Quantum state engineering by a coherent superposition of photon subtraction and addition

We study a coherent superposition of field annihilation and creation operator acting on continuous variable systems and propose its application for quantum state engineering. Specifically, it is investigated how the superposed operation transforms a classical state to a nonclassical one, together with emerging nonclassical effects. We also propose an experimental scheme to implement this elementary coherent operation and discuss its usefulness to produce an arbitrary superposition of number states involving up to two photons.Comment: published version, 7 pages, 8 figure

Quantum phase estimation using path-symmetric entangled states

We study the sensitivity of phase estimation using a generic class of path-symmetric entangled states $|\varphi\rangle|0\rangle+|0\rangle|\varphi\rangle$, where an arbitrary state $|\varphi\rangle$ occupies one of two modes in quantum superposition. This class of states includes the previously considered states, i.e. $NOON$ states and entangled coherent states, as special cases. With its generalization, we identify the practical limit of phase estimation under energy constraint that is characterized by the photon statistics of the component state $|\varphi\rangle$. We first show that quantum Cramer-Rao bound (QCRB) can be lowered with super-Poissonianity of the state $|\varphi\rangle$. By introducing a component state of the form $|\varphi\rangle=\sqrt{q}|1\rangle+\sqrt{1-q}|N\rangle$, we particularly show that an arbitrarily small QCRB can be achieved even with a finite energy in an ideal situation. For practical measurement schemes, we consider a parity measurement and a full photon-counting method to obtain phase-sensitivity. Without photon loss, the latter scheme employing any path-symmetric states $|\varphi\rangle|0\rangle+|0\rangle|\varphi\rangle$ achieves the QCRB over the entire range $[0,2\pi]$ of unknown phase shift $\phi$ whereas the former does so in a certain confined range of $\phi$. We find that the case of $|\varphi\rangle=\sqrt{q}|1\rangle+\sqrt{1-q}|N\rangle$ provides the most robust resource against loss among the considered entangled states over the whole range of input energy. Finally we also propose experimental schemes to generate these path-symmetric entangled states.Comment: 10 pages, 5 figures, published versio

Increasing and decreasing entanglement characteristics for continuous variables by a local photon subtraction

We investigate how the entanglement characteristics of a non-Gaussian entangled state are increased or decreased by a local photon subtraction operation. The non-Gaussian entangled state is generated by injecting a single-mode non-Gaussian state and a vacuum state into a 50:50 beam splitter. We consider a photon-added coherent state and an odd coherent state as a single-mode non-Gaussian state. In the regime of small amplitude, we show that the performance of quantum teleportation and the second-order Einstein-Podolsky- Rosen-type correlation can both be enhanced, whereas the degree of entanglement decreases, for the output state when a local photon subtraction operation is applied to the non-Gaussian entangled state. The counterintuitive effect is more prominent in the limit of nearly zero amplitude.Comment: Published version, 7 pages, 3 figure

Generating arbitrary photon-number entangled states for continuous-variable quantum informatics

We propose two experimental schemes that can produce an arbitrary photon-number entangled state (PNES) in a finite dimension. This class of entangled states naturally includes non-Gaussian continuous-variable (CV) states that may provide some practical advantages over the Gaussian counterparts (two-mode squeezed states). We particularly compare the entanglement characteristics of the Gaussian and the non-Gaussian states in view of the degree of entanglement and the Einstein-Podolsky-Rosen correlation, and further discuss their applications to the CV teleportation and the nonlocality test. The experimental imperfection due to the on-off photodetectors with nonideal efficiency is also considered in our analysis to show the feasibility of our schemes within existing technologies.Comment: published version, 13 pages, 7 figure

Single-photon quantum nonlocality: Violation of the Clauser-Horne-Shimony-Holt inequality using feasible measurement setups

We investigate quantum nonlocality of a single-photon entangled state under feasible measurement techniques consisting of on-off and homodyne detections along with unitary operations of displacement and squeezing. We test for a potential violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, in which each of the bipartite party has a freedom to choose between 2 measurement settings, each measurement yielding a binary outcome. We find that single-photon quantum nonlocality can be detected when two or less of the 4 total measurements are carried out by homodyne detection. The largest violation of the CHSH inequality is obtained when all four measurements are squeezed-and-displaced on-off detections. We test robustness of violations against imperfections in on-off detectors and single-photon sources, finding that the squeezed-and-displaced measurement schemes perform better than the displacement-only measurement schemes.Comment: 7+ pages, 7 figures, 1 table, close to published versio

Second-order superposition operations via Hong-Ou-Mandel interference

We propose an experimental scheme to implement a second-order nonlocal superposition operation and its variants by way of Hong-Ou-Mandel interference. The second-order coherent operations enable us to generate a NOON state with high particle number in a heralded fashion and also can be used to enhance the entanglement properties of continuous variable states. We discuss the feasibility of our proposed scheme considering realistic experimental conditions such as on-off photodetectors with nonideal efficiency and imperfect single-photon sources.Comment: published version, 6 pages, 6 figure