Optimization of the transmission of observable expectation values and observable statistics in continuous-variable teleportation

Performance of quantum teleportation is typically measured by the average fidelity, an overlap between the input and output states. Along with the first moment, we introduce the second moment of fidelity in continuous-variable (CV) teleportation, i.e., the fidelity deviation as the figure of merit to assess the protocol's efficiency. We show that CV states, both Gaussian and non-Gaussian, can be better characterized by considering both average fidelity and fidelity deviation, which is not possible with only average fidelity. Moreover, we shed light on the performance of the teleportation protocol in two different input scenarios: One is when input states are sampled from constrained uniform distribution while the other one is Gaussian suppression of the input states which again leads to a different classification of CV states according to their performance. The entire analysis is carried out in noiseless and noisy scenarios with noise being incorporated in the measurement and the shared channels. We also report that one type of noise can make the protocol robust against the other one, which leads to a ``constructive effect,'' and identify the noise models which are responsible for decreasing average fidelity and the increment in fidelity deviation.

We investigate continuous variable (CV) quantum teleportation using relevant classes of non-Gaussian states of the radiation field as entangled resources. First, we introduce the class two-mode squeezed symmetric superposition of Fock states, including finite truncations of twin-beam Gaussian states as special realizations. These states depend on a set of free independent parameters that can be adjusted for the optimization of teleportation protocols, with an enhancement of the success probability of teleportation both for coherent and Fock input states. We show that the optimization procedure reduces the entangled resources to truncated twin beam states, which thus represents an optimal class of non-Gaussian resources for quantum teleportation. We then introduce a further class of two-mode non-Gaussian entangled resources, in the form of squeezed cat-like states. We analyze the performance and the properties of such states when optimized for (CV) teleportation, and compare them to the optimized squeezed Bell-like states introduced in a previous work [12]. We discuss how optimal resources for teleportation are characterized by a suitable balance of entanglement content and squeezed vacuum affinity. We finally investigate the effects of thermal noise on the efficiency of quantum teleportation. To this aim, a convenient framework is to describe noisy entangled resources as linear superpositions of non-Gaussian state and thermal states. Although the presence of the thermal component strongly reduces the teleportation fidelity, noisy non-Gaussian states remain preferred resources when compared to noisy twin-beam Gaussian states.

We study a continuous-variable (CV) teleportation protocol based on a shared entangled state produced by the quantum-nondemolition (QND) interaction of two vacuum states. The scheme utilizes the QND interaction or an unbalanced beam splitter in the Bell measurement. It is shown that in the non-unity gain regime the signal transfer coefficient can be enhanced while the conditional variance product remains preserved by applying appropriate local squeezing operation on sender's part of the shared entangled state. In the unity gain regime it is demonstrated that the fidelity of teleportation can be increased with the help of the local squeezing operations on parts of the shared entangled state that convert effectively our scheme to the standard CV teleportation scheme. Further, it is proved analytically that such a choice of the local symplectic operations minimizes the noise by which the mean number of photons in the input state is increased during the teleportation. Finally, our analysis reveals that the local symplectic operation on sender's side can be integrated into the Bell measurement if the interaction constant of the interaction in the Bell measurement can be adjusted properly.

Sabadini, Walters and others have developed a categorical, machine based theory of concurrency in which there are four essential aspects: a distributive category of data-types; a bicategory Mach whose objects are data types, and whose arrows are input-output machines built from data types; a semantic category (or categories) Sem, suitable to contain the behaviors of machines, and a functor, “behavior”: Mach→Sem. Suitable operations on machines and semantics are found so that the behavior functor preserves these operations. Then, if each machine is decomposable into primitive machines using these operations, the behavior of a general machine is deducible from the behavior of its parts. The theory of non-deterministic finite state automata provides an example of the paradigm and also throws some light on the classical theory of finite state automata. We describe a bicategory whose objects are natural numbers, in which an arrow M: n→p is a finite state automaton with n input states, p output states, and some additional internal states; we require that no transitions begin at output states or end at input states. A machine is represented by an q+n by q+p matrix. The bicategory supports additional operations: non-deterministic choice, parallel interleaving, and feedback. Enough operations are imposed on machines to show that each machine may be obtained from some atomic ones by means of the operations. The semantic category is the (Bloom-Esik) iteration theory Mat (X✶ whose objects are natural numbers and whose arrows from n to p are n×p matrices with entries in the semiring of languages. The behavior functor associates to a machine M: n→p a matrix |M| of languages, one language to each pair of input and output states. Behavior preserves composition, feedback, takes non-deterministic choice to union, and parallel-interleaving to shuffle. Thus, behavior gives a compositional semantics to a primitive notion of concurrent processes.

Summary form only given. The concept of quantum teleportation of continuous variables was suggested by Vaidman [see Phys. Rev. A, vol. 49, p. 1473, 1994]. The protocol for this kind of teleportation was elaborated and demonstrated experimentally by Kimble with collaborators [see Science, vol. 282, p. 706, 1998]. In this scheme the state being teleported is that of a single transverse mode of the electromagnetic field with finite frequency bandwidth. We describe the quantum teleportation scheme that allows one to teleport the quantum state of the wavefront of an electromagnetic wave. In other words we propose teleportation of the quantum state of a spatially multimode electromagnetic field.

The paper presents a new algorithm for modulation recognition of digital communication signals based on higher order cumulants (HOCs) and support vector machines (SVM). The fourth and sixth order cumulants of the received signal are used as the input classification feature vector to the SVM. The SVM maps the input vectors nonlinearly into a high dimensional feature space, constructs the optimum separating hyperplane in that space and makes the non-separable data separable. This method is robust to Gaussian noise and constellation rotation due to the initial phase of the signal and avoids the overfitting and local minimum in a neural network. The high performance and robustness of the algorithms are proved by computer simulation.

Higher order symmetric cumulants of global collective observables in heavy ion collisions are studied. The symmetric cumulants can be straightforwardly constructed for scalar observables: the average transverse momentum, the multiplicity, and the squares of harmonic flow vectors. Third and fourth order cumulants are calculated in the hydrodynamic model. A linear predictor of the average transverse momentum and harmonic flow coefficients in a collision is used to predict the values of the cumulants from the moments of the initial distribution. The symmetric cumulants divided by the averages (or the standard deviations) of the considered observables can be used as a fine tool to study correlations present in the initial state of the collision.

An improved algorithm for joint direction of departure (DOD) and direction of arrival (DOA) estimation in bistatic MIMO radar based on fourth order cumulants is presented. Firstly, the data of receiver is reset and divided to acquire the rotational invariance property of transmitter and receiver, respectively. The fourth order cumulants matrixes in twain are constructed which are based on the basic definition of the cumulant. Then we use the propagator method (PM), which only requires linear operation but does not involve any eigendecomposition of the cumulant matrix, to estimate the DODs and DOAs, respectively. Finally, the maximum likelihood method is used to solve the pairing problem. The proposed method is effective in prohibiting the Gaussian colored noise and improves the performance of the angle estimation slightly. It does not need two-dimensional spectrum peak searching and eigenvalue decomposition on the cumulant matrix, thus the computation complexity is reduced. At the same time, it has no exceptive claim on the number of receive arrays or receive arrays. Simulation results verify the effectiveness and feasibility of the proposed method.

This paper explores the fourth order cumulants (FOC) of the LPC residual of speech signals and presents a new algorithm for Voice Activity detection (VAD) based on the newly established FOC properties. Analytical expressions for the horizontal slice of the 4th cumulant as well as the kurtosis of voiced speech are derived based on a reported sinusoidal model [4]. The derivations demonstrate that the kurtosis of voiced speech is distinct from that of Gaussian noise and can be used to aid in detecting voicing. The proposed VAD combines FOC metrics with SNR measures to classify speech and noise frames. Its performance is compared to the ITU-T G.729B VAD [1] in various noise conditions, and quantified using the probability of correct and false classifications. The results show the proposed VAD has overall comparable performance to the G.729B: Its probability of false classification is lower in low SNR and Gaussian-like noise, but higher in speech-like noises.

We discuss the cases where local decoherence selectively degrades one type of entanglement more than other types. A typical case is called state ordering change, in which two input states with different amounts of entanglement undergoes a local decoherence and the state with the larger entanglement results in an output state with less entanglement than the other output state. We are also interested in a special case where the state with the larger entanglement evolves to a separable state while the other output state is still entangled, which we call selective entanglement breaking. For three-level or larger systems, it is easy to find examples of the state ordering change and the selective entanglement breaking, but for two-level systems it is not trivial whether such situations exist. We present a general strategy to construct examples of two-qubit states exhibiting the selective entanglement breaking regardless of entanglement measure. We also give a more striking example of the selective entanglement breaking in which the less entangled input state has only an infinitesimal amount of entanglement.

We present two optimal quantum anti-cloning machines for real state in two dimensions, i.e., input state lying in the x–z equator. The first anti-cloning machine produces two outputs which are orthogonal to the input, and the second one produces two anti-parallel outputs for a single input state. The optimal fidelities are also derived.

In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global and local amounts of mixedness, and efficiently estimated by direct measurements of the associated purities. For multimode Gaussian states endowed with local symmetry with respect to a given bipartition, we show how the multimode block entanglement can be completely and reversibly localized onto a single pair of modes by local, unitary operations. We then analyze the distribution of entanglement among multiple parties in multimode Gaussian states. We introduce the continuous-variable tangle to quantify entanglement sharing in Gaussian states and we prove that it satisfies the CoffmanKundu-Wootters monogamy inequality. Nevertheless, we show that pure, symmetric three–mode Gaussian states, at variance with their discretevariable counterparts, allow a promiscuous sharing of quantum correlations, exhibiting both maximum tripartite residual entanglement and maximum couplewise entanglement between any pair of modes. Finally, we investigate the connection between multipartite entanglement and the optimal fidelity in a continuous-variable quantum teleportation network. We show how the fidelity can be maximized in terms of the best preparation of the shared entangled resources and, viceversa, that this optimal fidelity provides a clearcut operational interpretation of several measures of bipartite and multipartite entanglement, including the entanglement of formation, the localizable entanglement, and the continuous-variable tangle.

Generation of high fidelity photonic non-Gaussian states is a crucial\ningredient for universal quantum computation using continous-variable\nplatforms, yet it remains a challenge to do so efficiently. We present a\ngeneral framework for a probabilistic production of multimode non-Gaussian\nstates by measuring few modes of multimode Gaussian states via\nphoton-number-resolving detectors. We use Gaussian elements consisting of\nsqueezed displaced vacuum states and interferometers, the only non-Gaussian\nelements consisting of photon-number-resolving detectors. We derive analytic\nexpressions for the output Wigner function, and the probability of generating\nthe states in terms of the mean and the covariance matrix of the Gaussian state\nand the photon detection pattern. We find that the output states can be written\nas a Fock basis superposition state followed by a Gaussian gate, and we derive\nexplicit expressions for these parameters. These analytic expressions show\nexactly what non-Gaussian states can be generated by this probabilistic scheme.\nFurther, it provides a method to search for the Gaussian circuit and\nmeasurement pattern that produces a target non-Gaussian state with optimal\nfidelity and success probability. We present specific examples such as the\ngeneration of cat states, ON states, Gottesman-Kitaev-Preskill states, NOON\nstates and bosonic code states. The proposed framework has potential\nfar-reaching implications for the generation of bosonic error-correction codes\nthat require non-Gaussian states, resource states for the implementation of\nnon-Gaussian gates needed for universal quantum computation, among other\napplications requiring non-Gaussianity. The tools developed here could also\nprove useful for the quantum resource theory of non-Gaussianity.\n

Determination of the quantum nature of correlations between two spatially separated systems plays a crucial role in quantum information science. Of particular interest is the questions of if and how these correlations enable quantum information protocols to be more powerful. Here, we report on a distributed quantum computation protocol in which the input and output quantum states are considered to be classically correlated in quantum informatics. Nevertheless, we show that the correlations between the outcomes of the measurements on the output state cannot be efficiently simulated using classical algorithms. Crucially, at the same time, local measurement outcomes can be efficiently simulated on classical computers. We show that the only known classicality criterion violated by the input and output states in our protocol is the one used in quantum optics, namely, phase-space nonclassicality. As a result, we argue that the global phase-space nonclassicality inherent within the output state of our protocol represents true quantum correlations.

It is well-known that any quantum channel E satisfies the data processing inequality (DPI), with respect to various divergences, e.g., quantum χκ2 divergences and quantum relative entropy. More specifically, the data processing inequality states that the divergence between two arbitrary quantum states ρ and σ does not increase under the action of any quantum channel E. For a fixed channel E and a state σ, the divergence between output states E(ρ) and E(σ) might be strictly smaller than the divergence between input states ρ and σ, which is characterized by the strong data processing inequality (SDPI). Among various input states ρ, the largest value of the rate of contraction is known as the SDPI constant. An important and widely studied property for classical channels is that SDPI constants tensorize. In this paper, we extend the tensorization property to the quantum regime: we establish the tensorization of SDPIs for the quantum χκ1/22 divergence for arbitrary quantum channels and also for a family of χκ2 divergences (with κ≥κ1/2) for arbitrary quantum-classical channels.