We present a concept of non-Gaussian measurement composed of a non-Gaussian ancillary state, linear optics and adaptive heterodyne measurement, and on the basis of this we also propose a simple scheme of implementing a quantum cubic gate on a traveling light beam. In analysis of the cubic gate in the Heisenberg representation, we find that nonlinearity of the gate is independent from nonclassicality; the nonlinearity is generated solely by a classical nonlinear adaptive control in a measurement-and-feedforward process while the nonclassicality is attached by the non-Gaussian ancilla that suppresses excess noise in the output. By exploiting the noise term as a figure of merit, we consider the optimum non-Gaussian ancilla that can be prepared within reach of current technologies and discuss performance of the gate. It is a crucial step towards experimental implementation of the quantum cubic gate.

We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous variable systems.

Squeezing is a nonlinear Gaussian operation that is the key component in construction of other nonlinear Gaussian gates. In our implementation of the squeezing gate, the amount and the orientation of the squeezing can be controlled by an external driving signal with 1 MHz operational bandwidth. This opens a brand new area of dynamic Gaussian processing. In particular, the gate can be immediately employed as the feed-forward needed for the deterministic implementation of the quantum cubic gate, which is a key piece of universal quantum information processing.PACS numbers: 03.67. Lx, 42.50.Dv, 42.50.Ex, Quantum information processing with continuous variable systems (CV) has many tools. They could be divided into two broad categories -Gaussian and nonGaussian. The Gaussian tools comprise of Gaussian quantum states that can be represented by a Gaussian Wigner function, of Gaussian measurements that project on Gaussian states, and of Gaussian operations that transform Gaussian states into different Gaussian states [1]. The non-Gaussian tools category then includes everything else. The non-Gaussian category is much broader and much more powerful. There are many quantum information protocols that cannot be implemented with Gaussian tools alone, quantum computation [2, 3], entanglement distillation [4][5][6], and error correction [7] are just the three most prominent examples.As a consequence, there is an understandable thirst for all matters non-Gaussian. In quantum optics, which is the experimental platform of choice when it comes to tests of CV paradigms [8], the non-Gaussian features need to come from interactions with discrete variable physical systems [9][10][11][12][13][14][15][16][17], or from discrete measurements [1,7,18,19]. These two general approaches also differ with respect to quantum systems for which they can be applied. While the interaction with discrete variable systems is best realized by a standing wave mode in a resonator, the discrete projective measurements work better with traveling light. And here comes another distinction. The traveling modes of light are much more suitable for implementation of Gaussian operations. This is significant, because the non-Gaussian resources are useful only when the Gaussian tools are refined enough to operate without a hitch. To present a specific example, consider the issue of universal quantum information processing. In CV world this means the ability to implement a unitary operation with an arbitrary Hamiltonian [2,20]. For this we need to have access to the cubic operation -a quantum operation with Hamiltonian composed of third power of quadrature operators -as well as the complete range of Gaussian operations.The Gaussian states, operations, and measurements are the foundations on which the CV quantum information processing is built. Homodyne detection, squeezed states and Gaussian linear operations in the form of displacement and passive linear optics are already staples of the contemporary experimental practice. The measurement induced paradigm [21], whi...

Real-time controls based on quantum measurements are powerful tools for various quantum protocols. However, their experimental realization have been limited by mode-mismatch between temporal mode of quadrature measurement and that heralded by photon detection. Here, we demonstrate real-time quadrature measurement of a single-photon wavepacket induced by a photon detection, by utilizing continuous temporal-mode-matching between homodyne detection and an exponentially rising temporal mode. Single photons in exponentially rising modes are also expected to be useful resources for interactions with other quantum systems.PACS numbers: 03.67. Lx, 42.50.Dv, 42.50.Ex, Quantum measurement is a basic requirement for various quantum protocols. In many of them, realtime acquisition of the measurement outcomes is beneficial or even required. Real-time measurement enables real-time feedback or feedforward controls of quantum systems. Measurement-based quantum computation (MBQC) [1, 2] is a typical example of such real-time usage of the measurement results, where the measurement results are fedforward to the next computational step. In addition, quantum dynamics conditioned by measurements are often referred to as quantum trajectories or quantum filters [3][4][5], and form essential parts of developing quantum control theories. Based on them, basic cases of quantum controls, e.g., suppression of noises, have been tested with a variety of systems recently [6][7][8][9].In order to put the quantum measurement-based technologies further, an important adaptation is to bridge different quantum systems or different quantum variables in the measurement system [5,10,11]. As a general problem, one may want to connect different systems as a signal and probe. Aside from the issues of connecting different systems, even when restricting us to the light field, there are two fundamental variables reflecting the waveparticle duality. One is the continuous variable (CV) field quadrature amplitudex = (â +â † )/ √ 2, and the other is the discrete variable (DV) photon numbern =â †â , wherê a andâ † denote the field annihilation and creation operators, respectively. CV-DV hybrid architectures have been identified to offer crucial advantages, ranging from deterministic and fault-tolerant MBQC [12-15] to loopholefree Bell inequality test [16]. Experimental technologies for the hybridization are also rapidly developing [17][18][19][20]; however, combining them with real-time quantumoptical controls are facing difficulties.An obstacle is a mode mismatch between CV-based homodyne detection and DV-based photon detection. To be more precise, homodyne detection is sensitive to vacuum fluctuation, while photon detection is not. Therefore, filtration of the field quadrature, i.e. integration with an appropriate weight function f (t) asX = f (t)x(t)dt is essential in order to remove irrelevant vacuum noises and obtain meaningful quadrature information matching with the field mode heralded by photon detections. At this point, quadrature measurement often fails ...

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