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If a single-mode nonclassical light is combined with the vacuum on a beam splitter, then the output state is entangled. As proposed in [Phys. Rev. Lett. 94, 173602 (2005)], by measuring this output-state entanglement for a balanced lossless beam splitter, one can quantify the input-state nonclassicality. These measures of nonclassicality (referred to as entanglement potentials) can be based, in principle, on various entanglement measures, leading to the negativity (NP) and concurrence (CP) potentials, and the potential for the relative entropy of entanglement (REEP). We search for the maximal relative nonclassicality, which can be achieved by comparing two entanglement measures for (i) arbitrary two-qubit states and (ii) those which can be generated from a photon-number qubit via a balanced lossless beam splitter, where the qubit basis states are the vacuum and single-photon states. Surprisingly, we find that the maximal relative nonclassicality, measured by the REEP for a given value of the NP, can be increased (if NP < 0.527) by using either a tunable beam splitter or by amplitude damping of the output state of the balanced beam splitter. We also show that the maximal relative nonclassicality, measured by the NP for a given value of the REEP, can be increased by phase damping (dephasing). Note that the entanglement itself is not increased by these losses (since they act locally), but the possible ratios of different measures are affected. Moreover, we show that partially dephased states can be more nonclassical than both pure states and completely dephased states, by comparing the NP for a given value of the REEP. Thus, one can conclude that not all standard entanglement measures can be used as entanglement potentials. Alternatively, one can infer that a single balanced lossless beam splitter is not always transferring the whole nonclassicality of its input state into the entanglement of its output modes. The application of a lossy beam splitter can solve this problem, at least for the cases analyzed in this paper. [ABSTRACT FROM AUTHOR]

We present an error analysis of various tomographic protocols based on the linear inversion for the reconstruction of an unknown two-qubit state. We solve the problem of finding a tomographic protocol which is the most robust against errors in terms of the lowest value (i.e., equal to 1) of a condition number, as required by the Gastinel-Kahan theorem. In contrast, standard tomographic protocols, including those based on mutually unbiased bases, are nonoptimal for determining all the 16 elements of an unknown two-qubit density matrix. Our method is based on the measurements of the 16 generalized Pauli operators, where twelve of them can be locally measured, and the other four require nonlocal Bell measurements. Our method corresponds to selectively measuring, one by one, all the real and imaginary elements of an unknown two-qubit density matrix. We describe two experimentally feasible setups of this protocol for the optimal reconstruction of two photons in an unknown polarization state using conventional detectors and linear-optical elements. Moreover, we define the operators for the optimal reconstruction of the states of multiqubit or multilevel (qudit) systems. [ABSTRACT FROM AUTHOR]

We show how analogs of a large number of well-known nonlinear-optics phenomena can be realized with one or more two-level atoms coupled to one or more resonator modes. Through higher-order processes, where virtual photons are created and annihilated, an effective deterministic coupling between two states of such a system can be created. In this way, analogs of three-wave mixing, four-wave mixing, higher-harmonic and -subharmonic generation (i.e., up- and down-conversion), multiphoton absorption, parametric amplification, Raman and hyper-Raman scattering, the Kerr effect, and other nonlinear processes can be realized. In contrast to most conventional implementations of nonlinear optics, these analogs can reach unit efficiency, only use a minimal number of photons (they do not require any strong external drive), and do not require more than two atomic levels. The strength of the effective coupling in our proposed setups becomes weaker the more intermediate transition steps are needed. However, given the recent experimental progress in ultrastrong light-matter coupling and improvement of coherence times for engineered quantum systems, especially in the field of circuit quantum electrodynamics, we estimate that many of these nonlinear-optics analogs can be realized with currently available technology. [ABSTRACT FROM AUTHOR]

Single-photon devices at microwave frequencies are important for applications in quantum information processing and communication in the microwave regime. In this work we describe a proposal of a multioutput single-photon device. We consider two superconducting resonators coupled to a gap-tunable qubit via both its longitudinal and transverse degrees of freedom. Thus, this qubit-resonator coupling differs from the coupling in standard circuit quantum-electrodynamic systems described by the Jaynes-Cummings model. We demonstrate that an effective quadratic coupling between one of the normal modes and the qubit can be induced and this induced second-order nonlinearity is much larger than that for conventional Kerr-type systems exhibiting photon blockade. Assuming that a coupled normal mode is resonantly driven, we observe that the output fields from the resonators exhibit strong sub-Poissonian photon-number statistics and photon antibunching. Contrary to previous studies on resonant photon blockade, the first-excited state of our device is a pure single-photon Fock state rather than a polariton state, i.e., a highly hybridized qubit-photon state. In addition, it is found that the optical state truncation caused by the strong qubit-induced nonlinearity can lead to an entanglement between the two resonators, even in their steady state under the Markov approximation. [ABSTRACT FROM AUTHOR]

Phonon blockade is a purely quantum phenomenon, analogous to Coulomb and photon blockades, in which a single phonon in an anharmonic mechanical resonator can impede the excitation of a second phonon. We propose an experimental method to realize phonon blockade in a driven harmonic nanomechanical resonator coupled to a qubit, where the coupling is proportional to the second-order nonlinear susceptibility χ(2). This is in contrast to the standard realizations of phonon and photon blockade effects in Kerr-type χ(3) nonlinear systems. The nonlinear coupling strength can be adjusted conveniently by changing the coherent drive field. As an example, we apply this model to predict and describe phonon blockade in a nanomechanical resonator coupled to a Cooper-pair box (i.e., a charge qubit) with a linear longitudinal coupling. By obtaining the solutions of the steady state for this composite system, we give the conditions for observing strong antibunching and sub-Poissonian phonon-number statistics in this induced second-order nonlinear system. Besides using the qubit to produce phonon blockade states, the qubit itself can also be employed to detect blockade effects by measuring its states. Numerical simulations indicate that the robustness of the phonon blockade, and the sensitivity of detecting it, will benefit from this strong induced nonlinear coupling. [ABSTRACT FROM AUTHOR]

A single phonon in a nonlinear nanomechanical resonator (NAMR) can block the excitation of a second phonon [Phys. Rev. A 82, 032101 (2010)]. This intrinsically quantum effect is called phonon blockade, and is an analog of Coulomb blockade and photon blockade. Here we predict tunable multiphonon blockade in coupled nonlinear NAMRs, where nonlinearity is induced by two-level systems (TLSs) assuming dispersive (far off-resonance) interactions. Specifically, we derive an effective Kerr-type interaction in a hybrid system consisting of two nonlinearly interacting NAMRs coupled to two TLSs and driven by classical fields. The interaction between a given NAMR and a TLS is described by a Jaynes-Cummings-like model. We show that by properly tuning the frequency of the driving fields one can induce various types of phonon blockade, corresponding to the entangled phonon states of either two qubits, a qutrit and quartit, or two qudits. Thus, a k-phonon Fock state (with k = 1,2,3) can impede the excitation of more phonons in a given NAMR, which we interpret as a k-phonon blockade (or, equivalently, phonon tunneling). Our results can be explained in terms of resonant transitions in the Fock space and via phase-space interference using the s-parametrized Cahill-Glauber quasiprobability distributions including the Wigner function. We study the nonclassicality, entanglement, and dimensionality of the blockaded phonon states during both dynamics and in the stationary limits. [ABSTRACT FROM AUTHOR]

Heralded near-deterministic multiqubit controlled-phase gates with integrated error detection have recently been proposed by Borregaard et al. [Phys. Rev. Lett. 114, 110502 (2015)]. This protocol is based on a single four-level atom (a heralding quartit) and N three-level atoms (operational qutrits) coupled to a single-resonator mode acting as a cavity bus. Here we generalize this method for two distant resonators without the cavity bus between the heralding and operational atoms. Specifically, we analyze the two-qubit controlled-Z gate and its multiqubit-controlled generalization (i.e., a Toffoli-like gate) acting on the two-lowest levels of N qutrits inside one resonator, with their successful actions being heralded by an auxiliary microwave-driven quartit inside the other resonator. Moreover, we propose a circuit-quantum-electrodynamics realization of the protocol with flux and phase qudits in linearly coupled transmission-line resonators with dissipation. These methods offer a quadratic fidelity improvement compared to cavity-assisted deterministic gates. [ABSTRACT FROM AUTHOR]

We study photon blockade and antibunching in the cavity of an optomechanical system in which the mechanical resonator is coupled to a two-level system (TLS). In particular, we analyze the effects of the coupling strength (to the mechanical mode), transition frequency, and decay rate of TLS on the photon blockade. The statistical properties of the cavity field are affected by the TLS. because the TLS changes the energy-level structure of the optomechanical system via dressed states formed by the TLS and the mechanical resonator. We find that the photon blockade and tunneling can be significantly changed by the transition frequency of the TLS and the coupling strength between the TLS and the mechanical resonator. Therefore, our study provides a method to tune the photon blockade and tunneling using a controllable TLS. [ABSTRACT FROM AUTHOR]

The nonclassicality, entanglement, and dimensionality of a noisy twin beam are determined using a characteristic function of the beam written in the Fock basis. One-to-one correspondence between the negativity quantifying entanglement and the nonclassicality depth is revealed. Twin beams, which are either entangled or nonclassical (independent of their entanglement), are observed only for the limited degrees of noise, which degrades their quantumness. The dimensionality of the twin beam quantified by the participation ratio is compared with the dimensionality of entanglement determined from the negativity. Partitioning of the degrees of freedom of the twin beam into those related to entanglement and to noise is suggested. Both single-mode and multimode twin beams are analyzed. Weak nonclassicality based on integrated-intensity quasidistributions of multimode twin beams is studied. The relation of the model to the experimental twin beams is discussed. [ABSTRACT FROM AUTHOR]

Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental implementation of a necessary and sufficient test of entanglement has been designed even for a general two-qubit state. Here we propose an experimental method for detecting a collective universal witness, which is a necessary and sufficient test of two-photon polarization entanglement. It allows us to detect entanglement for any two-qubit mixed state and to establish tight upper and lower bounds on its amount. A different element of this method is the sequential character of its main components, which allows us to obtain relatively complicated information about quantum correlations with the help of simple linear-optical elements. As such, this proposal realizes a universal two-qubit entanglement test within the present state of the art of quantum optics. We show the optimality of our setup with respect to the minimal number of measured quantities. [ABSTRACT FROM AUTHOR]

We describe a direct method to determine the negativity of an arbitrary two-qubit state in experiments. The method is derived by analyzing the relation between the purity, negativity, and a universal entanglement witness for two-qubit entanglement. We show how the negativity of a two-qubit state can be calculated from just three experimentally accessible moments of the partially transposed density matrix of a two-photon state. Moreover, we show that the negativity can be given as a function of only six invariants, which are linear combinations of nine invariants from the complete set of 21 fundamental and independent two-qubit invariants. We analyze the relation between these moments and the concurrence for some classes of two-qubit states (including the X states, as well as pure states affected by the amplitude-damping and phase-damping channels). We also discuss the possibility of using the universal entanglement witness as an entanglement measure for various classes of two-qubit states. Moreover, we analyze how noise affects the estimation of entanglement via this witness. [ABSTRACT FROM AUTHOR]

Spontaneous parametric down-conversion is a well-known process in quantum nonlinear optics in which a photon incident on a nonlinear crystal spontaneously splits into two photons. Here we propose an analogous physical process where one excited atom directly transfers its excitation to a pair of spatially separated atoms with probability approaching 1. The interaction is mediated by the exchange of virtual rather than real photons. This nonlinear atomic process is coherent and reversible, so the pair of excited atoms can transfer the excitation back to the first one: the atomic analog of sum-frequency generation of light. The parameters used to investigate this process correspond to experimentally demonstrated values in ultrastrong circuit quantum electrodynamics. This approach can be extended to realize other nonlinear interatomic processes, such as four-atom mixing, and is an attractive architecture for the realization of quantum devices on a chip. We show that four-qubit mixing can efficiently implement quantum repetition codes and, thus, can be used for error-correction codes. [ABSTRACT FROM AUTHOR]

We propose and experimentally implement an efficient procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995)] and the fully entangled fraction of Bennett et al. [Phys. Rev. A 54, 3824 (1996)] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. This is an experimental determination of these quantities without quantum state tomography or continuous monitoring of all measurement bases in the usual CHSH inequality tests. We analyze how well the measured degrees of Bell nonlocality and other entanglement witnesses (including the fully entangled fraction and a nonlinear entropic witness) of an arbitrary two-qubit state can estimate its entanglement. In particular, we measure these witnesses and estimate the negativity of various two-qubit Werner states. Our approach could especially be useful for quantum communication protocols based on entanglement swapping. [ABSTRACT FROM AUTHOR]

The behavior of general nonclassical two-mode Gaussian states at a beam splitter is investigated. Single-mode nonclassicality as well as two-mode entanglement of both input and output states are analyzed suggesting their suitable quantifiers. These quantifiers are derived from local and global invariants of linear unitary two-mode transformations such that the sum of input (or output) local nonclassicality measures and entanglement measure gives a global invariant. This invariant quantifies the global nonclassicality resource. Mutual transformations of local nonclassicalities and entanglement induced by the beam splitter are analyzed considering incident noisy twin beams, single-mode noisy squeezed vacuum states, and states encompassing both squeezed states and twin beams. A rich tapestry of interesting nonclassical output states is predicted. [ABSTRACT FROM AUTHOR]

Temporal steering, which is a temporal analog of Einstein-Podolsky-Rosen steering, refers to temporal quantum correlations between the initial and final state of a quantum system. Our analysis of temporal steering inequalities in relation to the average quantum bit error rates reveals the interplay between temporal steering and quantum cloning, which guarantees the security of quantum key distribution based on mutually unbiased bases against individual attacks. The key distributions analyzed here include the Bennett-Brassard 1984 protocol and the six-state 1998 protocol by Bruss. Moreover, we define a temporal steerable weight, which enables us to identify a kind of monogamy of temporal correlation that is essential to quantum cryptography and useful for analyzing various scenarios of quantum causality. [ABSTRACT FROM AUTHOR]