In this work, we investigate quantum phase transition (QPT) in a generic family of spin chains using the geometric measure of entanglement (GE). In many of prior works, GE per site was used. Here, we also consider GE per block with each block size being two. This can be regarded as a coarse grain of GE per site. We introduce a useful parameterization for the family of spin chains that includes the XY models with $n$-site interaction, the GHZ-cluster model and a cluster-antiferromagnetic model, the last of which exhibits QPT between a symmetry-protected topological phase and an antiferromagnetic phase. As the models are exactly solvable, their ground-state wavefunctions can be obtained and thus their GE can be studied. It turns out that the overlap of the ground states with translationally invariant product states can be exactly calculated and hence the GE can be obtained via further parameter optimization. The QPTs exhibited in these models are studied and detected by the energy gap and singular behavior of geometric entanglement. In particular, the XzY model exhibits transitions from the nontrivial SPT phase to a trivial paramagnetic phase. Moreover, the halfway XY model exhibits a first-order transition across the Barouch-McCoy circle, on which it was only a crossover in the standard XY model. However, the halfway Ising model has no such transition.

We show, at one-loop approximation, that the QED photon acquires a negative gauge-invariant mass-squared in the near-horizon region of an evaporating Schwarzschild black hole. This result may imply that information about the inner structure of black holes is accessible, even without invoking the modification of the basic QFT and GR principles.

We investigate the single qubit transformations under several typical coherence-free operations, such as, incoherent operation (IO), strictly incoherent operation (SIO), physically incoherent operation (PIO), and coherence preserving operation (CPO). Quantitative connection has been built between IO and SIO in single qubit systems. Moreover, these coherence-free operations have a clear hierarchical relationship in single qubit systems: CPO $\subset$ PIO $\subset$ SIO=IO. A new and explicit proof for the necessary and sufficient condition of single qubit transformation via IO or SIO has been provided, which indicates that SIO with only two Kraus operators are enough to realize this transformation. The transformation regions of single qubits via CPO and PIO are also given. Our method provides a geometric illustration to analyze single qubit coherence transformations by introducing the Bloch sphere depiction of the transformation regions, and tells us how to construct the corresponding coherence-free operations.

We show via tensor network methods that the Harper-Hofstadter Hamiltonian for hard-core bosons on a square geometry supports a topological phase realizing the $\nu=1/2$ fractional quantum Hall effect on the lattice. We address the robustness of the ground state degeneracy and of the energy gap, measure the many-body Chern number, and characterize the system using Green functions, showing that they decay algebraically at the edges of open geometries, indicating the presence of gapless edge modes. Moreover, we estimate the topological entanglement entropy by taking a combination of lattice bipartitions that reproduces the topological structure of the original proposals by Kitaev and Preskill, and Levin and Wen. The numerical results show that the topological contribution is compatible with the expected value $\gamma = 1/2$. Our results provide extensive evidence that FQH states are within reach of state-of-the-art cold atom experiments.

We show that the energy-transport efficiency in a chain of two-level emitters can be drastically enhanced by the presence of a photonic topological insulator (PTI). This is obtained by exploiting the peculiar properties of its nonreciprocal surface plasmon polariton (SPP), which is unidirectional, and immune to backscattering, and propagates in the bulk band gap. This amplification of transport efficiency can be as much as 2 orders of magnitude with respect to reciprocal SPPs. Moreover, we demonstrate that despite the presence of considerable imperfections at the interface of the PTI, the efficiency of the SPP-assisted energy transport is almost unaffected by discontinuities. We also show that the SPP properties allow energy transport over considerably much larger distances than in the reciprocal case, and we point out a particularly simple way to tune the transport. Finally, we analyze the specific case of a two-emitter chain and unveil the origin of the efficiency amplification. The efficiency amplification and the practical advantages highlighted in this work might be particularly useful in the development of new devices intended to manage energy at the atomic scale.

The paper is concerned with the number of open gaps in spectra of periodic quantum graphs. The well-known conjecture by Bethe and Sommerfeld (1933) says that the number of open spectral gaps for a system periodic in more than one direction is finite. To the date its validity is established for numerous systems, however, it is known that quantum graphs do not comply with this law as their spectra have typically infinitely many gaps, or no gaps at all. These facts gave rise to the question about the existence of quantum graphs with the `Bethe-Sommerfeld property', that is, featuring a nonzero finite number of gaps in the spectrum. In this paper we prove that the said property is impossible for graphs with the vertex couplings which are either scale-invariant or associated to scale-invariant ones in a particular way. On the other hand, we demonstrate that quantum graphs with a finite number of open gaps do indeed exist. We illustrate this phenomenon on an example of a rectangular lattice with a $\delta$ coupling at the vertices and a suitable irrational ratio of the edges. Our result allows to find explicitly a quantum graph with any prescribed exact number of gaps, which is the first such example to the date.

The superscars phenomena (Heller, E.J., Phys. Rev. Lett. 53, (1984) 1515) in the rational polygon billiards (RPB) are analysed using the high energy semiclassical wave functions (SWF) built on classical trajectories forming skeletons. Considering examples of the pseudointegrable billiards such as the Bogomolny-Schmit triangle, the parallelogram and the L-shape billiards as well as the integrable rectangular one the constructed SWFs allow us to verify the idea of Bogomolny and Schmit (Phys. Rev. Lett. 92 (2004) 244102) of SWFs (superscars) propagating along periodic orbit channels (POC) and vanishing outside of them. It is shown that the superscars effects in RPB appear as natural properties of SWFs built on the periodic skeletons. The latter skeletons are commonly present in RPB and are always composed of POCs. The SWFs built on the periodic skeletons satisfy all the basic principles of the quantum mechanics contrary to the superscar states of Bogomolny and Schmit which break them. Therefore the superscars effects need not to invoke the idea of the superscar states of Bogomolny and Schmit at least in the cases considered in our paper.

Single-photon detectors are widely used in modern quantum optics experiments and applications. Like all detectors, it is important for these devices to be accurately calibrated. A single-photon detector is calibrated by determining its detection efficiency; the standard method to measure this quantity requires comparison to another detector. Here, we suggest a method to measure the detection efficiency of a single photon detector without requiring an external reference detector. Our method is valid for individual single-photon detectors as well as multiplexed detectors, which are known to be photon number resolving. The method exploits the photon-number correlations of a nonlinear source, as well as the nonlinear loss of a single photon detector that occurs when multiple photons are detected simultaneously. We have analytically modeled multiplexed detectors and used the results to experimentally demonstrate calibration of a single photon detector without the need for an external reference detector.

Certain wave functions of non-interacting quantum chaotic systems can exhibit "scars" in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories. We introduce the notion of many-body quantum scars which reflect the existence of a subset of special many-body eigenstates concentrated in certain parts of the Hilbert space. We demonstrate the existence of scars in the Fibonacci chain -- the one- dimensional model with a constrained local Hilbert space realized in the 51 Rydberg atom quantum simulator [H. Bernien et al., arXiv:1707.04344]. The quantum scarred eigenstates are embedded throughout the thermalizing many-body spectrum, but surprisingly lead to direct experimental signatures such as robust oscillations following a quench from a charge-density wave state found in experiment. We develop a model based on a single particle hopping on the Hilbert space graph, which quantitatively captures the scarred wave functions up to large systems of L = 32 atoms. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.

Public key quantum money can be seen as a version of the quantum no-cloning theorem that holds even when the quantum states can be verified by the adversary. In this work, investigate quantum lightning, a formalization of "collision-free quantum money" defined by Lutomirski et al. [ICS'10], where no-cloning holds even when the adversary herself generates the quantum state to be cloned. We then study quantum money and quantum lightning, showing the following results:

- We demonstrate the usefulness of quantum lightning by showing several potential applications, such as generating random strings with a proof of entropy, to completely decentralized cryptocurrency without a block-chain, where transactions is instant and local.

- We give win-win results for quantum money/lightning, showing that either signatures/hash functions/commitment schemes meet very strong recently proposed notions of security, or they yield quantum money or lightning.

- We construct quantum lightning under the assumed multi-collision resistance of random degree-2 systems of polynomials.

- We show that instantiating the quantum money scheme of Aaronson and Christiano [STOC'12] with indistinguishability obfuscation that is secure against quantum computers yields a secure quantum money scheme

We present a ground-to-space quantum key distribution (QKD) mission concept and the accompanying feasibility study for the development of the low earth orbit CubeSat payload. The quantum information is carried by single photons with the binary codes represented by polarization states of the photons. Distribution of entangled photons between the ground and the satellite can be used to certify the quantum nature of the link: a guarantee that no eavesdropping can take place. By placing the entangled photon source on the ground, the space segments contains only the less complex detection system, enabling its implementation in a compact enclosure, compatible with the 12U CubeSat standard (12 dm3). This reduces the overall cost of the project, making it an ideal choice as a pathfinder for future European quantum communication satellite missions. The space segment is also more versatile than one that contains the source since it is compatible with a multiple of QKD protocols (not restricted to entangled photon schemes) and can be used in quantum physics experiments, such as the investigation of entanglement decoherence. Other possible experiments include atmospheric transmission/turbulence characterization, dark area mapping, fine pointing and tracking, and accurate clock synchronization; all crucial for future global scale quantum communication efforts.

We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications.

The addition or subtraction of a photon from a Gaussian state of light is a versatile and experimentally feasible procedure to create non-Gaussian states. In multimode setups, these states manifest a wide range of phenomena when the photon is added or subtracted in a mode-tunable way. In this contribution, we derive the truncated correlations, which are multimode generalisations of cumulants, between quadratures in different modes as statistical signatures of these states. These correlations are then used to obtain the full multimode Wigner function, the properties of which are subsequently studied. In particular we investigate the effect of impurity in the subtraction or addition process, and evaluate its impact on the negativity of the Wigner function. Finally, we elaborate on the generation of inherent entanglement through subtraction or addition of a photon from a pure squeezed vacuum.

Single-shot qubit readout typically combines high readout contrast with long-lived readout signals, leading to large signal-to-noise ratios and high readout fidelities. In recent years, it has been demonstrated that both readout contrast and readout signal lifetime, and thus the signal-to-noise ratio, can be enhanced by forcing the qubit state to transition through intermediate states. In this work, we demonstrate that the sub-Poissonian relaxation statistics introduced by intermediate states can reduce the single-shot readout error rate by orders of magnitude even when there is no increase in signal-to-noise ratio. These results hold for moderate values of the signal-to-noise ratio ($\mathcal{S} \lesssim 100$) and a small number of intermediate states ($N \lesssim 10$). The ideas presented here could have important implications for readout schemes relying on the detection of transient charge states, such as spin-to-charge conversion schemes for semiconductor spin qubits and parity-to-charge conversion schemes for topologically protected Majorana qubits.

Topological- and strongly-correlated- materials are exciting frontiers in condensed matter physics, married prominently in studies of the fractional quantum hall effect [1]. There is an active effort to develop synthetic materials where the microscopic dynamics and ordering arising from the interplay of topology and interaction may be directly explored. In this work we demonstrate a novel architecture for exploration of topological matter constructed from tunnel-coupled, time-reversalbroken microwave cavities that are both low loss and compatible with Josephson junction-mediated interactions [2]. Following our proposed protocol [3] we implement a square lattice Hofstadter model at a quarter flux per plaquette ({\alpha} = 1/4), with time-reversal symmetry broken through the chiral Wannier-orbital of resonators coupled to Yttrium-Iron-Garnet spheres. We demonstrate site-resolved spectroscopy of the lattice, time-resolved dynamics of its edge channels, and a direct measurement of the dispersion of the edge channels. Finally, we demonstrate the flexibility of the approach by erecting a tunnel barrier investigating dynamics across it. With the introduction of Josephson-junctions to mediate interactions between photons, this platform is poised to explore strongly correlated topological quantum science for the first time in a synthetic system.

We consider the problem of estimating the temperature $ T $ of a very cold equilibrium sample. The temperature estimates are drawn from measurements performed on a quantum probe strongly coupled to it. We model this scenario by resorting to the canonical Caldeira-Leggett Hamiltonian and find analytically the exact stationary state of the probe for arbitrary coupling strength. In general, the probe does not reach thermal equilibrium with the sample, due to their non-perturbative interaction. We argue that this is advantageous for low temperature thermometry, as we show in our model that: (i) The thermometric precision at low $ T $ can be significantly enhanced by strengthening the probe-sampling coupling, (ii) the variance of a suitable quadrature of our Brownian thermometer can yield temperature estimates with nearly minimal statistical uncertainty, and (iii) the spectral density of the probe-sample coupling may be engineered to further improve thermometric performance. These observations may find applications in practical nanoscale thermometry at low temperatures---a regime which is particularly relevant to quantum technologies.

We derive general conditions for the compatibility of channels in general probabilistic theory. We introduce formalism that allows us to easily formulate steering by channels and Bell nonlocality of channels as generalizations of the well-known concepts of steering by measurements and Bell nonlocality of measurements. The generalization does not follow the standard line of thinking stemming from the Einstein-Podolsky-Rosen paradox, but introduces steering and Bell nonlocality as entanglement-assisted incompatibility tests. We show that all of the proposed definitions are, in the special case of measurements, the same as the standard definitions, but not all of the known results for measurements generalize to channels. For example, we show that for quantum channels, steering is not a necessary condition for Bell nonlocality. We further investigate the introduced conditions and concepts in the special case of quantum theory and we provide many examples to demonstrate these concepts and their implications.

The recent discovery of gravitational waves by LIGO created renewed interest in the investigation of alternative gravitational detector designs, such as small scale resonant detectors. In this article, it is shown how proposed small scale detectors can be tested by generating dynamical gravitational near fields with appropriate distributions of moving masses. This opens up the possibility to evaluate detector proposals very early in the development phase and may help to progress quickly in their development.

Author(s): Martin Reitter, Jakob Näger, Karen Wintersperger, Christoph Sträter, Immanuel Bloch, André Eckardt, and Ulrich Schneider

Experiments confirm that photon interactions cause heating of ultracold atoms in a periodically driven optical lattice. Driving at higher frequencies causes the highest-energy atoms to leave the trap, which cools the system.

[Phys. Rev. Lett. 119, 200402] Published Thu Nov 16, 2017

Author(s): Majid Hassani, Chiara Macchiavello, and Lorenzo Maccone

Quantum metrology calculates the ultimate precision of all estimation strategies, measuring what is their root-mean-square error (RMSE) and their Fisher information. Here, instead, we ask *how many bits* of the parameter we can recover; namely, we derive an information-theoretic quantum metrology. In ...

[Phys. Rev. Lett. 119, 200502] Published Thu Nov 16, 2017