We propose a test of nonlocality for continuous variables using a two-mode squeezed state as the source of nonlocal correlations and a measurement scheme based on conditional homodyne detection. Both the CHSH-and the CH-inequality are constructed from the conditional homodyne data and found to be violated for a squeezing parameter larger than r ≈ 0.48.

We address the joint estimation of the two defining parameters of a displacement operation in phase space. In a measurement scheme based on a Gaussian probe field and two homodyne detectors, it is shown that both conjugated parameters can be measured below the standard quantum limit when the probe field is entangled. We derive the most informative Cram\'er-Rao bound, providing the theoretical benchmark on the estimation and observe that our scheme is nearly optimal for a wide parameter range characterizing the probe field. We discuss the role of the entanglement as well as the relation between our measurement strategy and the generalized uncertainty relations.Comment: 8 pages, 3 figures; v2: references added and sections added to the supplemental material; v3: minor changes (published version

We study a coherent superposition tâ + râ † 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.

We derive a class of inequalities, from the uncertainty relations of the su͑1,1͒ and the su͑2͒ algebra in conjunction with partial transposition, that must be satisfied by any separable two-mode states. These inequalities are presented in terms of the su͑2͒ operators J, and the total photon number ͗N a + N b ͘. They include as special cases the inequality derived by Hillery and Zubairy ͓Phys. Rev. Lett. 96, 050503 ͑2006͔͒, and the one by Agarwal and Biswas ͓New J. Phys. 7, 211 ͑2005͔͒. In particular, optimization over the whole inequalities leads to the criterion obtained by Agarwal and Biswas. We show that this optimal criterion can detect entanglement for a broad class of non-Gaussian entangled states, i.e., the su͑2͒ minimum-uncertainty states. Experimental schemes to test the optimal criterion are also discussed, especially the one using linear optical devices and photodetectors.

We investigate how the entanglement properties of a two-mode state can be improved by performing a coherent superposition operation tâ + râ † of photon subtraction and addition, proposed by Lee and Nha [Phys. Rev. A 82, 053812 (2010)], on each mode. We show that the degree of entanglement, the EPR-type correlation, and the performance of quantum teleportation can be all enhanced for the output state when the coherent operation is applied to a two-mode squeezed state. The effects of the coherent operation are more prominent than those of the mere photon subtraction a and the additionâ † particularly in the small squeezing regime, whereas the optimal operation becomes the photon subtraction (case of r = 0) in the large-squeezing regime.

Single-quantum level operations are important tools to manipulate a quantum state. Annihilation or creation of single particles translates a quantum state to another by adding or subtracting a particle, depending on how many are already in the given state. The operations are probabilistic and the success rate has yet been low in their experimental realization. Here we experimentally demonstrate (near) deterministic addition and subtraction of a bosonic particle, in particular a phonon of ionic motion in a harmonic potential. We realize the operations by coupling phonons to an auxiliary two-level system and applying transitionless adiabatic passage. We show handy repetition of the operations on various initial states and demonstrate by the reconstruction of the density matrices that the operations preserve coherences. We observe the transformation of a classical state to a highly non-classical one and a Gaussian state to a non-Gaussian one by applying a sequence of operations deterministically.

We study an experimental scheme to generate Gaussian two-mode entangled states via beam splitter. Specifically, we consider a nonclassical Gaussian state ͑squeezed state͒ and a thermal state as two input modes, and evaluate the degree of entanglement at the output. Experimental conditions to generate entangled outputs are completely identified and the critical thermal noise to destroy entanglement is analytically obtained. By doing so, we discuss the possibility to link the resistance to noise in entanglement generation with the degree of single-mode nonclassicality.

In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudospin observables for an arbitrary nonpositive Hermitian matrix whose uncertainty relation is violated. This method enables us to systematically derive separability conditions for all negative partial-transpose states in experimentally accessible forms. In particular, generalized entanglement criteria are derived from the Schrödinger-Robertson inequalities for bipartite continuous-variable states.