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.

We propose a generalized Bell inequality for two three-dimensional systems with three settings in each local measurement. It is shown that this inequality is maximally violated if local measurements are configured to be mutually unbiased and a composite state is maximally entangled. This feature is similar to Clauser-Horne-Shimony-Holt inequality for two qubits but is in contrast with the two types of inequalities, Collins-Gisin-Linden-Massar-Popescu and Son-Lee-Kim, for high-dimensional systems. The generalization to aribitrary prime-dimensional systems is discussed.

It is a topic of fundamental and practical importance how a quantum correlated state can be reliably distributed through a noisy channel for quantum information processing. The concept of quantum steering recently defined in a rigorous manner is relevant to study it under certain circumstances and we here address quantum steerability of Gaussian states to this aim. In particular, we attempt to reformulate the criterion for Gaussian steering in terms of local and global purities and show that it is sufficient and necessary for the case of steering a 1-mode system by a N -mode system. It subsequently enables us to reinforce a strong monogamy relation under which only one party can steer a local system of 1-mode. Moreover, we show that only a negative partial-transpose state can manifest quantum steerability by Gaussian measurements in relation to the Peres conjecture. We also discuss our formulation for the case of distributing a two-mode squeezed state via one-way quantum channels making dissipation and amplification effects, respectively. Finally, we extend our approach to include non-Gaussian measurements, more precisely, all orders of higher-order squeezing measurements, and find that this broad set of non-Gaussian measurements is not useful to demonstrate steering for Gaussian states beyond Gaussian measurements.

We examine nonclassical properties of the field states generated by applying the photon annihilation-then-creation operation (AC) and creation-thenannihilation operation (CA) to the thermal and coherent states. Effects of repeated applications of AC and of CA are also studied. We also discuss experimental schemes to realize AC and CA with a cavity system using atom-field interactions.

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An experimental scheme is proposed that allows direct measurement of the concurrence of a twoqubit cavity system. It is based on the cavity-QED technology using atoms as flying qubits and relies on the identity of the two-particle visibility of the atomic probability with the concurrence of the cavity system. The scheme works for any arbitrary pure initial state of the two-qubit cavity system.The question of how to detect the presence and amount of entanglement is one of the central issues in quantum information science. There exist theoretical criteria and measures such as the positive partial transpose (PPT) criterion [1,2], entanglement of formation [3] and concurrence [4] that, in principle, allow one to determine the presence and amount of entanglement. It is, however, difficult to observe such criteria and measures experimentally. The PPT criterion involves a nonphysical operation of partial transposition (complex conjugation) of the density matrix elements, while the entanglement of formation and the concurrence are complicated nonlinear functions of the system state. One is thus led to think that one may have to rely on the technique of a full tomographic reconstruction of the quantum state to measure the entanglement of an unknown quantum state. This technique, although successfully implemented for small systems [5,6], is highly inefficient and difficult especially for large systems, as a large number of observables need to be measured. The question naturally arises whether entanglement can be estimated without having to fully reconstruct the unknown state. It has been shown that the answer to this question is yes at least for the case of pure two-qubit states [7,8], although, even in this case, more than one observable need to be measured.In recent years, several methods [9,10,11,12,13] have been proposed for detecting and measuring entanglement without a full reconstruction of the state; e.g., the method [9] based on the technique of minimal and optimal tomography [14,15] performed on one of the entangled pair, the method [10] based on entanglement witness [16,17] which was realized experimentally [18], the method [11,12] based on PPT criterion [1,2], and the method [13] based on two-particle interferometry [19,20]. These methods, although much simpler than the full state reconstruction, are not completely free of experimental difficulties, as they require either controlled unitary operations or some prior knowledge about the quantum state in question, or they can detect entanglement but not measure its amount.Very recently, direct measurement of the concurrence of a two-photon pure entangled state was demonstrated experimentally using linear optical means [21]. The experiment is based on the realization [22] that entanglement properties are well captured by the expectation value of a certain Hermitian operator with respect to two copies of a pure state. As such, this method requires measurements on two copies of a state. It also requires CNOT operations. Application of this method to matter qubits (a...

We introduce a measure of quantum non-Gaussianity (QNG) for those quantum states not accessible by a mixture of Gaussian states in terms of quantum relative entropy. Specifically, we employ a convex-roof extension using all possible mixed-state decompositions beyond the usual pure-state decompositions. We prove that this approach brings a QNG measure fulfilling the properties desired as a proper monotone under Gaussian channels and conditional Gaussian operations. As an illustration, we explicitly calculate QNG for the noisy single-photon states and demonstrate that QNG coincides with non-Gaussianity of the state itself when the single-photon fraction is sufficiently large.

A deterministic quantum amplifier inevitably adds noise to an amplified signal due to the uncertainty principle in quantum physics. We here investigate how a quantum-noise-limited amplifier can be improved by additionally employing the photon subtraction, the photon addition, and a coherent superposition of the two, thereby making a probabilistic, heralded, quantum amplifier. We show that these operations can enhance the performance in amplifying a coherent state in terms of intensity gain, fidelity, and phase uncertainty. In particular, the photon subtraction turns out to be optimal for the fidelity and the phase concentration among these elementary operations, while the photon addition also provides a significant reduction in the phase uncertainty with the largest gain effect.