Robustness of two-qubit and three-qubit states in correlated quantum channels

We investigate how the correlated actions of quantum channels affect the robustness of entangled states. We consider the Bell-like state and random two-qubit pure states in the correlated depolarizing, bit flip, bit-phase flip, and phase flip channels. It is found that the robustness of two-qubit pure states can be noticeably enhanced due to the correlations between consecutive actions of these noisy channels, and the Bell-like state is always the most robust state. We also consider the robustness of three-qubit pure states in correlated noisy channels. For the correlated bit flip and phase flip channels, the result shows that although the most robust and most fragile states are locally unitary equivalent, they exhibit different robustness in different correlated channels, and the effect of channel correlations on them is also significantly different. However, for the correlated depolarizing and bit-phase flip channels, the robustness of two special three-qubit pure states is exactly the same. Moreover, compared with the random three-qubit pure states, they are neither the most robust states nor the most fragile states.

Parisi’s Theory of Spin Glass

The spin-glass phase is characterized by the existence of many pure states due to random exchange interactions between spins. Parisi established the novel concept of replica symmetry breaking (RSB) from Sherrington Kirkpatrick’s mean-field theory via an abstract replica trick. In this article, his RSB scheme is reviewed from the view point of infinitely many pure states.

The entanglement entropy of typical pure states and replica wormholes

In a 1+1 dimensional QFT on a circle, we consider the von Neumann entanglement entropy of an interval for typical pure states. As a function of the interval size, we expect a Page curve in the entropy. We employ a specific ensemble average of pure states, and show how to write the ensemble-averaged Rényi entropy as a path integral on a singular replicated geometry. Assuming that the QFT is a conformal field theory with a gravitational dual, we then use the holographic dictionary to obtain the Page curve. For short intervals the thermal saddle is dominant. For large intervals (larger than half of the circle size), the dominant saddle connects the replicas in a non-trivial way using the singular boundary geometry. The result extends the ‘island conjecture’ to a non-evaporating setting.

Clustering and enhanced classification using a hybrid quantum autoencoder

Quantum machine learning (QML) is a rapidly growing area of research at the intersection of classical machine learning and quantum information theory. One area of considerable interest is the use of QML to learn information contained within quantum states themselves. In this work, we propose a novel approach in which the extraction of information from quantum states is undertaken in a classical representational-space, obtained through the training of a hybrid quantum autoencoder (HQA). Hence, given a set of pure states, this variational QML algorithm learns to identify – and classically represent – their essential distinguishing characteristics, subsequently giving rise to a new paradigm for clustering and semi-supervised classification. The analysis and employment of the HQA model are presented in the context of amplitude encoded states – which in principle can be extended to arbitrary states for the analysis of structure in non-trivial quantum data sets.

Construction of genuinely entangled subspacesand the associated bounds on entanglement measures for mixed states

Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information processing. A recent direction of research is the construction of genuinely entangled subspaces — the class of subspaces consisting entirely of genuinely entangled pure states. In this paper we present methods of construction of such subspaces including those of maximal possible dimension. The approach is based on the composition of bipartite entangled subspaces and quantum channels of certain types. The examples include maximal subspaces for systems of three qubits, four qubits, three qutrits. We also provide lower bounds on two entanglement measures for mixed states, the concurrence and the convex-roof extended negativity, which are directly connected with the projection on genuinely entangled subspaces.

Quantum combinatorial designs and k-uniform states

Goyeneche et al.\ [Phys.\ Rev.\ A \textbf{97}, 062326 (2018)] introduced several classes of quantum combinatorial designs, namely quantum Latin squares, quantum Latin cubes, and the notion of orthogonality on them. They also showed that mutually orthogonal quantum Latin arrangements can be entangled in the same way in which quantum states are entangled. Moreover, they established a relationship between quantum combinatorial designs and a remarkable class of entangled states called $k$-uniform states, i.e., multipartite pure states such that every reduction to $k$ parties is maximally mixed. In this article, we put forward the notions of incomplete quantum Latin squares and orthogonality on them and present construction methods for mutually orthogonal quantum Latin squares and mutually orthogonal quantum Latin cubes. Furthermore, we introduce the notions of generalized mutually orthogonal quantum Latin squares and generalized mutually orthogonal quantum Latin cubes, which are equivalent to quantum orthogonal arrays of size $d^2$ and $d^3$, respectively, and thus naturally provide $2$- and $3$-uniform states.

Local transformations of multiple multipartite states

Understanding multipartite entanglement is vital, as it underpins a wide range of phenomena across physics. The study of transformations of states via Local Operations assisted by Classical Communication (LOCC) allows one to quantitatively analyse entanglement, as it induces a partial order in the Hilbert space. However, it has been shown that, for systems with fixed local dimensions, this order is generically trivial, which prevents relating multipartite states to each other with respect to any entanglement measure. In order to obtain a non-trivial partial ordering, we study a physically motivated extension of LOCC: multi-state LOCC. Here, one considers simultaneous LOCC transformations acting on a finite number of entangled pure states. We study both multipartite and bipartite multi-state transformations. In the multipartite case, we demonstrate that one can change the stochastic LOCC (SLOCC) class of the individual initial states by only applying Local Unitaries (LUs). We show that, by transferring entanglement from one state to the other, one can perform state conversions not possible in the single copy case; provide examples of multipartite entanglement catalysis; and demonstrate improved probabilistic protocols. In the bipartite case, we identify numerous non-trivial LU transformations and show that the source entanglement is not additive. These results demonstrate that multi-state LOCC has a much richer landscape than single-state LOCC.