The entanglement entropy S is calculated on the system boundary of the square-lattice ±J Ising model by the time-evolving block decimation (TEBD) method. The random average ⟨S&rangle is evaluated on the Nishimori line, through the successive multiplications of transfer matrices, whose width N is up to 300. It is confirmed that ⟨S⟩ shows critical singularity around the Nishimori point.

The ability to convert spin accumulation to charge currents is essential for applications in spintronics. In semiconductors, spin-to-charge conversion is typically achieved using the inverse spin Hall effect or using a large magnetic field. Here we demonstrate a general method that exploits the nonlinear interactions between spin and charge currents to perform all-electrical, rapid, and noninvasive detection of spin accumulation without the need for a magnetic field. We demonstrate the operation of this technique with ballistic GaAs holes as a model system with strong spin-orbit coupling, in which a quantum point contact provides the nonlinear energy filter. This approach is generally applicable to electron and hole systems with strong spin-orbit coupling.

We show that thefidelity offered by the standard teleportation protocol under noisy channels appliedsuccessively can be significantly improved, when used in conjunction with a quantum switch. Inparticular, wefind that for two such teleportation channels conjugated with an indefinite causal order,teleportationfidelity beyond the classical threshold is achieved for significantly larger noise thanwould be possible conventionally. One can even make the effective teleportation channel perfectlyfaithful for very large noise. We also discuss the generalization of our scheme for more than twopathways, and define afigure of merit in that context.

Slováci testujú neprelomiteľný spôsob šifrovania, idú spojiť Bratislavu a Viedeň. Pri súčasnej vedomosti o tom, ako vyzerá fyzika a svet, nie je kvantovú šifru možné zlomiť, hovorí o prevratnej technológii profesor Vladimír Bužek, jeden z najcitovanejších slovenských fyzikov ... || pdf ||

Probabilistic storage and retrieval (PSR) of unitary quantum dynamics is possible with exponentially small failure probability with respect to the number of systems used as a quantum memory [M. Sedlák, A. Bisio, and M. Ziman, Phys. Rev. Lett. 122, 170502 (2019)]. Here we study improvements due to a priori knowledge about the unitary transformation to be stored. In particular, we study N→1 PSR of qubit phase gates, i.e., qubit rotations around the Z axis with an unknown angle, and show that if we access the gate only N times the optimal probability of perfect retrieving of its single use is N/(N+1). We propose a quantum circuit realization for the optimal protocol and show that a programmable phase gate [G. Vidal, L. Masanes, and J. I. Cirac, Phys. Rev. Lett. 88, 047905 (2002)] can be turned into a (2k−1)→1 optimal PSR of phase gates and requires only k controlled-not gates, while having exponentially small failure probability in k.

Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems. However, in many interesting situations, QMC methods are faced with a sign problem, causing the severe limitation of an exponential increase in the runtime of the QMC algorithm. In this work, we develop a systematic, generally applicable, and practically feasible methodology for easing the sign problem by efficiently computable basis changes and use it to rigorously assess the sign problem. Our framework introduces measures of non-stoquasticity that—as we demonstrate analytically and numerically—at the same time provide a practically relevant and efficiently computable figure of merit for the severity of the sign problem. Complementing this pragmatic mindset, we prove that easing the sign problem in terms of those measures is generally an NP-complete task for nearest-neighbor Hamiltonians and simple basis choices by a reduction to the MAXCUT-problem.

Entanglement entropy is a powerful tool to detect continuous, discontinuous and even topological phase transitions in quantum as well as classical systems. In this work, von Neumann and Renyi entanglement entropies are studied numerically for classical lattice models in a square geometry. A cut is made from the center of the square to the midpoint of one of its edges, say the right edge. The entanglement entropies measure the entanglement between the left and right halves of the system. As in the strip geometry, von Neumann and Renyi entanglement entropies diverge logarithmically at the transition point while they display a jump for first-order phase transitions. The analysis is extended to a classical model of non-overlapping finite hard rods deposited on a square lattice for which Monte Carlo simulations have shown that, when the hard rods span over 7 or more lattice sites, a nematic phase appears in the phase diagram between two disordered phases. A new Corner Transfer Matrix Renormalization Group algorithm (CTMRG) is introduced to study this model. No logarithmic divergence of entanglement entropies is observed at the phase transitions in the CTMRG calculation discussed here. We therefore infer that the transitions neither can belong to the Ising universality class, as previously assumed in the literature, nor be discontinuous.

We consider the symmetric two-state 16-vertex model on the square lattice whose vertex weights are invariant under any permutation of adjacent edge states. The vertex-weight parameters are restricted to a critical manifold which is self-dual under the gauge transformation. The critical properties of the model are studied numerically with the Corner Transfer Matrix Renormalization Group method. Accuracy of the method is tested on two exactly solvable cases: the Ising model and a specific version of the Baxter eight-vertex model in a zero field that belong to different universality classes. Numerical results show that the two exactly solvable cases are connected by a line of critical points with the polarization as the order parameter. There are numerical indications that critical exponents vary continuously along this line in such a way that the weak universality hypothesis is violated.

We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer matrix renormalization group (CTMRG). Scaling analyses for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension m at the fixed point of the CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed-point spectrum of the corner-transfer matrix in the critical intermediate phase of the six-state clock model is characterized by the scaling dimension consistent with the c=1 boundary conformal field theory associated with the effective Z_6 dual sine-Gordon model.

In classical thermodynamic processes the unavoidable presence of irreversibility, quantified by the entropy production, carries two energetic footprints: the reduction of extractable work from the optimal, reversible case, and the generation of a surplus of heat that is irreversibly dissipated to the environment. Recently it has been shown that in the quantum regime an additional quantum irreversibility occurs that is linked to decoherence into the energy basis. Here we employ quantum trajectories to construct distributions for classical heat and quantum heat exchanges, and show that the heat footprint of quantum irreversibility differs markedly from the classical case. We also quantify how quantum irreversibility reduces the amount of work that can be extracted from a state with coherences. Our results show that decoherence leads to both entropic and energetic footprints which both play an important role in the optimization of controlled quantum operations at low temperature.

Magnetic properties of the transverse-field Ising model on curved (hyperbolic) lattices are studied by a tensor product variational formulation that we have generalized for this purpose. First we identify the quantum phase transition for each hyperbolic lattice by calculating the magnetization. We study the entanglement entropy at the phase transition in order to analyze the correlations of various subsystems located at the center with the rest of the lattice. We confirm that the entanglement entropy satisfies the area law at the phase transition for fixed coordination number, i.e., it scales linearly with increasing size of the subsystems. On the other hand, the entanglement entropy decreases as power-law with respect to the increasing coordination number.

The Berezinskii-Kosterlitz-Thouless transitions of the six-state clock model on the square lattice are investigated by means of the corner-transfer matrix renormalization group method. A classical analog of the entanglement entropy S(L,T) is calculated for L×L square system up to L=129, as a function of temperature T. The entropy exhibits a peak at T=T*(L), where the temperature depends on both L and the boundary conditions. Applying the finite-size scaling to T*(L) and assuming presence of the Berezinskii-Kosterlitz-Thouless transitions, the two distinct phase-transition temperatures are estimated to be T1=0.70 and T2=0.88. The results are in agreement with earlier studies. It should be noted that no thermodynamic functions have been used in this study.

It is shown that Popescu-Rohrlich nonlocal boxes (beating the Tsirelson bound for Bell inequality) do exist in the existing structures of both quantum and classical theory. In particular, we design an explicit example of measure-and-prepare nonlocal (but no-signaling) channel being the realization of nonlocal and no-signaling Popescu-Rohrlich box within the generalized probabilistic theory of processes. Further we present a post-selection-based spatially non-local implementation and show it does not require truly quantum resources, hence, improving the previously known results. Interpretation and potential (spatially non-local) simulation of this form of process nonlocality and the protocol is discussed.

Based on the work of Vershik (J Sov Math 59(5):1029–1040, 1992), we introduce two new combinatorial identities. We show how these identities can be used to prove a new hook-content identity. The main motivation for deriving this identity was a particular optimization problem in the field of quantum information processing.

We study the ground entangled state of the one-dimensional spin-1/2 Ising ferromagnet at its transverse-field critical point. When this problem is expressed in terms of independent fermions, we show that the usual thermostatistical sums emerging within Fermi-Dirac statistics can, for an L-sized subsystem, be indistinctively taken up to L terms or up to lnL terms, providing a neat understanding of the origin of the logarithmic scaling of the entanglement entropy in the system. This is interpreted as a compact occupancy of the phase-space of the L-subsystem, hence standard Boltzmann-Gibbs thermodynamics quantities with an effective system size V ≈ ln(L) are appropriate and are explicitly calculated. The calculations are then to be done in a Hilbert space whose effective dimension is 2ln(L) instead of 2L. In this we can assume ergodicity. Our analysis suggests a scenario where the physical systems are essentially grouped into three classes, in terms of their phase-space occupancy, ergodicity and Lebesgue measure.

The coherence of electron spin qubits in semiconductor quantum dots suffers mostly from low-frequency noise. During the past decade, efforts have been devoted to mitigate such noise by material engineering, leading to substantial enhancement of the spin dephasing time for an idling qubit. However, the role of the environmental noise during spin manipulation, which determines the control fidelity, is less understood. We demonstrate an electron spin qubit whose coherence in the driven evolution is limited by high-frequency charge noise rather than the quasistatic noise inherent to any semiconductor device. We employ a feedback-control technique to actively suppress the latter, demonstrating a π-flip gate fidelity as high as 99.04±0.23% in a gallium arsenide quantum dot. We show that the driven-evolution coherence is limited by the longitudinal noise at the Rabi frequency, whose spectrum resembles the 1/f noise observed in isotopically purified silicon qubits.

The combination of an exact and Corner Transfer Matrix Renormalization Group (CTMRG) methods is used to study an influence of external electric and magnetic fields on existence of intriguing reentrant magnetic transitions in a coupled spin-electron model on a decorated square lattice. The two-dimensional (2D) decorated square lattice with localized nodal spins and delocalized electrons is taken into account. It was found that the competition among all involved interactions (the electron hopping, spin-spin and spin-electron interaction, external electric and magnetic fields) in combination with thermal fluctuations can produce new type of reentrant magnetic transitions. Depending on the model parameters the non-zero fields can stabilize or destabilize magnetic reentrance. In addition, an alternative and more effective way, for modulating the magnetic reentrance is found. An origin of intriguing low-temperature round maximum in the specific heat was explained as a consequence of rapid changes in the sublattice magnetizations, which is induced through a competition of all presented interactions.