We discuss a parameter estimation problem using quantum decoherece in the double-slit interferometer. We consider a particle coupled to a massive scalar field after the particle passing through the double slit and solve the dynamics non-perturbatively for the coupling by the WKB approximation. This allows us to analyze the estimation problem which cannot be treated by master equation used in the research of quantum probe. In this model, the scalar field reduces the interference fringes of the particle and the fringe pattern depends on the field mass and coupling. To evaluate the contrast and the estimation precision obtained from the pattern, we introduce the interferometric visibility and the Fisher information matrix of the field mass and coupling. For the fringe pattern observed on the distant screen, we derive a simple relation between the visibility and the Fisher matrix. Also, focusing on the estimation precision of the mass, we find that the Fisher information characterizes the wave-particle duality in the double-slit interferometer.

Local operations assisted by classical communication (LOCC) constitute the free operations in entanglement theory. Hence, the determination of LOCC transformations is crucial for the understanding of entanglement. We characterize here almost all LOCC transformations among pure multipartite multilevel states. Combined with the analogous results for qubit states shown by Gour \emph{et al.} [J. Math. Phys. 58, 092204 (2017)], this gives a characterization of almost all local transformations among multipartite pure states. We show that nontrivial LOCC transformations among generic, fully entangled, pure states are almost never possible. Thus, almost all multipartite states are isolated. They can neither be deterministically obtained from local-unitary-inequivalent (LU-inequivalent) states via local operations, nor can they be deterministically transformed to pure, fully entangled LU-inequivalent states. In order to derive this result, we prove a more general statement, namely, that, generically, a state possesses no nontrivial local symmetry. We discuss further consequences of this result for the characterization of optimal, probabilistic single copy and probabilistic multi-copy LOCC transformations and the characterization of LU-equivalence classes of multipartite pure states.

Present quantum computers often work with distinguishable qubits as their computational units. In order to simulate indistinguishable fermionic particles, it is first required to map the fermionic state to the state of the qubits. The Bravyi-Kitaev Superfast (BKSF) algorithm can be used to accomplish this mapping. The BKSF mapping has connections to quantum error correction and opens the door to new ways of understanding fermionic simulation in a topological context. Here, we present the first detailed exposition of BKSF algorithm for molecular simulation. We provide the BKSF transformed qubit operators and report on our implementation of the BKSF fermion-to-qubits transform in OpenFermion. In this initial study of the hydrogen molecule, we have compared BKSF, Jordan-Wigner and Bravyi-Kitaev transforms under the Trotter approximation. We considered different orderings of the exponentiated terms and found lower Trotter errors than previously reported for Jordan-Wigner and Bravyi-Kitaev algorithms. These results open the door to further study of the BKSF algorithm for quantum simulation.

It was recently shown [S. Lorenzo et al., Sci. Rep. 7, 42729 (2017)] that the presence of static disorder in a bosonic bath - whose normal modes thus become all Anderson-localised - leads to non-Markovianity in the emission of an atom weakly coupled to it (a process which in absence of disorder is fully Markovian). Here, we extend the above analysis beyond the weak-coupling regime for a finite-band bath so as to account for band edge effects. We study the interplay of these with static disorder in the emergence of non-Markovian behaviour in terms of a suitable non-Markovianity measure.

We consider the interaction between distinct superradiance (SR) systems and use the dressed state formalism to solve the case of two interacting two-atom SR samples at resonance. We show that the ensuing entanglement modifies the transition rates and intensities of radiation, as well as introduces a potentially measurable frequency chirp in the SR cascade, the magnitude of which being a function of the separation between the samples. For the dominant SR cascade we find a significant reduction in the duration and an increase of the intensity of the SR pulse relative to the case of a single two-atom SR sample.

Rayleigh's criterion states that it becomes essentially difficult to resolve two incoherent optical point sources separated by a distance below the width of point spread functions (PSF), namely in the subdiffraction limit. Recently, researchers have achieved superresolution for two incoherent point sources with equal strengths using a new type of measurement technique, surpassing Rayleigh's criterion. However, situations where more than two point sources needed to be resolved have not been fully investigated. Here we prove that for any incoherent sources with arbitrary strengths, a one- or two-dimensional image can be precisely resolved up to its second moment in the subdiffraction limit, i.e. the Fisher information (FI) is non-zero. But the FI with respect to higher order moments always tends to zero polynomially as the size of the image decreases, for any type of non-adaptive measurement. We call this phenomenon a modern description of Rayleigh's criterion. For PSFs under certain constraints, the optimal measurement basis estimating all moments in the subdiffraction limit for 1D weak-source imaging is constructed. Such basis also generates the optimal-scaling FI with respect to the size of the image for 2D or strong-source imaging, which achieves an overall quadratic improvement compared to direct imaging.

Quantum states of light with multiple spatial modes are fundamental for quantum imaging and parallel quantum information processing. Thus, their characterization, which can be achieved through measurements of the coherence area, is an important area of research. We present a comparative study between two different measurement techniques for the coherence area of bright entangled twin beams of light generated with a four-wave mixing process in a hot rubidium vapor cell. The first one provides a direct characterization of the size of the coherence area and is based on correlation measurements between spatial intensity fluctuations of the twin beams with an electron-multiplying charge-coupled-device camera. The second one provides an indirect measure and is based on a noise analysis of different spatial regions of the twin beams in the temporal domain with a single photodiode. We show that the indirect technique, which can be implemented with a significantly less complicated measurement scheme, gives an estimate of the size of the coherence area consistent with the direct measurement technique performed in the spatial domain.

We present a derivation of the third postulate of Relational Quantum Mechanics (RQM) from the properties of conditional probabilities.The first two RQM postulates are based on the information that can be extracted from interaction of different systems, and the third postulate defines the properties of the probability function. Here we demonstrate that from a rigorous definition of the conditional probability for the possible outcomes of different measurements, the third postulate is unnecessary and the Born's rule naturally emerges from the first two postulates by applying the Gleason's theorem. We demonstrate in addition that the probability function is uniquely defined for classical and quantum phenomena. The presence or not of interference terms is demonstrated to be related to the precise formulation of the conditional probability where distributive property on its arguments cannot be taken for granted. In the particular case of Young's slits experiment, the two possible argument formulations correspond to the possibility or not to determine the particle passage through a particular path.

Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some phase-transition threshold. Such a counterintuitive discovery has aroused extensive theoretical interest in extending canonical quantum theory by including non-Hermitian but PT-symmetric operators in the last two decades. Despite much fundamental theoretical success in the development of PT-symmetric quantum mechanics, an experimental observation of pseudo-Hermiticity remains elusive as these systems with a complex potential seem absent in Nature. But nevertheless, the notion of PT symmetry has highly survived in many other branches of physics including optics, photonics, AMO physics, acoustics, electronic circuits, material science over the past ten years, and others, where a judicious balance of gain and loss constitutes a PT-symmetric system. Here, although we concentrate upon reviewing recent progress on PT symmetry in optical microcavity systems, we also wish to present some new results that may help to accelerate the research in the area. Such compound photonic structures with gain and loss provide a powerful platform for testing various theoretical proposals on PT symmetry, and initiate new possibilities for shaping optical beams and pulses beyond conservative structures. Throughout this article there is an effort to clearly present the physical aspects of PT-symmetry in optical microcavity systems, but mathematical formulations are reduced to the indispensable ones. Readers who prefer strict mathematical treatments should resort to the extensive list of references. Despite the rapid progress on the subject, new ideas and applications of PT symmetry using optical microcavities are still expected in the future.

We obtain multiple exact results on the entanglement of the exact excited states of non-integrable models we introduced in arXiv:1708.05021. We first discuss a general formalism to analytically compute the entanglement spectra of exact excited states using Matrix Product States and Matrix Product Operators and illustrate the method by reproducing a general result on single-mode excitations. We then apply this technique to analytically obtain the entanglement spectra of the infinite tower of states of the spin-$S$ AKLT models in the zero and finite energy density limits. We show that in the zero density limit, the entanglement spectra of the tower of states are multiple shifted copies of the ground state entanglement spectrum in the thermodynamic limit. We show that such a resemblance is destroyed at any non-zero energy density. Furthermore, the entanglement entropy $\mathcal{S}$ of the states of the tower that are in the bulk of the spectrum is sub-thermal $\mathcal{S} \propto \log L$, as opposed to a volume-law $\mathcal{S} \propto L$, thus indicating a violation of the strong Eigenstate Thermalization Hypothesis (ETH). These states are examples of what are now called many-body scars. Finally, we analytically study the finite-size effects and symmetry-protected degeneracies in the entanglement spectra of the excited states, extending the existing theory.

We present exact numerical calculations of supercurrent density, inductance, and impurity-induced flux noise of cylindrical superconducting wires in the non-local Pippard regime, which occurs when the Pippard coherence length is larger than the London penetration depth. In this regime the supercurrent density displays a peak away from the surface of the superconductor, signalling a breakdown of the usual approximation of local London electrodynamics with a renormalized penetration depth. Our calculations show that the internal inductance and the bulk flux noise power increases with increasing non-locality. In contrast, the kinetic inductance is reduced and the surface flux noise remains the same. As a result, impurity spins in the bulk may dominate the flux noise in superconducting qubits in the Pippard regime, such as the ones using aluminum superconductors with large electron mean free path.

In this paper, we propose a scheme to implement the two-qubit controlled-Z gate via the Stark-tuned F\"orster interaction of Rydberg atoms, where the F\"orster defect is driven by a time-dependent electric field of a simple sinusoidal function while dipole-dipole interactions are time-independent. It is shown that when the system is initially in a specific state, it makes a cyclic evolution after a preset interaction time, returning to the initial state, but picks up a phase, which can be used for realizing a two-atom controlled-Z gate. Due to the interference of sequential Landau-Zener transitions, the population and phase of the state is quasi-deterministic after the cyclic evolution and therefore the gate fidelity is insensitive to fluctuations of the interaction time and the dipole-dipole interaction strength. Feasibility of the scheme realized with Cs atoms is discussed in detail, which shows that the two-qubit gate via Landau-Zener control can be realized with the state-of-the-art experimental setup.

In physics, causality has two faces. Traditionally, causality meant that states evolve according to a deterministic law. Recently, due to the influence of quantum information theory and statistical modeling, causality has also come to be understood as the power to influence the probability of an event by manipulating its causes. This raises some new questions: are causal relations properties of systems in themselves, or are they relative properties of a system and an observer (where an `observer' may here be construed as another physical system)? Does causality play any role in restricting the amount by which quantum systems can violate classical inequalities? In this work, I argue that causal relations are observer-dependent. Leveraging a result of the Quantum Bayesian (QBist) program, I argue that the Born rule can be interpreted as a causal principle, which serves to define bounds on quantum correlations. An interesting side-effect of this approach is that the resulting causal model turns out to be symmetric under reversal of the direction of causality, suggesting that the orientation of cause and effect is a genuinely observer-dependent feature of causality that has no meaning in a system independently of its observation.

The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited state energies and their degeneracies. We propose an implementation that requires the same number of qubits as VQE and at most twice the circuit depth. Our method is robust to control errors, is compatible with error-mitigation strategies and can be implemented on near-term quantum computers.

We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical harmonics. The Wigner representation of a propagator can be experimentally recovered by measuring expectation values of rotated axial spherical tensor operators in an augmented system with an additional ancilla qubit. The methodology is experimentally demonstrated for standard one-qubit quantum gates using nuclear magnetic resonance spectroscopy. In particular, this approach provides a direct and compelling visualization of the spinor property of the propagators corresponding to the rotation of a spin 1/2 particle.

We propose a way to encode acceleration directly into quantum fields, establishing a new class of fields. Accelerated quantum fields, as we have named them, have some very interesting properties. The most important is that they provide a mathematically consistent way to quantize space-time in the same way that energy and momentum are quantized in standard quantum field theories.

Author(s): G. Buonaiuto, D. M. Whittaker, and E. Cancellieri

We present a theoretical investigation of the properties of quantum correlation functions in a multimode system. We define a total mth order equal-time correlation function, summed over all modes, which is shown to be conserved if the Hamiltonian possesses U(1) symmetry. It is also conserved in the ...

[Phys. Rev. Lett. 121, 020404] Published Thu Jul 12, 2018

Author(s): Renato Pakter and Yan Levin

It has been observed empirically that two-dimensional vortices tend to cluster, forming a giant vortex. To account for this observation, Onsager introduced the concept of negative absolute temperature in equilibrium statistical mechanics. In this Letter, we show that in the thermodynamic limit a sys...

[Phys. Rev. Lett. 121, 020602] Published Thu Jul 12, 2018

Author(s): Xun-Wei Xu, Hai-Quan Shi, Ai-Xi Chen, and Yu-xi Liu

We study photon, phonon statistics, and the cross-correlation between photons and phonons in a quadratically coupled optomechanical system. Photon blockade, phonon blockade, and strong anticorrelation between photons and phonons can be observed in the same parameter regime with the effective nonline...

[Phys. Rev. A 98, 013821] Published Thu Jul 12, 2018

Author(s): Zeki Hayran, Ramon Herrero, Muriel Botey, Hamza Kurt, and Kestutis Staliunas

We propose a feasible invisibility approach to suppress the scattering of waves from or to given directions and for particular frequencies, i.e., invisibility on demand. We derive a generalized Hilbert transform for a specific invisibility arrangement relating the two quadratures of the complex perm...

[Phys. Rev. A 98, 013822] Published Thu Jul 12, 2018