An algorithmic approach to entanglement-assisted quantum error-correcting codes from the Hermitian curve

<p style='text-indent:20px;'>We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is <inline-formula><tex-math id="M1">\begin{document}$ c $\end{document}</tex-math></inline-formula>, the number of required maximally entangled quantum states since the Hermitian dual of an AG code is unknown. In this article, we present an efficient algorithmic approach for computing <inline-formula><tex-math id="M2">\begin{document}$ c $\end{document}</tex-math></inline-formula> for this family of EAQECCs. As a result, this algorithm allows us to provide EAQECCs with excellent parameters over any field size.</p>

Correlations in twisted double-layer graphene with virtual photons in a microcavity

We analyze the entanglement generation of a system composed of two decoupled rotated graphene layers inside a planar microcavity. By considering the electromagnetic field of the cavity in the vacuum state and using time-dependent perturbation theory it is possible to obtain the range of geometric parameters at which the quantum states of electrons in different layers are entangled. By employing the negativity measure, correlations between layers are obtained for time scales smaller than the light-crossing time of the layers. It is shown that the negativity measure is modulated by the rotation angle between layers, allowing manipulation of X states. Finally, an experimental protocol is analyzed in order to detect non-causal effects between layers, by allowing back-voltage switching functions in the two layers with supports that do not overlap in time. By turning off the second-back voltage at a time smaller than the light-crossing time, it is possible to obtain correlations between layers through the independent interaction with virtual photons. The exchange of virtual photons implies that the propagator can be nonzero outside the light cone and this non-causal propagation can create entangled quantum states.

The dynamic of quantum entanglement of two dimensional harmonic oscillator in non-commutative space

In the present paper, we study the influence of non-commutativity on entanglement in a system of two oscillators-modes in interaction with its environment. The considered system is a two-dimensional harmonic oscillator in non-commuting spatial coordinates coupled to its environment. The dynamics of the covariance matrix, the separability criteria for two Gaussian states in non-commutative space coordinates, and the logarithmic negativity are used to evaluate the quantum entanglement in the system, which is compared to the commutative space coordinates case. The result is applied for two initially entangled states, namely the squeezed vacuum and squeezed thermal states. It can be observed that the phenomenon of entanglement sudden death appears more early in the system for the case of squeezed vacuum state than in the case of squeezed thermal state. Thereafter, it is also observed that non-commutativity effects lead to an increasing of entanglement of initially entangled quantum states, and reduce the separability in the open quantum system. It turns out that a separable state in the usual commutative quantum mechanics might be entangled in non-commutative extension.

Topological protection of continuous frequency entangled biphoton states

Topological quantum optics that manipulates the topological protection of quantum states has attracted special interests in recent years. Here we demonstrate valley photonic crystals implementing topologically protected transport of the continuous frequency entangled biphoton states. We numerically simulate the nonlinear four-wave mixing interaction of topological valley kink states propagating along the interface between two valley photonic crystals. We theoretically clarify that the signal and idler photons generated from the four-wave mixing interaction are continuous frequency entangled. The numerical simulation results imply that the entangled biphoton states are robust against the sharp bends and scattering, giving clear evidence of topological protection of entangled photon pairs. Our proposal paves a concrete way to perform topological protection of entangled quantum states operating at telecommunication wavelengths.

Quantum Networks and Symmetries

Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress of the field, but so far only results for small basic network structures or pure quantum states are known. Here we show that symmetries provide a versatile tool for the analysis of correlations in quantum networks. We provide an analytical approach to characterize correlations in large network structures with arbitrary topologies. As examples, we show that entangled quantum states with a bosonic or fermionic symmetry can not be generated in networks; moreover, cluster and graph states are not accessible. Our methods can be used to design certification methods for the functionality of specific links in a network and have implications for the design of future network structures.

Currencies in Resource Theories

How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like perfectly independent copies of states or exact knowledge of a quantum state. Here we introduce the general tool of “currencies” to quantify realistic descriptions of resources, applicable in experimental settings when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when slight correlations cannot be ruled out. Currencies are a subset of resources chosen to quantify all the other resources—like Bell pairs in LOCC or a lifted weight in thermodynamics. We show that from very weak assumptions in the theory we can already find useful currencies that give us necessary and sufficient conditions for resource conversion, and we build up more results as we impose further structure. This work generalizes axiomatic approaches to thermodynamic entropy, work and currencies made of local copies. In particular, by applying our approach to the resource theory of unital maps, we derive operational single-shot entropies for arbitrary, non-probabilistic descriptions of resources.

Strategies for Positive Partial Transpose (PPT) States in Quantum Metrologies with Noise

Quantum metrology overcomes standard precision limits and has the potential to play a key role in quantum sensing. Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurements. Conventional bounds to the measurement precision such as the shot noise limit are not as fundamental as the Heisenberg limits, and can be beaten with quantum strategies that employ `quantum tricks’ such as squeezing and entanglement. Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered to be too weakly entangled for applications. Since no pure entanglement can be distilled from them, they are also called bound entangled states. We provide strategies, using which multipartite quantum states that have a positive partial transpose with respect to all bi-partitions of the particles can still outperform separable states in linear interferometers.

Designing locally maximally entangled quantum states with arbitrary local symmetries

One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with arbitrarily large local unitary symmetry. We explain that such states can be realised in a quantum system of distinguishable traps with bosons or fermions occupying a finite number of modes. Then, local symmetries of the designed quantum state are equal to the unitary group of local mode operations acting diagonally on all traps. Therefore, such a group of symmetries is naturally protected against errors that occur in a physical realisation of mode operators. We also link our results with the existence of so-called strictly semistable states with particular asymptotic diagonal symmetries. Our main technical result states that the Nth tensor power of any irreducible representation of SU(N) contains a copy of the trivial representation. This is established via a direct combinatorial analysis of Littlewood-Richardson rules utilising certain combinatorial objects which we call telescopes.

Introduction, generation and entanglement of entangled displaced even and odd squeezed states

In this paper, first, we introduce special types of entangled quantum states named “entangled displaced even and odd squeezed states” by using displaced even and odd squeezed states which are constructed via the action of displacement operator on the even and odd squeezed states, respectively. Next, we present a theoretical scheme to generate the introduced entangled states. This scheme is based on the interaction between a [Formula: see text]-type three-level atom and a two-mode quantized field in the presence of two strong classical fields. In the continuation, we consider the entanglement feature of the introduced entangled states by evaluating concurrence. Moreover, we study the influence of the displacement parameter on the entanglement degree of the introduced entangled states and compare the results. It will be observed that the concurrence of the “entangled displaced odd squeezed states” has less decrement with respect to the “entangled displaced even squeezed states” by increasing the displacement parameter.