Overcoming noise in quantum teleportation with multipartite hybrid entanglement.

Quantum entanglement and decoherence are the two counterforces of many quantum technologies and protocols. For example, while quantum teleportation is fueled by a pair of maximally entangled resource qubits, it is vulnerable to decoherence. Here, we propose an efficient quantum teleportation protocol in the presence of pure decoherence and without entangled resource qubits entering the Bell-state measurement. Instead, we use multipartite hybrid entanglement between the auxiliary qubits and their local environments within the open-quantum system context. With a hybrid-entangled initial state, it is the decoherence that allows us to achieve high fidelities. We demonstrate our protocol in an all-optical experiment.

Complex networks approach to study comorbidities in patients with unruptured intracranial aneurysms.

The role of complex network analysis in patients with diagnosis of unruptured intracranial aneurysm is unexplored. The objective of this study is to assess the applicability of this methodology in aneurysm patients. We retrospectively analyze comprehensive unbiased local digital data of a large number of patients treated for any reason between January 2004 and July 2019. We apply an age-cohort approach to a total of 628,831 patients and construct the diagnostic history of each patient-and include the information how old the patient was when diagnosed for the first time with each diagnosis coded according to International Classification of Diseases. For each cohort of age within a 10 year interval and for each gender, we construct a statistically validated comorbidity network and focused on crucial comorbidity links that the aneurysm code has to other disease codes within the whole network. For all cohorts of different age and gender, the analysis shows that 267 diagnose codes have nearest neighbour statistically validated links to unruptured aneurysm ICD code. Among the 267 comorbidities, 204 (76%) were found in patients aged from 40 to 69-years old. Patterns of connectivity with aneurysms were found for smoking, hypertension, chronic obstructive pulmonary disease, dyslipidemia, and mood disorders. A few uncommon connections are also detected in cohorts of female patients. Our study explored the applicability of network analysis and statistical validation in aneurysm observational study.

High-frequency trading and networked markets.

Financial markets have undergone a deep reorganization during the last 20 y. A mixture of technological innovation and regulatory constraints has promoted the diffusion of market fragmentation and high-frequency trading. The new stock market has changed the traditional ecology of market participants and market professionals, and financial markets have evolved into complex sociotechnical institutions characterized by a great heterogeneity in the time scales of market members' interactions that cover more than eight orders of magnitude. We analyze three different datasets for two highly studied market venues recorded in 2004 to 2006, 2010 to 2011, and 2018. Using methods of complex network theory, we show that transactions between specific couples of market members are systematically and persistently overexpressed or underexpressed. Contemporary stock markets are therefore networked markets where liquidity provision of market members has statistically detectable preferences or avoidances with respect to some market members over time with a degree of persistence that can cover several months. We show a sizable increase in both the number and persistence of networked relationships between market members in most recent years and how technological and regulatory innovations affect the networked nature of the markets. Our study also shows that the portfolio of strategic trading decisions of high-frequency traders has evolved over the years, adding to the liquidity provision other market activities that consume market liquidity.

Diffusive Limit of Non-Markovian Quantum Jumps.

We solve two long-standing problems for stochastic descriptions of open quantum system dynamics. First, we find the classical stochastic processes corresponding to non-Markovian quantum state diffusion and non-Markovian quantum jumps in projective Hilbert space. Second, we show that the diffusive limit of non-Markovian quantum jumps can be taken on the projective Hilbert space in such a way that it coincides with non-Markovian quantum state diffusion. However, the very same limit taken on the Hilbert space leads to a completely new diffusive unraveling, which we call non-Markovian quantum diffusion. Further, we expand the applicability of non-Markovian quantum jumps and non-Markovian quantum diffusion by using a kernel smoothing technique allowing a significant simplification in their use. Lastly, we demonstrate the applicability of our results by studying a driven dissipative two level atom in a non-Markovian regime using all of the three methods.

Rate Operator Unraveling for Open Quantum System Dynamics.

Stochastic methods with quantum jumps are often used to solve open quantum system dynamics. Moreover, they provide insight into fundamental topics, such as the role of measurements in quantum mechanics and the description of non-Markovian memory effects. However, there is no unified framework to use quantum jumps to describe open-system dynamics in any regime. We solve this issue by developing the rate operator quantum jump (ROQJ) approach. The method not only applies to both Markovian and non-Markovian evolutions, but also allows us to unravel master equations for which previous methods do not work. In addition, ROQJ yields a rigorous measurement-scheme interpretation for a wide class of dynamics, including a set of master equations with negative decay rates, and sheds light on different types of memory effects which arise when using stochastic quantum jump methods.

Experimental implementation of fully controlled dephasing dynamics and synthetic spectral densities.

Engineering, controlling, and simulating quantum dynamics is a strenuous task. However, these techniques are crucial to develop quantum technologies, preserve quantum properties, and engineer decoherence. Earlier results have demonstrated reservoir engineering, construction of a quantum simulator for Markovian open systems, and controlled transition from Markovian to non-Markovian regime. Dephasing is an ubiquitous mechanism to degrade the performance of quantum computers. However, all-purpose quantum simulator for generic dephasing is still missing. Here, we demonstrate full experimental control of dephasing allowing us to implement arbitrary decoherence dynamics of a qubit. As examples, we use a photon to simulate the dynamics of a qubit coupled to an Ising chain in a transverse field and also demonstrate a simulation of nonpositive dynamical map. Our platform opens the possibility to simulate dephasing of any physical system and study fundamental questions on open quantum systems.

Local probe for connectivity and coupling strength in quantum complex networks.

We develop a local probe to estimate the connectivity of complex quantum networks. Our results show how global properties of different classes of complex networks can be estimated - in quantitative manner with high accuracy - by coupling a probe to a single node of the network. Here, our interest is focused on probing the connectivity, i.e. the degree sequence, and the value of the coupling constant within the complex network. The scheme combines results on classical graph theory with the ability to develop quantum probes for networks of quantum harmonic oscillators. Whilst our results are proof-of-principle type, within the emerging field of quantum complex networks they may have potential applications for example to the efficient transfer of quantum information or energy or possibly to shed light on the connection between network structure and dynamics.

Symmetry in the open-system dynamics of quantum correlations.

We study the symmetry properties in the dynamics of quantum correlations for two-qubit systems in one-sided noisy channels, with respect to a switch in the location of noise from one qubit to the other. We consider four different channel types, namely depolarizing, amplitude damping, bit-flip, and bit-phase-flip channel, and identify the classes of initial states leading to symmetric decay of entanglement, non-locality and discord. Our results show that the symmetric decay of quantum correlations is not directly linked to the presence or absence of symmetry in the initial state, while it does depend on the type of correlation considered as well as on the type of noise. We prove that asymmetric decay can be used to infer, in certain cases, characteristic properties of the channel. We also show that the location of noise may lead to dramatic changes in the persistence of phenomena such as entanglement sudden death and time-invariant discord.

Eternal non-Markovianity: from random unitary to Markov chain realisations.

The theoretical description of quantum dynamics in an intriguing way does not necessarily imply the underlying dynamics is indeed intriguing. Here we show how a known very interesting master equation with an always negative decay rate [eternal non-Markovianity (ENM)] arises from simple stochastic Schrödinger dynamics (random unitary dynamics). Equivalently, it may be seen as arising from a mixture of Markov (semi-group) open system dynamics. Both these approaches lead to a more general family of CPT maps, characterized by a point within a parameter triangle. Our results show how ENM quantum dynamics can be realised easily in the laboratory. Moreover, we find a quantum time-continuously measured (quantum trajectory) realisation of the dynamics of the ENM master equation based on unitary transformations and projective measurements in an extended Hilbert space, guided by a classical Markov process. Furthermore, a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) representation of the dynamics in an extended Hilbert space can be found, with a remarkable property: there is no dynamics in the ancilla state. Finally, analogous constructions for two qubits extend these results from non-CP-divisible to non-P-divisible dynamics.

Quantum Zeno-type effect and non-Markovianity in a three-level system.

We study the coexistence of the quantum Zeno-type effect and non-Markovianity for a system decaying in a structured bosonic environment and subject to a control field. The interaction with the environment induces decay from the excited to the ground level, which, in turn, is coherently coupled to another meta-stable state. The control of the strength of the coherent coupling between the stable levels allows the engineering of both the dissipation and of the memory effects, without modifying neither the system-reservoir interaction, nor environmental properties. We use this framework in two different parameter regimes corresponding to fast (bad cavity limit) and slow dissipation (good cavity limit) in the original and un-controlled qubit system. Our results show a non-monotonic behavior of memory effects when increasing the effectiveness of the Zeno-like freezing. Moreover, we identify a new source of memory effects which allows the persistence of non-Markovianity for long times while the excited state has already been depleted.

Thermodynamic power of non-Markovianity.

The natural framework to discuss thermodynamics at the quantum level is the theory of open quantum systems. Memory effects arising from strong system-environment correlations may lead to information back-flow, that is non-Markovian behaviour. The relation between non-Markovianity and quantum thermodynamics has been until now largely unexplored. Here we show by means of Landauer's principle that memory effects control the amount of work extraction by erasure in presence of realistic environments.

Complex quantum networks as structured environments: engineering and probing.

We consider structured environments modeled by bosonic quantum networks and investigate the probing of their spectral density, structure, and topology. We demonstrate how to engineer a desired spectral density by changing the network structure. Our results show that the spectral density can be very accurately detected via a locally immersed quantum probe for virtually any network configuration. Moreover, we show how the entire network structure can be reconstructed by using a single quantum probe. We illustrate our findings presenting examples of spectral densities and topology probing for networks of genuine complexity.

Nonlocal memory effects allow perfect teleportation with mixed states.

One of the most striking consequences of quantum physics is quantum teleportation - the possibility to transfer quantum states over arbitrary distances. Since its theoretical introduction, teleportation has been demonstrated experimentally up to the distance of 143 km. In the original proposal two parties share a maximally entangled quantum state acting as a resource for the teleportation task. If, however, the state is influenced by decoherence, perfect teleportation can no longer be accomplished. Therefore, one of the current major challenges in accomplishing teleportation over long distances is to overcome the limitations imposed by decoherence and the subsequent mixedness of the resource state. Here we show that, in the presence of nonlocal memory effects, perfect quantum teleportation can be achieved even with mixed photon polarisation states. Our results imply that memory effects can be exploited in harnessing noisy quantum systems for quantum communication and that non-Markovianity is a resource for quantum information tasks.

Quantitative analysis of gender stereotypes and information aggregation in a national election.

By analyzing a database of a questionnaire answered by a large majority of candidates and elected in a parliamentary election, we quantitatively verify that (i) female candidates on average present political profiles which are more compassionate and more concerned with social welfare issues than male candidates and (ii) the voting procedure acts as a process of information aggregation. Our results show that information aggregation proceeds with at least two distinct paths. In the first case candidates characterize themselves with a political profile aiming to describe the profile of the majority of voters. This is typically the case of candidates of political parties which are competing for the center of the various political dimensions. In the second case, candidates choose a political profile manifesting a clear difference from opposite political profiles endorsed by candidates of a political party positioned at the opposite extreme of some political dimension.

Nonlocal memory effects in the dynamics of open quantum systems.

We explore the possibility to generate nonlocal dynamical maps of an open quantum system through local system-environment interactions. Employing a generic decoherence process induced by a local interaction Hamiltonian, we show that initial correlations in a composite environment can lead to nonlocal open system dynamics which exhibit strong memory effects, although the local dynamics is Markovian. In a model of two entangled photons interacting with two dephasing environments, we find a direct connection between the degree of memory effects and the amount of correlation in the initial environmental state. The results demonstrate that, contrary to conventional wisdom, enlarging an open system can change the dynamics from Markovian to non-Markovian.

Statistically validated networks in bipartite complex systems.

Many complex systems present an intrinsic bipartite structure where elements of one set link to elements of the second set. In these complex systems, such as the system of actors and movies, elements of one set are qualitatively different than elements of the other set. The properties of these complex systems are typically investigated by constructing and analyzing a projected network on one of the two sets (for example the actor network or the movie network). Complex systems are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set, and this heterogeneity makes it very difficult to discriminate links of the projected network that are just reflecting system's heterogeneity from links relevant to unveil the properties of the system. Here we introduce an unsupervised method to statistically validate each link of a projected network against a null hypothesis that takes into account system heterogeneity. We apply the method to a biological, an economic and a social complex system. The method we propose is able to detect network structures which are very informative about the organization and specialization of the investigated systems, and identifies those relationships between elements of the projected network that cannot be explained simply by system heterogeneity. We also show that our method applies to bipartite systems in which different relationships might have different qualitative nature, generating statistically validated networks in which such difference is preserved.

Measure for the degree of non-markovian behavior of quantum processes in open systems.

We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the dynamical map describing the time evolution of physical states, and can be interpreted in terms of the information flow between the open system and its environment. The measure takes on nonzero values whenever there is a flow of information from the environment back to the open system, which is the key feature of non-Markovian dynamics.

Non-Markovian quantum jumps.

Open quantum systems that interact with structured reservoirs exhibit non-Markovian dynamics. We present a quantum jump method for treating the dynamics of such systems. This approach is a generalization of the standard Monte Carlo wave function (MCWF) method for Markovian dynamics. The MCWF method identifies decay rates with jump probabilities and fails for non-Markovian systems where the time-dependent rates become temporarily negative. Our non-Markovian quantum jump approach circumvents this problem and provides an efficient unraveling of the ensemble dynamics.

Zeno and anti-Zeno effects for quantum Brownian motion.

In this Letter, we investigate the occurrence of the Zeno and anti-Zeno effects for quantum Brownian motion. We single out the parameters of both the system and the reservoir governing the crossover between Zeno and anti-Zeno dynamics. We demonstrate that, for high reservoir temperatures, the short time behavior of environment induced decoherence is ultimately responsible for the occurrence of either the Zeno or the anti-Zeno effect. Finally, we suggest a way to manipulate the decay rate of the system and to observe a controlled continuous passage from decay suppression to decay acceleration using engineered reservoirs in the trapped ion context.

Feshbach-resonant interactions in 40K and 6Li degenerate Fermi gases.

We theoretically examine a system of Fermi degenerate atoms coupled to bosonic molecules by a Feshbach resonance, focusing on the superfluid transition to a molecular Bose-Einstein condensate dressed by Cooper pairs of atoms. This problem raises interest because it is unclear at present whether bimodal density distributions observed recently in 40K and 6Li are due to a condensate of bosonic molecules or fermionic atom pairs. As opposed to 40K, we find that any measurable fraction of above-threshold bosonic molecules is necessarily absent for the 6Li system in question, which strongly implicates Cooper pairs as the culprit behind its bimodal distributions.