Continuous-variable Quantum States Research Articles

Quantum network dialogue protocol based on continuous-variable GHZ states

Quantum dialogue network, as a considerable topic, promotes high efficiency and instantaneousness in quantum communication through simultaneously deducing the secret information over the quantum channel. A new quantum network dialogue protocol is proposed based on continuous-variable GHZ states. In the protocol, the quantum dialogue could be conducted simultaneously among multiple legitimate communication parties. The security of the proposed protocol is ensured by the correlation of continuous-variable GHZ entangled states and the decoy states inserted into the GHZ states in the randomly selected time slots. In addition, the proposed quantum network dialogue protocol with continuous-variable quantum states improves the communication efficiency with the perfect utilization of quantum bits greatly.

Quadrature histograms in maximum-likelihood quantum state tomography.

Quantum state tomography aims to determine the quantum state of a system from measured data and is an essential tool for quantum information science. When dealing with continuous variable quantum states of light, tomography is often done by measuring the field amplitudes at different optical phases using homodyne detection. The quadrature-phase homodyne measurement outputs a continuous variable, so to reduce the computational cost of tomography, researchers often discretize the measurements. We show that this can be done without significantly degrading the fidelity between the estimated state and the true state. This paper studies different strategies for determining the histogram bin widths. We show that computation time can be significantly reduced with little loss in the fidelity of the estimated state when the measurement operators corresponding to each histogram bin are integrated over the bin width.

Detection of squeezed light with glass-integrated technology embedded into a homodyne detector setup

We design and demonstrate on-chip homodyne detection operating in the quantum regime, i.e. able to detect genuine nonclassical features. Our setup exploits a glass-integrated homodyne analyzer (IHA) entirely fabricated by femtosecond laser micromachining. The IHA incorporates on the same chip a balanced waveguide beam splitter and a thermo-optic phase shifter, allowing us to record homodyne traces at different phases and to perform reliable quantum state tomography. In particular, we show that the IHA allows for the detection of nonclassical features of continuous-variable quantum states, such as squeezed states.

Roton entanglement in quenched dipolar Bose-Einstein condensates

We study quasi-two-dimensional dipolar Bose-Einstein condensates, in which the Bogoliubov excitation spectrum displays, at sufficiently large gas density, a deep roton minimum due to the spatially anisotropic behavior of the dipolar two-body potential. A rapid quench, performed on the speed of sound of excitations propagating on the condensate background, leads to the dynamical Casimir effect, which can be characterized by measuring the density-density correlation function. It is shown, for both zero and finite initial temperatures, that the continuous-variable bipartite quantum state of the created quasiparticle pairs with opposite momenta, resulting from the quench, displays an enhanced potential for the presence of entanglement (represented by nonseparable and steerable quasiparticle states), when compared to a gas with solely repulsive contact interactions. Steerable quasiparticle pairs contain momenta from close to the roton, and hence quantum correlations significantly increase in the presence of a deep roton minimum.

Pedagogical introduction to the entropy of entanglement for Gaussian states

In quantum information theory, the entropy of entanglement is a standard measure of bipartite entanglement between two partitions of a composite system. For a particular class of continuous variable quantum states, the Gaussian states, the entropy of entanglement can be expressed elegantly in terms of symplectic eigenvalues, elements that characterise a Gaussian state and depend on the correlations of the canonical variables. We give a rigorous step-by-step derivation of this result and provide physical insights, together with an example that can be useful in practice for calculations.

An operational measure for squeezing

We propose and analyse a mathematical measure for the amount of squeezing contained in a continuous variable quantum state. We show that the proposed measure operationally quantifies the minimal amount of squeezing needed to prepare a given quantum state and that it can be regarded as a squeezing analogue of the ‘entanglement of formation’. We prove that the measure is convex and subadditive and we provide analytic bounds as well as a numerical convex optimisation algorithm for its computation. By example, we then show that the amount of squeezing needed for the preparation of certain multi-mode quantum states can be significantly lower than naive state preparation suggests.

Quantum non-Gaussianity dynamics of two-mode single-photon squeezed Bell states based on cumulant theory

We characterize the non-Gaussianity of continuous-variable quantum states in terms of the cumulant theory and derive the exact formula of the cumulant of any order for such states. Exploiting the fourth-order cumulant method, we evaluate the quantum non-Gaussianity of two-mode single-photon squeezed Bell states and investigate their dynamics under the influence of two different types of decoherence models. It is shown that in a two-reservoir model, all the fourth-order cumulants of these states are very fragile, while in single-reservoir model, the fourth-order cumulants of one such state are insensitive to thermal noise, showing the time-invariant non-Gaussianity.

Metrology with Unknown Detectors.

The best possible precision is one of the key figures in metrology, but this is established by the exact response of the detection apparatus, which is often unknown. There exist techniques for detector characterization that have been introduced in the context of quantum technologies but apply as well for ordinary classical coherence; these techniques, though, rely on intense data processing. Here, we show that one can make use of the simpler approach of data fitting patterns in order to obtain an estimate of the Cramér-Rao bound allowed by an unknown detector, and we present applications in polarimetry. Further, we show how this formalism provides a useful calculation tool in an estimation problem involving a continuous-variable quantum state, i.e., a quantum harmonic oscillator.

Distribution of squeezed states through an atmospheric channel.

Continuous variable quantum states of light are used in quantum information protocols and quantum metrology and known to degrade with loss and added noise. We were able to show the distribution of bright polarization squeezed quantum states of light through an urban free-space channel of 1.6km length. To measure the squeezed states in this extreme environment, we utilize polarization encoding and a postselection protocol that is taking into account classical side information stemming from the distribution of transmission values. The successful distribution of continuous variable squeezed states is accentuated by a quantum state tomography, allowing for determining the purity of the state.

Tripartite separability conditions exponentially violated by Gaussian states

Starting with a set of conditions for bipartite separability of arbitrary quantum states in any dimension and expressed in terms of arbitrary operators whose commutator is a $c$-number, we derive a hierarchy of conditions for tripartite separability of continuous-variable three-mode quantum states. These conditions have the form of inequalities for higher-order moments of linear combinations of the mode operators. They enable one to distinguish between all possible kinds of tripartite separability, while the strongest violation of these inequalities is a sufficient condition for genuine tripartite entanglement. We construct Gaussian states for which the violation of our conditions grows exponentially with the order of the moments of the mode operators. By going beyond second moments, our conditions are expected to be useful as well for the detection of tripartite entanglement of non-Gaussian states.

High-fidelity teleportation of continuous-variable quantum states with discrete-variable resources

The need for high fidelity quantum teleportation arises in a variety of quantum algorithms and protocols. Unfortunately, conventional continuous variable teleportation schemes rely on EPR states that yield a fidelity that approaches unity only in the limit of an unphysical amount of squeezing. A new method, which utilizes an ensemble of single photon entangled states to teleport continuous variable states with fidelity approaching unity with finite resources was recently proposed by Andersen and Ralph [Phys. Rev. Lett. 111, 050504 (2013)]. We extend these ideas to consider the general case of using maximally entangled states of an arbitrary dimension to teleport a continuous variable state and discuss how the corresponding results are affected.

High-Fidelity Teleportation of Continuous-Variable Quantum States Using Delocalized Single Photons

Traditional continuous-variable teleportation can only approach unit fidelity in the limit of an infinite (and unphysical) amount of squeezing. We describe a new method for continuous-variable teleportation that approaches unit fidelity with finite resources. The protocol is not based on squeezed states as in traditional teleportation but on an ensemble of single photon entangled states. We characterize the teleportation scheme with coherent states, mesoscopic superposition states, and two-mode squeezed states and we find several situations in which near-unity teleportation fidelity can be obtained with modest resources.

Experimental determination of the degree of polarization of quantum states

We demonstrate excitation-manifold resolved polarisation characterisation of continuous-variable (CV) quantum states. In contrast to traditional characterisation of polarisation that is based on the Stokes parameters, we experimentally determine the Stokes vector of each excitation manifold separately. Only for states with a given photon number does the methods coincide. For states with an indeterminate photon number, for example Gaussian states, the employed method gives a richer and more accurate description. We apply the method both in theory and in experiment to some common states to demonstrate its advantages.

Quantum State Orthogonalization and a Toolset for Quantum Optomechanical Phonon Control

We introduce a method that can orthogonalize any pure continuous variable quantum state, i.e., generate a state |ψ (perpindicular)} from |ψ} where {ψ|ψ(perpindicular)}= 0, which does not require significant a priori knowledge of the input state. We illustrate how to achieve orthogonalization using the Jaynes-Cummings or beamsplitter interaction, which permits realization in a number of physical systems. Furthermore, we demonstrate how to orthogonalize the motional state of a mechanical oscillator in a cavity optomechanics context by developing a set of coherent phonon level operations. As the mechanical oscillator is a stationary system, such operations can be performed at multiple times providing considerable versatility for quantum state engineering applications. Utilizing this, we additionally introduce a method how to transform any known pure state into any desired target state.

Theory of complex ridgelet transform based on the entangled state

Based on the results of constructing the wavelet transform in continuous variable quantum state and the classical continuous ridgelet transform, we construct the continuous complex ridgelet transform in the expression of quantum operators and representations. We study the theory of the complex ridgelet transform in quantum optic state via calculating the inner product and projection of quantum states.

Toward quantum state tomography of a single polariton state of an atomic ensemble

We present a proposal and a feasibility study for the creation and quantum state tomography of a single polariton state of an atomic ensemble. The collective non-classical and non-Gaussian state of the ensemble is generated by detection of a single forward-scattered photon. The state is subsequently characterized by atomic state tomography performed using strong dispersive light–atom interaction followed by a homodyne measurement on the transmitted light. The proposal is backed by preliminary experimental results showing projection noise limited sensitivity and a simulation demonstrating the feasibility of the proposed method for the detection of a non-classical and non-Gaussian state of the mesoscopic atomic ensemble. This work represents the first attempt at hybrid discrete–continuous variable quantum state processing with atomic memories.

Optomechanical circuits for nanomechanical continuous variable quantum state processing

We propose and analyze a nanomechanical architecture where light is used to perform linear quantum operations on a set of many vibrational modes. Suitable amplitude modulation of a single laser beam is shown to generate squeezing, entanglement and state transfer between modes that are selected according to their mechanical oscillation frequency. Current optomechanical devices based on photonic crystals, as well as other systems with sufficient control over multiple mechanical modes, may provide a platform for realizing this scheme.

Entanglement quasiprobabilities of squeezed light

We demonstrate the feasibility to completely characterize entanglement by negativities of quasiprobabilities. This requires the complete solution of a sophisticated mathematical problem, the so-called separability eigenvalue problem. Its solution is obtained for a non-Gaussian continuous variable quantum state, a two-mode squeezed state undergoing dephasing. This is a standard scenario for experiments with quantum-correlated radiation fields.

Continuous-variable entanglement purification with atomic systems

We present a proposal for entanglement purification of the continuous-variable quantum state of two propagating optical fields. The scheme is based on letting each field interact with a local node, an atomic ensemble, whose internal collective excitation plays the role of an ancillary continuous variable resource. Entanglement purification is achieved by a dichotomic measurement, representing the required non-Gaussian element, and which consists in detecting the presence or absence of collective excitations in the atomic ensemble. This scheme can be extended to networks, where the nodes are single trapped atoms, and constitutes an important building block for the implementation of a continuous-variable quantum repeater.

Non-negative Wigner functions for orbital angular momentum states

The Wigner function of a pure continuous-variable quantum state is non-negative if and only if the state is Gaussian. Here we show that for the canonical pair angle and angular momentum, the only pure states with non-negative Wigner functions are the eigenstates of the angular momentum. Some implications of this surprising result are discussed.