We establish a connection between orthogonal arrays and pure states of finite-dimensional quantum systems having nonnegative integer entries. This identification allows us to develop a technique to represent the full set of orthogonal arrays with a given number of columns, symbols and strength in terms of a finite set of generators. The corresponding states turn out to play an important role in quantum theory: they exhibit a high degree of multipartite entanglement and include the full set of maximum distance separable codes. We provide a simple construction of the generators and show explicit solutions for orthogonal arrays with two symbols composed of two, three and four columns and two symbols, which correspond to pure quantum states of two, three and four qubits, respectively.

In this Letter, we mainly investigate the dynamic behavior of quantum steering and how to effectively recover the lost steerability of quantum states within non-Markovian environments. We consider two different cases (one-subsystem or all-subsystem interacts with the dissipative environments), and obtain that the dynamical interaction between system initialized by a Werner state and the non-Markovian environments can induce the quasi-periodic quantum entanglement (concurrence) resurgence, however, quantum steering cannot retrieve in such a condition. And we can obtain that the resurgent quantum entanglement cannot be utilized to achieve quantum steering. Subsequently, we put forward a feasible physical scheme for recovering the steerability of quantum states within the non-Markovian noises by prior weak measurement on each subsystem before the interaction with dissipative environments followed by post weak measurement reversal. It is shown that the steerability of quantum states and the fidelity can be effectively restored. Furthermore, the results show that the larger the weak measurement strength is, the better the effectiveness of the scheme is. Consequently, our investigations might be beneficial to recover the lost steerability of quantum states within the non-Markovian regimes.

For the recently introduced $\mu$-deformed analog of Bose gas model ($\mu$-Bose gas model), its thermodynamical aspects e.g. total number of particles and the partition function are certain functions of the parameter $\mu$. This basic $\mu$-dependence of thermodynamics of the $\mu$-Bose gas arises through the so-called $\mu$-calculus, an alternative to the known $q$-calculus (Jackson derivative, etc.), so we include main elements of $\mu$-calculus. Likewise, virial expansion of EOS and virial coefficients, the internal energy, specific heat and the entropy of $\mu$-Bose gas show $\mu$-dependence. Herein, we study thermodynamical geometry of $\mu$-Bose gas model and find the singular behavior of (scalar) curvature, signaling for Bose-like condensation. The critical temperature of condensation $T^{(\mu)}_c$ depending on $\mu$ is given and compared with the usual $T_c$, and with known $T_c^{(p,q)}$ of $p,q$-Bose gas model. Using the results on $\mu$-thermodynamics we argue that the condensate of $\mu$-Bose gas, like the earlier proposed infinite statistics system of particles, can serve for effective modeling of dark matter.

We know that in empty space there is no preferred state of rest. This is true both in special relativity but also in Newtonian mechanics with its associated Galilean relativity. It comes as something of a surprise, therefore, to discover the existence a friction force associated with spontaneous emission. he resolution of this paradox relies on a central idea from special relativity even though our derivation of it is non-relativistic. We examine the possibility that the physics underlying this effect might be explored in an ion trap, via the observation of a superposition of different mass states.

The aim of this essay is to analyze the role of quantum mechanics as an inherent characteristic of life. During the last ten years the problem of the origin of life has become an innovative research subject approached by many authors. The essay is divided in to three parts: the first deals with the problem of life from a philosophical and biological perspective. The second presents the conceptual and methodological basis of the essay which is founded on the Information Theory and the Quantum Theory. This basis is then used, in the third part, to discuss the different arguments and conjectures of a quantum origin of life. There are many philosophical views on the problem of life, two of which are especially important at the moment: reductive physicalism and biosystemic emergentism. From a scientific perspective, all the theories and experimental evidences put forward by Biology can be summed up in to two main research themes: the RNA world and the vesicular theory. The RNA world, from a physicalist point of view, maintains that replication is the essence of life while the vesicular theory, founded on biosystemic grounds, believes the essence of life can be found in cellular metabolism. This essay uses the Information Theory to discard the idea of a spontaneous emergency of life through replication. Understanding the nature and basis of quantum mechanics is fundamental in order to be able to comprehend the advantages of using quantum computation to be able increase the probabilities of existence of auto replicative structures. Different arguments are set forth such as the inherence of quantum mechanics to the origin of life. Finally, in order to try to resolve the question of auto replication, three scientific propositions are put forward: Q-life, the quantum combinatory library and the role of algorithms in the origin of genetic language.

We calculate numerically the heat transfer rate between a spatially dispersive sphere and a half-space. By utilising Huygens' principle and the extinction theorem, we derive the necessary reflection coefficients at the sphere and the plate without the need to resort to additional boundary conditions. We find for small distances $d\sim 1$nm a significant modification of the spectral heat transfer rate due to spatial dispersion. As a consequence, the spurious divergencies that occur in spatially local approach are absent.

We theoretically investigate the non-equilibrium dynamics in a quenched pair of 1D Bose gases with density imbalance. We describe the system using its low-energy effective theory, the Luttinger liquid model. In this framework the system shows strictly integrable relaxation dynamics via dephasing of its approximate many-body eigenstates. In the balanced case, this leads to the well-known light-cone-like establishment of a prethermalized state, which can be described by a generalized Gibbs ensemble. In the imbalanced case the integrable dephasing leads to a state that, counter-intuitively, closely resembles a thermal equilibrium state. The approach to this state is characterized by two separate light-cone dynamics with distinct characteristic velocities. This behavior is rooted in the fact that in the imbalanced case observables are not aligned with the conserved quantities of the integrable system. We discuss a concrete experimental realization to study this effect using matterwave interferometry and many-body revivals on an atom chip.

We develop a Landauer-B\"uttiker theory of entropy evolution in time-dependent strongly coupled electron systems. This formalism naturally avoids the problem of system-bath distinction caused by the strong hybridization of central system and surrounding reservoirs. In an adiabatic expansion up to first order beyond the quasistatic limit, it provides a clear understanding of the connection between heat and entropy currents generated by time-dependent potentials and shows their connection to the occurring dissipation. Combined with the work required to change the potential, the developed formalism provides a full thermodynamic description from an outside perspective, applicable to arbitrary non-interacting electron systems.

Producing advanced quantum states of light is a priority in quantum information technologies. While remarkable progress has been made on single photons and photon pairs, multipartite correlated photon states are usually produced in purely optical systems by post-selection or cascading, with extremely low efficiency and exponentially poor scaling. Multipartite states enable improved tests of the foundations of quantum mechanics as well as implementations of complex quantum optical networks and protocols. It would be favorable to directly generate these states using solid state systems, for better scaling, simpler handling, and the promise of reversible transfer of quantum information between stationary and flying qubits. Here we use the ground states of two optically active coupled quantum dots to directly produce photon triplets. The wavefunctions of photogenerated excitons localized in these ground states are correlated via molecular hybridization and Coulomb interactions. The formation of a triexciton leads to a triple cascade recombination and sequential emission of three photons with strong correlations. The quantum dot molecule is embedded in an epitaxially grown nanowire engineered for single-mode waveguiding and improved extraction efficiency at the emission wavelength. We record 65.62 photon triplets per minute, surpassing rates of all earlier reported sources, in spite of the moderate efficiency of our detectors. Our structure and data represent a breakthrough towards implementing multipartite photon entanglement and multi-qubit readout schemes in solid state devices, suitable for integrated quantum information processing.

In this paper we intend to discuss the importance of providing a physical representation of quantum superpositions which goes beyond the mere reference to mathematical structures and measurement outcomes. This proposal goes in the opposite direction to the project present in orthodox contemporary philosophy of physics which attempts to "bridge the gap" between the quantum formalism and common sense "classical reality" --precluding, right from the start, the possibility of interpreting quantum superpositions through non-classical notions. We will argue that in order to restate the problem of interpretation of quantum mechanics in truly ontological terms we require a radical revision of the problems and definitions addressed within the orthodox literature. On the one hand, we will discuss the need of providing a formal redefinition of superpositions which captures explicitly their contextual character. On the other hand, we will attempt to replace the focus on the measurement problem, which concentrates on the justification of measurement outcomes from "weird" superposed states, and introduce the superposition problem which focuses instead on the conceptual representation of superpositions themselves. In this respect, after presenting three necessary conditions for objective physical representation, we will provide arguments which show why the classical (actualist) representation of physics faces severe difficulties to solve the superposition problem. Finally, we will also argue that, if we are willing to abandon the (metaphysical) presupposition according to which 'Actuality = Reality', then there is plenty of room to construct a conceptual representation for quantum superpositions.

A first quantized free photon is a complex massless vector field $A=(A^\mu)$ whose field strength satisfies Maxwell's equations in vacuum. We construct the Hilbert space $\mathscr{H}$ of the photon by endowing the vector space of the fields $A$ in the temporal-Coulomb gauge with a positive-definite and relativistically invariant inner product. We give an explicit expression for this inner product, identify the Hamiltonian for the photon with the generator of time translations in $\mathscr{H}$, determine the operators representing the momentum and the helicity of the photon, and introduce a chirality operator whose eigenfunctions correspond to fields having a definite sign of energy. We also construct a position operator for the photon whose components commute with each other and with the chirality and helicity operators. This allows for the construction of the localized states of the photon with a definite sign of energy and helicity. We derive an explicit formula for the latter and compute the corresponding electric and magnetic fields. These turn out to diverge not just at the point where the photon is localized but on a plane containing this point. We identify the axis normal to this plane with an associated symmetry axis, and show that each choice of this axis specifies a particular position operator, a corresponding position basis, and a position representation of the quantum mechanics of photon. In particular, we examine the position wave functions determined by such a position basis, elucidate their relationship with the Riemann-Silberstein and Landau-Peierls wave functions, and give an explicit formula for the probability density of the spatial localization of the photon.

Spontaneous collapse models predict that a weak force noise acts on any mechanical system, as a consequence of the collapse of the wave function. Significant upper limits on the collapse rate have been recently inferred from precision mechanical experiments, such as ultracold cantilevers and the space mission LISA Pathfinder. Here, we report new results from an experiment based on a high-Q cantilever cooled to millikelvin temperatures, which is potentially able to improve the current bounds on the continuous spontaneous localization (CSL) model by 1 order of magnitude. High accuracy measurements of the cantilever thermal fluctuations reveal a nonthermal force noise of unknown origin. This excess noise is compatible with the CSL heating predicted by Adler. Several physical mechanisms able to explain the observed noise have been ruled out.ler. Several physical mechanisms able to explain the observed noise have been ruled out.

Non-Markovian stochastic Schr\"odinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only in some specific cases or perturbatively. This article is focused on the NMSSE themselves rather than on the open-system evolution they unravel and aims at making them less abstract. Namely, we propose to write the stochastic realizations of linear NMSSE as averages over the solutions of an auxiliary equation with an additional random field. Our method yields a non-perturbative numerical simulation algorithm for generic linear NMSSE that can be made arbitrarily accurate for reasonably short times. For isotropic complex noises, the method extends from linear to non-linear NMSSE and allows to sample the solutions of norm-preserving NMSSE directly.

Physical implementations of quantum annealing unavoidably operate at finite temperatures. We point to a fundamental limitation of fixed finite temperature quantum annealers that prevents them from functioning as competitive scalable optimizers and show that to serve as optimizers annealer temperatures must be appropriately scaled down with problem size. We derive a temperature scaling law dictating that temperature must drop at the very least in a logarithmic manner but also possibly as a power law with problem size. We corroborate our results by experiment and simulations and discuss the implications of these to practical annealers.

The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment correlations by examining the system dynamics alone. Our approach is based on the possibility or impossibility to simulate open system dynamics with Hamiltonian ensembles. As we show, such (im)possibility to simulate is closely linked to the system-environment correlations. We thus define the nonclassicality of open system dynamics in terms of the nonexistence of a Hamiltonian-ensemble simulation. This classifies any nonunital open system dynamics as nonclassical. We give examples for open system dynamics that are unital and classical, as well as unital and nonclassical.

Near-term quantum computers will soon reach sizes that are challenging to directly simulate, even when employing the most powerful supercomputers. Yet, the ability to simulate these early devices using classical computers is crucial for calibration, validation, and benchmarking. In order to make use of the full potential of systems featuring multi- and many-core processors, we use automatic code generation and optimization of compute kernels, which also enables performance portability. We apply a scheduling algorithm to quantum supremacy circuits in order to reduce the required communication and simulate a 45-qubit circuit on the Cori II supercomputer using 8,192 nodes and 0.5 petabytes of memory. To our knowledge, this constitutes the largest quantum circuit simulation to this date. Our highly-tuned kernels in combination with the reduced communication requirements allow an improvement in time-to-solution over state-of-the-art simulations by more than an order of magnitude at every scale.

We derive a monogamy inequality for any local quantum resource and entanglement. It results from the fact that there is always a convex measure for a quantum resource, as shown here, and from the relation between entanglement and local entropy. One of its consequences is an entanglement monogamy different from that usually discussed. If the local resource is nonuniformity or coherence, it is satisfied by familiar resource and entanglement measures. The ensuing upper bound for the local coherence, determined by the entanglement, is independent of the basis used to define the coherence.

It is commonly claimed that only Hamiltonians with a spectrum unbounded both above and below can give purely exponential decay. Because such Hamiltonians have no ground state, they are considered unphysical. Here we show that Hamiltonians which are bounded below can give purely exponential decay. This is possible when, instead of looking at the global survival probability, one considers a subsystem only. We conclude that purely exponential decay might not be as unphysical as previously thought.

Most quantum-error correcting codes assume that the decoherence of each physical qubit is independent of the decoherence of any other physical qubit. We can test the validity of this assumption in an experimental setup where a microwave feedline couples to multiple qubits by examining correlations between the qubits. Here, we investigate the correlations between fluxonium qubits located in a single waveguide. Despite being in a wide-bandwidth electromagnetic environment, the qubits have measured relaxation times in excess of 100 us. We use cascaded Josephson parametric amplifiers to measure the quantum jumps of two fluxonium qubits simultaneously. No correlations are observed between the relaxation times of the two fluxonium qubits, which indicates that the sources of relaxation are local to each qubit. Our architecture can easily be scaled to monitor larger numbers of qubits.

We use the Holevo information to estimate distinguishability of microstates of a black hole in anti-de Sitter space by measurements one can perform on a subregion of a Cauchy surface of the dual conformal field theory. We find that microstates are not distinguishable at all until the subregion reaches a certain size and that perfect distinguishability can be achieved before the subregion covers the entire Cauchy surface. We will compare our results with expectations from the entanglement wedge reconstruction, tensor network models, and the bit threads interpretation of the Ryu-Takayanagi formula.