Noisy Gaussian Channel Research Articles

Redundancy and Synergy of an Entangling Cloner in Continuous-Variable Quantum Communication

We address minimization of information leakage from continuous-variable quantum channels. It is known, that regime of minimum leakage can be accessible for the modulated signal states with variance equivalent to a shot noise, i.e., vacuum fluctuations, in the case of collective attacks. Here we derive the same condition for the individual attacks and analytically study the properties of the mutual information quantities in and out of this regime. We show that in such regime a joint measurement on the modes of a two-mode entangling cloner, being the optimal individual eavesdropping attack in a noisy Gaussian channel, is no more effective that independent measurements on the modes. Varying variance of the signal out of this regime, we observe the nontrivial statistical effects of either redundancy or synergy between the measurements of two modes of the entangling cloner. The result reveals the non-optimality of entangling cloner individual attack for sub-shot-noise modulated signals. Considering the communication between the cloner modes, we show the advantage of knowing the residual noise after its interaction with the cloner and extend the result to a two-cloner scheme.

Quantifying quantum correlations in noisy Gaussian channels

The Gaussian states are essential ingredients in many tasks of quantum information processing. The presence of the noises imposes limitations on achieving these quantum protocols. Therefore, examining the evolution of quantum entanglement and quantum correlations under the coherence of Gaussian states in noisy channels is of paramount importance. In this paper, we propose and analyze a scheme that aims to specify and examine the dynamic evolution of the quantum correlations in two-mode Gaussian states submitted to the influence of the Gaussian thermal environment. We describe the time evolution of the quantum correlations in an open system consisting of two coupled bosonic modes embedded in a Gaussian thermal environment. We discuss the influence of the environment in terms of the initial parameters of the input states. The quantum correlations are quantified using Gaussian interferometric power and the Gaussian entanglement of formation. The behavior of these quantum correlations quantifiers is strictly dependent on the parameters of the input states that are employed. We show that the Gaussian interferometric power is a measurement quantifier that can capture the essential quantum correlations beyond quantum entanglement. In addition, we show that the Gaussian interferometric power is less influenced than the Gaussian entanglement of formation.

Activation and superactivation of single-mode Gaussian quantum channels

Activation of quantum capacity is a surprising phenomenon according to which the quantum capacity of a certain channel may increase by combining it with another channel with zero quantum capacity. Superactivation describes an even more particular occurrence, in which both channels have zero quantum capacity, but their composition has a nonvanishing one. We investigate these effects for all single-mode phase-insensitive Gaussian channels, which include thermal attenuators and amplifiers, assisted by a two-mode positive-partial-transpose channel. Our result shows that activation phenomena are special but not uncommon. We can reveal superactivation in a broad range of thermal attenuator channels, even when the transmissivity is quite low. This means that we can transmit quantum information reliably through very noisy Gaussian channels having zero quantum capacity. We further show that no superactivation is possible for entanglement-breaking Gaussian channels in physically relevant circumstances by proving the non-activation property of the coherent information of bosonic entanglement-breaking channels with finite input energy.

Multimode theory of Gaussian states in uniformly accelerated frames

We use the formalism of noisy Gaussian channels to derive explicit transformation laws describing how an arbitrary multimode Gaussian state of a scalar quantum field is perceived by a number of accelerating observers, each having access to at least one of the modes. Our work, which generalizes earlier results of Ahmadi, et al., Phys. Rev. D 93, 124031 (2016), is the next step torwards a better understanding of the effect of gravity on the states of quantum fields.

Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels

We present a framework for studying bosonic non-Gaussian channels of continuous-variable systems. Our emphasis is on a class of channels that we call photon-added Gaussian channels, which are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian domain for numerous tasks in continuous-variable quantum information processing such as entanglement distillation from Gaussian states and universal quantum computation. The single-mode photon-added channels we consider are obtained by using two-mode beam splitters and squeezing operators with photon addition applied to the ancilla ports giving rise to families of non-Gaussian channels. For each such channel, we derive its operator-sum representation, indispensable in the present context. We observe that these channels are Fock preserving (coherence nongenerating). We then report two examples of activation using our scheme of photon addition, that of quantum-optical nonclassicality at outputs of channels that would otherwise output only classical states and of both the quantum and private communication capacities, hinting at far-reaching applications for quantum-optical communication. Further, we see that noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We also present other physical and information-theoretic properties of these channels.

Kalman meets Shannon

We consider the problem of communicating the state of a dynamical system via a Shannon Gaussian channel with a given power constraint and no feedback. The transmitter observes a possibly noisy measurement of the state. These measurements are then used to encode the message to be transmitted over a noisy Gaussian channel, where a power constraint is imposed on the transmitted message. The receiver, which acts as both a decoder and estimator, observes the noisy measurement of the channel output and makes an optimal estimate of the state of the dynamical system in the minimum mean square sense. Thus, we get a mixed problem of Shannon's source-channel coding problem and a sort of Kalman filtering problem. We show that optimal encoders and decoders are linear filters with a finite memory and we give explicitly the state space realization of the optimal filters. We also present the solution of the case where the transmitter has access to noisy measurements of the state where we derive a separation principle for this communication scheme. Finally, we give necessary and sufficient conditions for the existence of a stationary solution.

Detecting quantum non-Gaussianity via the Wigner function

We introduce a family of criteria to detect quantum non-Gaussian states of a harmonic oscillator, that is, quantum states that can not be expressed as a convex mixture of Gaussian states. In particular we prove that, for convex mixtures of Gaussian states, the value of the Wigner function at the origin of phase space is bounded from below by a non-zero positive quantity, which is a function only of the average number of excitations (photons) of the state. As a consequence, if this bound is violated then the quantum state must be quantum non-Gaussian. We show that this criterion can be further generalized by considering additional Gaussian operations on the state under examination. We then apply these criteria to various non-Gaussian states evolving in a noisy Gaussian channel, proving that the bounds are violated for high values of losses, and thus also for states characterized by a positive Wigner function.

Entanglement distillation for continuous variables in a thermal environment: Effectiveness of a non-Gaussian operation

We study the task of distilling entanglement by a coherent superposition operation $t\hat{a}+r\hat{a}^\dagger$ applied to a continuous-variable state under a thermal noise. In particular, we compare the performances of two different strategies, i.e., the non-Gaussian operation $t\hat{a}+r\hat{a}^\dagger$ is applied before or after the noisy Gaussian channel. This is closely related to a fundamental problem of whether Gaussian or non-Gaussian entanglement can be more robust under a noisy channel and also provides a useful insight into the practical implementation of entanglement distribution for a long-distance quantum communication. We specifically look into two entanglement characteristics, the logarithmic negativity as a measure of entanglement and the teleportation fidelity as a usefulness of entanglement, for each distilled state. We find that the non-Gaussian operation after (before) the thermal noise becomes more effective in the low (high) temperature regime.

Security of continuous-variable quantum cryptography with Gaussian postselection

We extend the security analysis of continuous variable quantum-key-distribution protocols using a family of post selection schemes to account for arbitrary eavesdropping attacks. We show that the postselection protocol is equivalent to a virtual entanglement-based protocol including a distillation stage. We introduce a particular `Gaussian' post selection and demonstrate that the security can be calculated using only experimentally accessible quantities. Finally, we explicitly evaluate the performance for the case of a noisy Gaussian channel in the limit of unbounded key length and find improvements over all pre-existing continuous variable protocols in realistic regimes.

Operator-sum representation for bosonic Gaussian channels

Operator-sum or Kraus representations for single-mode bosonic Gaussian channels are developed, and several of their consequences explored. The fact that the two-mode metaplectic operators acting as unitary purification of these channels do not, in their canonical form, mix the position and momentum variables is exploited to present a procedure which applies uniformly to all families in the Holevo classification. In this procedure the Kraus operators of every quantum-limited Gaussian channel can be simply read off from the matrix elements of a corresponding metaplectic operator. Kraus operators are employed to bring out, in the Fock basis, the manner in which the antilinear, unphysical matrix transposition map when accompanied by injection of a threshold classical noise becomes a physical channel, denoted $\mathcal{D}(\ensuremath{\kappa})$ in the Holevo classification. The matrix transposition channels $\mathcal{D}(\ensuremath{\kappa})$, $\mathcal{D}({\ensuremath{\kappa}}^{\ensuremath{-}1})$ turn out to be a dual pair in the sense that their Kraus operators are related by the adjoint operation. The amplifier channel with amplification factor $\ensuremath{\kappa}$ and the beam-splitter channel with attenuation factor ${\ensuremath{\kappa}}^{\ensuremath{-}1}$ turn out to be mutually dual in the same sense. The action of the quantum-limited attenuator and amplifier channels as simply scaling maps on suitable quasiprobabilities in phase space is examined in the Kraus picture. Consideration of cumulants is used to examine the issue of fixed points. The semigroup property of the amplifier and attenuator families leads in both cases to a Zeno-like effect arising as a consequence of interrupted evolution. In the cases of entanglement-breaking channels a description in terms of rank 1 Kraus operators is shown to emerge quite simply. In contradistinction, it is shown that there is not even one finite rank operator in the entire linear span of Kraus operators of the quantum-limited amplifier or attenuator families, an assertion far stronger than the statement that these are not entanglement breaking channels. A characterization of extremality in terms of Kraus operators, originally due to Choi, is employed to show that all quantum-limited Gaussian channels are extremal. The fact that almost every noisy Gaussian channel can be realized as a product of a pair of quantum-limited channels is used to construct a discrete set of linearly independent Kraus operators for these noisy Gaussian channels, including the classical noise channel, and these Kraus operators have a particularly simple structure.

Fidelity of Gaussian Channels

A noisy Gaussian channel is defined as a channel in which an input field mode is subjected to random Gaussian displacements in phase space. We introduce the quantum fidelity of a Gaussian channel for pure and mixed input states, and we derive a universal scaling law of the fidelity for pure initial states. We also find the maximum fidelity of a Gaussian channel over all input states. Quantum cloning and continuous-variable teleportation are presented as physical examples of Gaussian channels to which the fidelity results can be applied.