arXiv subjects
Publications and source records attributed to Stefano Mancini.
The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting to Gaussian encodings, for which we provide analytical expressions.
We investigate the possibility of correcting errors occurring on a multipartite system through a feedback mechanism that acquires information from partial access to the environment. A partial control scheme of this kind might be useful when dealing with correlated errors. In fact, in such a case, it could be enough to gather local information to decide what kind of global recovery to perform. Then, we apply this scheme to the depolarizing and correlated errors, and quantify its performance by means of the entanglement fidelity.
We consider the problem of quantum communication mediated by an optical refocusing system, which is schematized as a thin lens with a finite pupil. This model captures the basic features of all those situations in which a signal is either refocused by a repeater for long distance communication, or it is focused on a detector prior to the information decoding process. Introducing a general method for linear optical systems, we compute the communication capacity of the refocusing apparatus. Although the finite extension of the pupil may cause loss of information, we show that the presence of the refocusing system can substantially enhance the rate of reliable communication with respect to the free-space propagation.
We investigate the possibility of chaining qubits by letting pairs of nearest neighbours qubits dissipating into common environments. We then study entanglement dynamics within the chain and show that steady state entanglement can be achieved.
We characterize the complexity of geodesic paths on a curved statistical manifold M_{s} through the asymptotic computation of the information geometric complexity V_{M_{s}} and the Jacobi vector field intensity J_{M_{s}}. The manifold M_{s} is a 2l-dimensional Gaussian model reproduced by an appropriate embedding in a larger 4l-dimensional Gaussian manifold and endowed with a Fisher-Rao information metric g_{μν}(Θ) with non-trivial off diagonal terms. These terms emerge due to the presence of a correlational structure (embedding constraints) among the statistical variables on the larger manifold and are characterized by macroscopic correlational coefficients r_{k}. First, we observe a power law decay of the information geometric complexity at a rate determined by the coefficients r_{k} and conclude that the non-trivial off diagonal terms lead to the emergence of an asymptotic information geometric compression of the explored macrostates Θ on M_{s}. Finally, we observe that the presence of such embedding constraints leads to an attenuation of the asymptotic exponential divergence of the Jacobi vector field intensity.
With increasing communication rates via quantum channels, memory effects become unavoidable whenever the use rate of the channel is comparable to the typical relaxation time of the channel environment. We introduce a model of a bosonic memory channel, describing correlated noise effects in quantum-optical processes via attenuating or amplifying media. To study such a channel model, we make use of a proper set of collective field variables, which allows us to unravel the memory effects, mapping the n-fold concatenation of the memory channel to a unitarily equivalent, direct product of n single-mode bosonic channels. We hence estimate the channel capacities by relying on known results for the memoryless setting. Our findings show that the model is characterized by two different regimes, in which the cross correlations induced by the noise among different channel uses are either exponentially enhanced or exponentially reduced.
We compute the asymptotic temporal behavior of the dynamical complexity associated with the maximum probability trajectories on Gaussian statistical manifolds in presence of correlations between the variables labeling the macrostates of the system. The algorithmic structure of our asymptotic computations is presented and special focus is devoted to the diagonalization procedure that allows to simplify the problem in a remarkable way. We observe a power law decay of the information geometric complexity at a rate determined by the correlation coefficient. We conclude that macro-correlations lead to the emergence of an asymptotic information geometric compression of the statistical macrostates explored on the configuration manifold of the model in its evolution between the initial and final macrostates.
We review a communication protocol recently proposed by us that makes use of a two-way quantum channel. We provide a characterization of such a protocol from a practical perspective, and consider the most relevant eavesdropping strategies against it. This allows us to compare its potentialities with those of a standard protocol which uses a one-way quantum channel.
We study the performance of simple error correcting and error avoiding quantum codes together with their concatenation for correlated noise models. Specifically, we consider two error models: i) a bit-flip (phase-flip) noisy Markovian memory channel (model I); ii) a memory channel defined as a memory degree dependent linear combination of memoryless channels with Kraus decompositions expressed solely in terms of tensor products of X-Pauli (Z-Pauli) operators (model II). The performance of both the three-qubit bit flip (phase flip) and the error avoiding codes suitable for the considered error models is quantified in terms of the entanglement fidelity. We explicitly show that while none of the two codes is effective in the extreme limit when the other is, the three-qubit bit flip (phase flip) code still works for high enough correlations in the errors, whereas the error avoiding code does not work for small correlations. Finally, we consider the concatenation of such codes for both error models and show that it is particularly advantageous for model II in the regime of partial correlations.
We investigate the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science. First, using the multiparticle spacetime algebra (MSTA, the geometric algebra of a relativistic configuration space), we present an explicit algebraic description of one and two-qubit quantum states together with a MSTA characterization of one and two-qubit quantum computational gates. Second, using the above mentioned characterization and the GA description of the Lie algebras SO(3) and SU(2) based on the rotor group Spin+(3, 0) formalism, we reexamine Boykin's proof of universality of quantum gates. We conclude that the MSTA approach does lead to a useful conceptual unification where the complex qubit space and the complex space of unitary operators acting on them become united, with both being made just by multivectors in real space. Finally, the GA approach to rotations based on the rotor group does bring conceptual and computational advantages compared to standard vectorial and matricial approaches.
We determine a general upper bound for the steady-state entanglement achievable by continuous feedback for systems of any number of bosonic degrees of freedom. We apply such a bound to the specific case of parametric interactions - the most common practical way to generate entanglement in quantum optics - and single out optimal feedback strategies that achieve the maximal entanglement. We also consider the case of feedback schemes entirely restricted to local operations and compare their performance to the optimal, generally nonlocal, schemes.
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.
We study the performance of common quantum stabilizer codes in the presence of asymmetric and correlated errors. Specifically, we consider the depolarizing noisy quantum memory channel and perform quantum error correction via the five and seven-qubit stabilizer codes. We characterize these codes by means of the entanglement fidelity as function of the error probability and the degree of memory. We show that their performances are lowered by the presence of correlations and we compute the error probability threshold values for codes effectiveness. Furthermore, we uncover that the asymmetry in the error probabilities does not affect the performance of the five-qubit code while it does affect the performance of the seven-qubit code which results less effective when considering correlated and symmetric depolarizing errors but more effective for correlated and asymmetric errors.
We study the performance of simple quantum error correcting codes with respect to correlated noise errors characterized by a finite correlation strength. Specifically, we consider bit flip (phase flip) noisy quantum memory channels and use repetition and noiseless quantum codes. We characterize the performance of the codes by means of the entanglement fidelity as function of the error probability and degree of memory. Finally, comparing the entanglement fidelities of repetition and noiseless quantum codes, we find a threshold for the correlation strength that allows to select the code with better performance.
We introduce a new control strategy on a two-way deterministic cryptographic scheme, which relies on a suitable unitary transformation rather than quantum measurement. The study is developed for d-ary alphabets and the particular choice of the transformation works when d is an odd prime power. It leads to an improvement of the protocol security, which we prove to increase with the alphabet order d.
We study manipulation of entanglement between two identical networks of quantum mechanical particles. Firstly, we reduce the problem of entanglement transfer to the problem of quantum state transfer. Then, we consider entanglement concentration and purification based on free dynamics on the networks and local measurements on the vertices. By introducing an appropriate measure of efficiency, we characterize the performance of the protocol. We give evidence that such a measure does not depend on the network topology, and we estimate the contribution given by the number of entangled pairs initially shared by the two networks.
We investigate the quantum information reclaim from the environment after amplitude damping has occurred. In particular we address the question of optimal measurement on the environment to perform the best possible correction on two and three dimensional quantum systems. Depending on the dimension we show that the entanglement fidelity (the measure quantifying the correction performance) is or is not the same for all possible measurements and uncover the optimal measurement leading to the maximum entanglement fidelity.
The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in order to be applied to the case of continuous channels. This is done in the context of quantum memory channels with Markovian noise. As a case study, we apply the notion of weak-forgetfulness to a bosonic memory channel with additive noise. A suitable encoding and decoding unitary transformation allows us to unravel the effects of the memory, hence the channel capacities can be computed using known results from the memoryless setting.