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1. Entanglement generation in a quantum network at distance-independent rate

   https://doi.org/10.1038/s41534-022-00536-0  

   Patil, Ashlesha; Pant, Mihir; Englund, Dirk; Towsley, Don; Guha, Saikat (May 2022, npj Quantum Information)

   Abstract We develop a protocol for entanglement generation in the quantum internet that allows a repeater node to usen-qubit Greenberger-Horne-Zeilinger (GHZ) projective measurements that can fusensuccessfully entangledlinks, i.e., two-qubit entangled Bell pairs shared acrossnnetwork edges, incident at that node. Implementingn-fusion, forn ≥ 3, is in principle not much harder than 2-fusions (Bell-basis measurements) in solid-state qubit memories. If we allow even 3-fusions at the nodes, we find—by developing a connection to a modified version of the site-bond percolation problem—that despite lossy (hence probabilistic) link-level entanglement generation, and probabilistic success of the fusion measurements at nodes, one can generate entanglement between end parties Alice and Bob at a rate that stays constant as the distance between them increases. We prove that this powerful network property is not possible to attain with any quantum networking protocol built with Bell measurements and multiplexing alone. We also design a two-party quantum key distribution protocol that converts the entangled states shared between two nodes into a shared secret, at a key generation rate that is independent of the distance between the two parties. 

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2. Bulk and boundary entanglement transitions in the projective gauge-Higgs model

   https://doi.org/10.1103/PhysRevB.110.245102  

   Sukeno, Hiroki; Ikeda, Kazuki; Wei, Tzu-Chieh (December 2024, Physical Review B)

   In quantum many-body spin systems, the interplay between the entangling effect of multiqubit Pauli measurements and the disentangling effect of single-qubit Pauli measurements may give rise to two competing effects. By introducing a randomized measurement pattern with such bases, a phase transition can be induced by altering the ratio between them. In this work, we numerically investigate a measurement-based model associated with the Fradkin-Shenker Hamiltonian that encompasses the deconfining, confining, and Higgs phases. We determine the phase diagram in our measurement-only model by employing entanglement measures. For the bulk topological order, we use the topological entanglement entropy. We also use the mutual information between separated boundary regions to diagnose the boundary phase transition associated with the Higgs or the bulk symmetry-protected topological (SPT) phase. We observe the structural similarity between our phase diagram and the one in the standard quantum Hamiltonian formulation of the Fradkin-Shenker model with the open rough boundary. First, a deconfining phase is detected by nonzero and constant topological entanglement entropy. Second, we find a (boundary) phase transition curve separating the Higgs=SPT phase from the rest. In certain limits, the topological phase transitions reside at the critical point of the formation of giant homological cycles in the bulk three-dimensional (3D) space-time lattice, as well as the bond percolation threshold of the boundary 2D space-time lattice when it is effectively decoupled from the bulk. Additionally, there are analogous mixed-phase properties at a certain region of the phase diagram, emerging from how we terminate the measurement-based procedure. Our findings pave an alternative pathway to study the physics of Higgs=SPT phases on quantum devices in the near future. 

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3. Optimizing fictitious states for Bell inequality violation in bipartite qubit systems with applications to the $t\overline{t}$ system

   https://doi.org/10.1103/PhysRevD.109.116005  

   Cheng, Kun; Han, Tao; Low, Matthew (June 2024, Physical Review D)

   There is a significant interest in testing quantum entanglement and Bell inequality violation in high-energy experiments. Since the analyses in high-energy experiments are performed with events statistically averaged over phase space, the states used to determine observables depend on the choice of coordinates through an event-dependent basis and are thus not genuine quantum states, but rather “fictitious states.” We find that the basis which diagonalizes the spin-spin correlations is optimal for constructing fictitious states to test the violation of Bell’s inequality. This result is applied directly to the bipartite qubit system of a top and antitop produced at a hadron collider. We show that the beam axis is the optimal basis choice near the $t\overline{t}$threshold production for measuring Bell inequality violation, while at high transverse momentum the basis that aligns along the momentum direction of the top is optimal. Published by the American Physical Society2024 

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4. Stabilizer Entanglement Distillation and Efficient Fault-Tolerant Encoders

   https://doi.org/10.1103/PRXQuantum.6.010339  

   Shi, Yu; Patil, Ashlesha; Guha, Saikat (March 2025, PRX Quantum)

   Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement distillation protocol to higher-rate n-to-(n−1) protocols that can correct any single-qubit errors. These protocols are evaluated through numerical simulations focusing on fidelity and yield. We also outline a method to adapt any classical error-correcting code for entanglement distillation, where the code can correct both bit-flip and phase-flip errors by incorporating Hadamard gates. (2) We propose a constant-depth decoder for stabilizer codes that transforms logical states into physical ones using single-qubit measurements. This decoder is applied to entanglement distillation protocols, reducing circuit depth and enabling protocols derived from high-performance quantum error-correcting codes. We demonstrate this by evaluating the circuit complexity for entanglement distillation protocols based on surface codes and quantum convolutional codes. (3) Our stabilizer entanglement distillation techniques advance quantum computing. We propose a fault-tolerant protocol for constant-depth encoding and decoding of arbitrary states in surface codes, with potential extensions to more general quantum low-density parity-check codes. This protocol is feasible with state-of-the-art reconfigurable atom arrays and surpasses the limits of conventional logarithmic depth encoders. Overall, our study integrates stabilizer formalism, measurement-based quantum computing, and entanglement distillation, advancing both quantum communication and computing. 

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5. Symmetric states and dynamics of three quantum bits

   https://doi.org/10.26421/QIC22.7-8-1  

   Albertini, Francesca; D'Alessandro, Domenico (May 2022, Quantum Information and Computation)

   The unitary group acting on the Hilbert space $${\cal H}:=(C^2)^{\otimes 3}$$ of three quantum bits admits a Lie subgroup, $$U^{S_3}(8)$$, of elements which permute with the symmetric group of permutations of three objects. Under the action of such a Lie subgroup, the Hilbert space $${\cal H}$$ splits into three invariant subspaces of dimensions $$4$$, $$2$$ and $$2$$ respectively, each corresponding to an irreducible representation of $su(2)$. The subspace of dimension $$4$$ is uniquely determined and corresponds to states that are themselves invariant under the action of the symmetric group. This is the so called {\it symmetric sector.} The subspaces of dimension two are not uniquely determined and we parametrize them all. We provide an analysis of pure states that are in the subspaces invariant under $$U^{S_3}(8)$. This concerns their entanglement properties, separability criteria and dynamics under the Lie subgroup $$U^{S_3}(8)$$. As a physical motivation for the states and dynamics we study, we propose a physical set-up which consists of a symmetric network of three spin $$\frac{1}{2}$$ particles under a common driving electro-magnetic field. {For such system, we solve the control theoretic problem of driving a separable state to a state with maximal distributed entanglement. 

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