \emph{I-concurrence} of generic high dimensional bipartite pure states produced in parametric down conversion process.

quant-ph↗
arXiv2007

Experimental demonstration of phase measurement precision beating standard quantum limit by projection measurement

We propose and demonstrate experimentally a projection scheme to measure the quantum phase with a precision beating the standard quantum limit. The initial input state is a twin Fock state $|N,N>$ proposed by Holland and Burnett [Phys. Rev. Lett. {\bf 71}, 1355 (1993)] but the phase information is extracted by a quantum state projection measurement. The phase precision is about $1.4/N$ for large photon number $N$, which approaches the Heisenberg limit of 1/N. Experimentally, we employ a four-photon state from type-II parametric down-conversion and achieve a phase uncertainty of $0.291\pm 0.001$ beating the standard quantum limit of $1/\sqrt{N} = 1/2$ for four photons.

quant-ph↗
arXiv2007

Four-Photon Interference with Asymmetric Beam Splitters

Two experiments of four-photon interference are performed with two pairs of photons from parametric down-conversion with the help of asymmetric beam splitters. The first experiment is a generalization of the Hong-Ou-Mandel interference effect to two pairs of photons while the second one utilizes this effect to demonstrate a four-photon de Broglie wavelength of $λ/4$ by projection measurement.

quant-ph↗
arXiv2007

Stimulated emission of two photons in parametric amplification and its interpretation as multi-photon interference

Stimulated emission of two photons is observed experimentally in the parametric amplification process and is compared to a three-photon interference scheme. We find that the underlying physics of stimulated emission is simply the constructive interference due to photon indistinguishability. So the observed signal enhancement upon the input of photons is a result of multi-photon interference of the input photons and the otherwise spontaneously emitted photon from the amplifier.

quant-ph↗
arXiv2006

Demonstration of three-photon de Broglie wavelength by projection measurement

Two schemes of projection measurement are realized experimentally to demonstrate the de Broglie wavelength of three photons without the need for a maximally entangled three-photon state (the NOON state). The first scheme is based on the proposal by Wang and Kobayashi (Phys. Rev. A {\bf 71}, 021802) that utilizes a couple of asymmetric beam splitters while the second one applies the general method of NOON state projection measurement to three-photon case. Quantum interference of three photons is responsible for projecting out the unwanted states, leaving only the NOON state contribution in these schemes of projection measurement.

quant-ph↗
arXiv2006

Demonstration of Controllable Temporal Distinguishability in a Three-Photon State

Multi-photon interference is at the heart of the recently proposed linear optical quantum computing scheme and plays an essential role in many protocols in quantum information. Indistinguishability is what leads to the effect of quantum interference. Optical interferometers such as Michaelson interferometer provide a measure for second-order coherence at one-photon level and Hong-Ou-Mandel interferometer was widely employed to describe two-photon entanglement and indistinguishability. However, there is not an effective way for a system of more than two photons. Recently, a new interferometric scheme was proposed to quantify the degree of multi-photon distinguishability. Here we report an experiment to implement the scheme for three-photon case. We are able to generate three photons with different degrees of temporal distinguishability and demonstrate how to characterize them by the visibility of three-photon interference. This method of quantitative description of multi-photon indistinguishability will have practical implications in the implementation of quantum information protocols.

quant-ph↗
arXiv2005

Observation of Four-Photon de Broglie Wavelength by State Projection Measurement

A measurement process is constructed to project an arbitrary two-mode $N$-photon state to a maximally entangled $N$-photon state (the {\it NOON}-state). The result of this projection measurement shows a typical interference fringe with an $N$-photon de Broglie wavelength. For an experimental demonstration, this measurement process is applied to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. Generalization to arbitrary $N$-photon states projection measurement can be easily made and may have wide applications in quantum information. As an example, we formulate it for precision phase measurement.

quant-ph↗