Quantum Physics

Quantum catalysis is an intricate feature of quantum entanglement. It demonstrates that in certain situations the very presence of entanglement can improve one's abilities of manipulating other entangled states. At the same time, however, it is not clear if using entanglement catalytically can provide additional power for any of the existing quantum protocols. Here we show, for the first time, that catalysis of entanglement can provide a genuine advantage in the task of quantum teleportation. More specifically, we show that extending the standard teleportation protocol by giving Alice and Bob the ability to use entanglement catalytically, allows them to achieve fidelity of teleportation at least as large as the regularisation of the standard teleportation quantifier, the so-called average fidelity of teleportation. Consequently, we show that this regularised quantifier surpasses the standard benchmark for a variety of quantum states, therefore demonstrating that there are quantum states whose ability to teleport can be further improved when assisted with entanglement in a catalytic way. This hints that entanglement catalysis can be a promising new avenue for exploring novel advantages in the quantum domain.

In quantum computation, the computation is achieved by linear operators in Hilbert spaces. In this work, we explain an idea of a new computation scheme, in which the linear operators are replaced by (higher) functors between two (higher) categories. The fundamental problem in realizing this idea is the physical realization of (higher) functors. We provide a theoretical idea of realizing (higher) functors based on the physics of topological orders.

A fundamental objective in quantum information science is to determine the cost in classical resources of simulating a particular quantum system. The classical simulation cost is quantified by the signaling dimension which specifies the minimum amount of classical communication needed to perfectly simulate a channel's input-output correlations when unlimited shared randomness is held between encoder and decoder. This paper provides a collection of device-independent tests that place lower and upper bounds on the signaling dimension of a channel. Among them, a single family of tests is shown to determine when a noisy classical channel can be simulated using an amount of communication strictly less than either its input or its output alphabet size. In addition, a family of eight Bell inequalities is presented that completely characterize when any four-outcome measurement channel, such as a Bell measurement, can be simulated using one communication bit and shared randomness. Finally, we bound the signaling dimension for all partial replacer channels in d dimensions. The bounds are found to be tight for the special case of the erasure channel.

Non-Gaussian receivers for optical communication with coherent states can achieve measurement sensitivities beyond the limits of conventional detection, given by the quantum-noise limit (QNL). However, the amount of information that can be reliably transmitted substantially degrades if there is noise in the communication channel, unless the receiver is able to efficiently compensate for such noise. Here, we investigate the use of a deep neural network as a computationally efficient estimator of phase and amplitude channel noise to enable a reliable method for noise tracking for non-Gaussian receivers. The neural network uses the data collected by the non-Gaussian receiver to estimate and correct for dynamic channel noise in real-time. Using numerical simulations, we find that this noise tracking method allows the non-Gaussian receiver to maintain its benefit over the QNL across a broad range of strengths and bandwidths of phase and intensity noise. The noise tracking method based on neural networks can further include other types of noise to ensure sub-QNL performance in channels with many sources of noise.

We map the infinite-range coupled quantum kicked rotors over an infinite-range coupled interacting bosonic model. In this way we can apply exact diagonalization up to quite large system sizes and confirm that the system tends to ergodicity in the large-size limit. In the thermodynamic limit the system is described by a set of coupled Gross-Pitaevskij equations equivalent to an effective nonlinear single-rotor Hamiltonian. These equations give rise to a power-law increase in time of the energy with exponent γ??/3 in a wide range of parameters. We explain this finding by means of a master-equation approach based on the noisy behaviour of the effective nonlinear single-rotor Hamiltonian and on the Anderson localization of the single-rotor Floquet states. Furthermore, we study chaos by means of the largest Lyapunov exponent and find that it decreases towards zero for portions of the phase space with increasing momentum. Finally, we show that some stroboscopic Floquet integrals of motion of the noninteracting dynamics deviate from their initial values over a time scale related to the interaction strength according to the Nekhoroshev theorem.

We theoretically study the dynamical phase diagram of the Dicke model in both classical and quantum limits using large, experimentally relevant system sizes. Our analysis elucidates that the model features dynamical critical points that are distinct from previously investigated excited-state equilibrium transitions. Moreover, our numerical calculations demonstrate that mean-field features of the dynamics remain valid in the exact quantum dynamics, but we also find that in regimes where quantum effects dominate signatures of the dynamical phases and chaos can persist in purely quantum metrics such as entanglement and correlations. Our predictions can be verified in current quantum simulators of the Dicke model including arrays of trapped ions.

We show that the functional analogue of QMA ??coQMA, denoted F(QMA ??coQMA), equals the complexity class Total Functional QMA (TFQMA). To prove this we need to introduce alternative definitions of QMA ??coQMA in terms of a single quantum verification procedure. We show that if TFQMA equals the functional analogue of BQP (FBQP), then QMA ??coQMA = BQP. We show that if there is a QMA complete problem that (robustly) reduces to a problem in TFQMA, then QMA ??coQMA = QMA. These results provide strong evidence that the inclusions FBQP ??TFQMA ??FQMA are strict, since otherwise the corresponding inclusions in BQP ??QMA ??coQMA ??QMA would become equalities.

Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes covariant with respect to continuous symmetries cannot correct erasure errors perfectly (an important case being the Eastin-Knill theorem), in contrast to the case without symmetry constraints. Furthermore, there are fundamental limits on the accuracy of such covariant codes for approximate quantum error correction. Here, we consider the quantum error correction capability of random covariant codes. In particular, we show that U(1) -covariant codes generated by Haar random U(1) -symmetric unitaries, i.e. unitaries that commute with the charge operator (or conserve the charge), typically saturate the fundamental limits to leading order in terms of both the average- and worst-case purified distances against erasure noise. We note that the results hold for symmetric variants of unitary 2-designs, and comment on the convergence problem of charge-conserving random circuits. Our results not only indicate (potentially efficient) randomized constructions of optimal U(1) -covariant codes, but also reveal fundamental properties of random charge-conserving unitaries, which may underlie important models of complex quantum systems in wide-ranging physical scenarios where conservation laws are present, such as black holes and many-body spin systems.

We propose a scheme for the circulator function in a superconducting circuit consisting of a three-Josephson junction loop and a trijunction. In this study we obtain the exact Lagrangian of the system by deriving the effective potential from the fundamental boundary conditions. We subsequently show that we can selectively choose the direction of current flowing through the branches connected at the trijunction, which performs a circulator function. Further, we use this circulator function for a non-Abelian braiding of Majorana zero modes (MZMs). In the branches of the system we introduce pairs of MZMs which interact with each other through the phases of trijunction. The circulator function determines the phases of the trijunction and thus the coupling between the MZMs to gives rise to the braiding operation. We modify the system so that MZMs might be coupled to the external ones to perform qubit operations in a scalable design.

The Schrödinger dynamics of photon excitation numbers together with entanglement in two non-resonant time-dependent coupled oscillators is investigated. By considering ???periodically pumped parameters and using suitable transformations, we obtain the coupled Meissner oscillators. Consequently, our analytical study shows two interesting results, which can be summarized as follows. (i): Classical instability of classical analog of quantum oscillators and photon excitation {averages ??N j ??} are strongly correlated. (ii): Photon excitation's and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts. Also it allow to control entanglement by engineering only classical systems where the experiments are less expensive.