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Uniformly accelerated quantum counting detector in Minkowski and Fulling vacuum states. (arXiv:2009.03970v2 [hep-th] UPDATED)

Fri, 2021-04-16 08:54

In this work we discuss the process of measurements by a detector in an uniformly accelerated rectilinear motion, interacting linearly with a massive scalar field. The detector model for field quanta is a point-like system with a ground state and a continuum of unbounded states. We employ the Glauber theory of photodetection. In an uniformly accelerated reference frame, the detector, interacting with the field prepared in an arbitrary state of the Rindler Fock space, is excited only by absorption processes. For the uniformly accelerated detector prepared in the ground state, we evaluate the transition probability rate in three important situations. In the first one the field is prepared in an arbitrary state of $n$-Rindler quanta, then we consider a thermal Rindler state at a given temperature $\beta^{-1}$, and finally the case in which the state of the field is taken to be the Minkowski vacuum. The well-known result that the latter excitation rates are equal is recovered. Accelerated or inertial observer interpretations of the measurements performed by the accelerated detector is presented. Finally, we investigate the behaviour of the detector in a frame which is inertial in the remote past but in the far future becomes uniformly accelerated. For the massless case, we obtain that the transition probability rate of the detector in the far future is tantamount to the analogous quantity for the detector at rest in a non-inertial reference frame interacting with the field prepared in an usual thermal state.

Categories: Journals, Physics

Bounding and simulating contextual correlations in quantum theory. (arXiv:2010.04751v2 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

We introduce a hierarchy of semidefinite relaxations of the set of quantum correlations in generalised contextuality scenarios. This constitutes a simple and versatile tool for bounding the magnitude of quantum contextuality. To illustrate its utility, we use it to determine the maximal quantum violation of several noncontextuality inequalities whose maximum violations were previously unknown. We then go further and use it to prove that certain preparation-contextual correlations cannot be explained with pure states, thereby showing that mixed states are an indispensable resource for contextuality. In the second part of the paper, we turn our attention to the simulation of preparation-contextual correlations in general operational theories. We introduce the information cost of simulating preparation contextuality, which quantifies the additional, otherwise forbidden, information required to simulate contextual correlations in either classical or quantum models. In both cases, we show that the simulation cost can be efficiently bounded using a variant of our hierarchy of semidefinite relaxations, and we calculate it exactly in the simplest contextuality scenario of parity-oblivious multiplexing.

Categories: Journals, Physics

Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices. (arXiv:2011.14113v2 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work, ultra-cold fermionic atoms have been proposed for these purposes by showing us how to simulate in an analog way the quantum chemistry Hamiltonian projected in a lattice basis set. Here, we continue exploring this path and go beyond these first results in several ways. First, we numerically benchmark the working conditions of the analog simulator, and find less demanding experimental setups where chemistry-like behaviour in three-dimensions can still be observed. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite size effects and provide a way to mitigate them. Finally, we benchmark the simulator characterizing the behaviour of two-electron atoms (He) and molecules (HeH$^+$) beyond the example considered in the original work.

Categories: Journals, Physics

Initial entanglement, entangling unitaries, and completely positive maps. (arXiv:2012.12292v2 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

The problem of conditions on the initial correlations between the system and the environment that lead to completely positive (CP) or not-completely positive (NCP) maps has been studied by various authors. Two lines of study may be discerned: one concerned with families of initial correlations that induce CP dynamics under the application of an arbitrary joint unitary on the system and environment; the other concerned with specific initial states that may be highly entangled. Here we study the latter problem, and highlight the interplay between the initial correlations and the unitary applied. In particular, for almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. Restricting to the case of initial, pure entangled states, we obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.

Categories: Journals, Physics

Graph connectivity based strong quantum nonlocality with genuine entanglement. (arXiv:2104.06662v2 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

Strong nonlocality based on local distinguishability is a stronger form of quantum nonlocality recently introduced in multipartite quantum systems: an orthogonal set of multipartite quantum states is said to be of strong nonlocality if it is locally irreducible for every bipartition of the subsystems. Most of the known results are limited to sets with product states. Shi et al. presented the first result of strongly nonlocal entangled sets in [Phys. Rev. A 102, 042202 (2020)] and there they questioned the existence of strongly nonlocal set with genuine entanglement. In this work, we relate the strong nonlocality of some speical set of genuine entanglement to the connectivities of some graphs. Using this relation, we successfully construct sets of genuinely entangled states with strong nonlocality. As a consequence, our constructions give a negative answer to Shi et al.'s question, which also provide another answer to the open problem raised by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)]. This work associates a physical quantity named strong nonlocality with a mathematical quantity called graph connectivity.

Categories: Journals, Physics

Optimizing the deployment of quantum key distribution switch-based networks. (arXiv:2104.04155v2 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

Quantum key distribution (QKD) networks provide an infrastructure for establishing information-theoretic secure keys between legitimate parties via quantum and authentic classical channels. The deployment of QKD networks in real-world conditions faces several challenges, which are related in particular to the high costs of QKD devices and the condition to provide reasonable secret key rates. In this work, we present a QKD network architecture that provides a significant reduction in the cost of deploying QKD networks by using optical switches and reducing the number of QKD receiver devices, which use single-photon detectors. We describe the corresponding modification of the QKD network protocol. We also provide estimations for a network link of a total of 670 km length consisting of 8 nodes, and demonstrate that the switch-based architecture allows achieving significant resource savings of up to 28%, while the throughput is reduced by 8% only.

Categories: Journals, Physics

Activating Hidden Teleportation Power: Theory and Experiment. (arXiv:2008.01689v3 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

Ideal quantum teleportation transfers an unknown quantum state intact from one party Alice to the other Bob via the use of a maximally entangled state and the communication of classical information. If Alice and Bob do not share entanglement, the maximal average fidelity between the state to be teleported and the state received, according to a classical measure-and-prepare scheme, is upper bounded by a function $f_{\mathrm{c}}$ that is inversely proportional to the Hilbert space dimension. In fact, even if they share entanglement, the so-called teleportation fidelity may still be less than the classical threshold $f_{\mathrm{c}}$. For two-qubit entangled states, conditioned on a successful local filtering, the teleportation fidelity can always be activated, i.e., boosted beyond $f_{\mathrm{c}}$. Here, for all dimensions larger than two, we show that the teleportation power hidden in a subset of entangled two-qudit Werner states can also be activated. In addition, we show that an entire family of two-qudit rank-deficient states violates the reduction criterion of separability, and thus their teleportation power is either above the classical threshold or can be activated. Using hybrid entanglement prepared in photon pairs, we also provide the first proof-of-principle experimental demonstration of the activation of teleportation power hidden in this latter family of qubit states. The connection between the possibility of activating hidden teleportation power with the closely-related problem of entanglement distillation is discussed.

Categories: Journals, Physics

Fisher Information in Noisy Intermediate-Scale Quantum Applications. (arXiv:2103.15191v2 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

The classical and quantum Fisher information are versatile tools to study parametrized quantum systems. These tools are firmly rooted in the field of quantum metrology. Their immense utility in the study of other applications of noisy intermediate-scale quantum devices, however, has only become apparent in recent years. This work aims to further popularize classical and quantum Fisher information as useful tools for near-term applications by giving an accessible and intuitive introduction to the topic. We build an intuitive understanding of classical and quantum Fisher information, outline how both quantities are calculated on near-term devices and explain their relationship and the influence of device noise. We further review the existing applications of these tools in the areas of quantum sensing, variational quantum algorithms and quantum machine learning.

Categories: Journals, Physics

Excitation relaxation in molecular chain and energy transfer at steady state. (arXiv:2103.12569v3 [cond-mat.stat-mech] UPDATED)

Fri, 2021-04-16 08:54

We consider the reduced dynamics of a molecular chain weakly coupled to a phonon bath. With a small and constant inhomogeneity in the coupling, the excitation relaxation rates are obtained in closed form. They are dominated by transitions between exciton modes lying next to each other in the energy spectrum. The rates are quadratic in the number of sites in a long chain. Consequently, the evolution of site occupation numbers exhibits longer coherence lifetime for short chains only. When external source and sink are added, the rate equations of exciton occupation numbers are similar to those obtained earlier by Fr\"{o}hlich to explain energy storage and energy transfer in biological systems. There is a clear separation of time scale into a faster one pertaining to internal influence of the chain and phonon bath, and a slower one determined by external influence, such as the pumping rate of the source, the absorption rate of the sink and the rate of radiation loss. The energy transfer efficiency at steady state depends strongly on these external parameters, and is robust against a change in the internal parameters, such as temperature and inhomogeneity. Excitations are predicted to concentrate to the lowest energy mode when the source power is sufficiently high. In the site basis, this implies that when sustained by a high power source, a sink positioned at the center of the chain is more efficient in trapping energy than a sink placed at its end. Analytic expressions of energy transfer efficiency are obtained in the high power and low power source limit. Parameters of a photosynthetic system are used as examples to illustrate the results.

Categories: Journals, Physics

Kelly Betting with Quantum Payoff: a continuous variable approach. (arXiv:2001.11395v4 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the quantum analog of the free-energy (i.e. ergotropy functional by Allahverdyan, Balian, and Nieuwenhuizen) of a single mode of the electromagnetic radiation which, depending on the outcome of the betting, experiences attenuation or amplification processes which model losses and winning events. The resulting stochastic evolution of the quantum memory resembles the dynamics of random lasing which we characterize within the theoretical setting of Bosonic Gaussian channels. As in the classical Kelly Criterion for optimal betting, we define the asymptotic doubling rate of the model and identify the optimal gambling strategy for fixed odds and probabilities of winning. The performance of the model are hence studied as a function of the input capital state under the assumption that the latter belongs to the set of Gaussian density matrices (i.e. displaced, squeezed thermal Gibbs states) revealing that the best option for the gambler is to devote all her/his initial resources into coherent state amplitude.

Categories: Journals, Physics

Ermakov-Pinney equation for time-varying mass systems. (arXiv:2103.10662v2 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

We extend Fring-Tenney approach of constructing invariants of constant mass time-dependent system to the case of a time-dependent mass particle. From a coupled set of equations described in terms of guiding parameter functions, we track down a modified Ermakov-Pinney equation involving a time-dependent mass function. As a concrete example we focus on an exponential choice of the mass function.

Categories: Journals, Physics

A Green's function approach to the linear response of a driven dissipative optomechanical system. (arXiv:2009.13381v3 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

In this paper, we first try to shed light on the ambiguities that exist in the literature in the generalization of the standard linear response theory (LRT) which has been basically formulated for closed systems to the theory of open quantum systems in the Heisenberg picture. Then, we investigate the linear response of a driven-dissipative optomechanical system (OMS) to a weak time-dependent perturbation using the so-called generalized LRT. It is shown how the Green's function equations of motion of a standard OMS as an open quantum system can be obtained from the quantum Langevin equations (QLEs) in the Heisenberg picture. The obtained results explain a wealth of phenomena, including the anti-resonance, normal mode splitting and the optomechanically induced transparency (OMIT). Furthermore, the reason why the Stokes or anti-Stokes sidebands are amplified or attenuated in the red or blue detuning regimes is clearly explained which is in exact coincidence, especially in the weak-coupling regime, with the Raman-scattering picture.

Categories: Journals, Physics

Quantum Information Dynamics between Quantum Ising Spins and a Central Qudit. (arXiv:2103.08517v2 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

Understanding the role of entanglement and its dynamics in composite quantum systems lies at the forefront of quantum matter studies. Here we investigate competing entanglement dynamics in an open Ising-spin chain that allows for exchange with an external central qudit probe. We propose a new metric dubbed the multipartite entanglement loss (MEL) that provides an upper bound on the amount of information entropy shared between the spins and the qudit probe that serves to unify physical spin-fluctuations, Quantum Fisher Information (QFI), and bipartite entanglement entropy.

Categories: Journals, Physics

Poisson Quantum Information. (arXiv:2103.08532v4 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

By taking a Poisson limit for a sequence of rare quantum particles, I derive simple formulas for the Uhlmann fidelity, the quantum Chernoff quantity, the relative entropy, and the Helstrom information. I also present analogous formulas in classical information theory for a Poisson model. An operator called the intensity operator emerges as the central quantity in the formalism to describe Poisson states. It behaves like a density operator but is unnormalized. The formulas in terms of the intensity operators not only resemble the general formulas in terms of the density operators, but also coincide with some existing definitions of divergences between unnormalized positive-semidefinite matrices. Furthermore, I show that the effects of certain channels on Poisson states can be described by simple maps for the intensity operators.

Categories: Journals, Physics

Boundary time crystals in collective $d$-level systems. (arXiv:2102.03374v2 [cond-mat.stat-mech] UPDATED)

Fri, 2021-04-16 08:54

Boundary time crystals (BTC's) are non-equilibrium phases of matter occurring in quantum systems in contact to an environment, for which a macroscopic fraction of the many body system breaks time translation symmetry. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$. We find that BTC's appear in different forms for the different cases. We first consider the model with collective $d=2$-level systems [presented in Phys. Rev. Lett. $121$, $035301$ ($2018$)], whose dynamics is described by a Lindblad master equation, and perform a throughout analysis of its phase diagram and Jacobian stability for different interacting terms in the coherent Hamiltonian. In particular, using perturbation theory for general (non Hermitian) matrices we obtain analytically how a specific $\mathbb{Z}_2$ symmetry breaking Hamiltonian term destroys the BTC phase in the model. Based on these results we define a $d=4$ model composed of a pair of collective $2$-level systems interacting with each other. We show that this model support richer dynamical phases, ranging from limit-cycles, period-doubling bifurcations and a route to chaotic dynamics. The BTC phase is more robust in this case, not annihilated by the former symmetry breaking Hamiltonian terms. The model with collective $d=3$-level systems is defined similarly, as competing pairs of levels, but sharing a common collective level. The dynamics can deviate significantly from the previous cases, supporting phases with the coexistence of multiple limit-cycles, closed orbits and a full degeneracy of zero Lyapunov exponents.

Categories: Journals, Physics

Local classical MAX-CUT algorithm outperforms $p=2$ QAOA on high-girth regular graphs. (arXiv:2101.05513v2 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

The $p$-stage Quantum Approximate Optimization Algorithm (QAOA$_p$) is a promising approach for combinatorial optimization on noisy intermediate-scale quantum (NISQ) devices, but its theoretical behavior is not well understood beyond $p=1$. We analyze QAOA$_2$ for the maximum cut problem (MAX-CUT), deriving a graph-size-independent expression for the expected cut fraction on any $D$-regular graph of girth $> 5$ (i.e. without triangles, squares, or pentagons).

We show that for all degrees $D \ge 2$ and every $D$-regular graph $G$ of girth $> 5$, QAOA$_2$ has a larger expected cut fraction than QAOA$_1$ on $G$. However, we also show that there exists a $2$-local randomized classical algorithm $A$ such that $A$ has a larger expected cut fraction than QAOA$_2$ on all $G$. This supports our conjecture that for every constant $p$, there exists a local classical MAX-CUT algorithm that performs as well as QAOA$_p$ on all graphs.

Categories: Journals, Physics

Locality of the windowed local density of states. (arXiv:2101.00272v2 [math-ph] UPDATED)

Fri, 2021-04-16 08:54

We introduce a generalization of local density of states which is "windowed" with respect to position and energy, called the windowed local density of states (wLDOS). This definition generalizes the usual LDOS in the sense that the usual LDOS is recovered in the limit where the position window captures individual sites and the energy window is a delta distribution. We prove that the wLDOS is local in the sense that it can be computed up to arbitrarily small error using spatial truncations of the system Hamiltonian. Using this result we prove that the wLDOS is well-defined and computable for infinite systems satisfying some natural assumptions. We finally present numerical computations of the wLDOS at the edge and in the bulk of a "Fibonacci SSH model", a one-dimensional non-periodic model with topological edge states.

Categories: Journals, Physics

Bose-Einstein Condensation and Supersolids. (arXiv:2012.14378v2 [cond-mat.quant-gas] UPDATED)

Fri, 2021-04-16 08:54

We consider interacting Bose particles in an external potential. It is shown that a Bose-Einstein condensate is possible at finite temperatures that describes a supersolid in three dimensions (3D) for a wide range of potentials in the absence of an external potential. However, for 2D, a self-organized supersolid exists for finite temperatures provided the interaction between bosons is nonlocal and of infinitely long-range. It is interesting that in the absence of the latter type of potential and in the presence of a lattice potential, there is no Bose-Einstein condensate and so in such a case, a 2D supersolid is not possible at finite temperatures. We also propose the correct Bloch form of the condensate wave function valid for finite temperatures, which may be used as the correct trial wave function.

Categories: Journals, Physics

Simple efficient decoders for quantum key distribution over quantum repeaters with encoding. (arXiv:2012.13011v3 [quant-ph] UPDATED)

Fri, 2021-04-16 08:54

We study the implementation of quantum key distribution (QKD) systems over quantum repeater infrastructures. We particularly consider quantum repeaters with encoding and compare them with probabilistic quantum repeaters. To that end, we propose two decoder structures for encoded repeaters that not only improve system performance but also make the implementation aspects easier by removing two-qubit gates from the QKD decoder. By developing several scalable numerical and analytical techniques, we then identify the resilience of the setup to various sources of error in gates, measurement modules, and initialization of the setup. We apply our techniques to three- and five-qubit repetition codes and obtain the normalized secret key generation rate per memory per second for encoded and probabilistic quantum repeaters. We quantify the regimes of operation, where one class of repeater outperforms the other, and find that there are feasible regimes of operation where encoded repeaters -- based on simple three-qubit repetition codes -- could offer practical advantages.

Categories: Journals, Physics

Critical Phenomena in Complex Networks: from Scale-free to Random Networks. (arXiv:2008.02319v2 [physics.soc-ph] CROSS LISTED)

Fri, 2021-04-16 08:54

Within the conventional statistical physics framework, we study critical phenomena in a class of configuration network models with hidden variables controlling links between pairs of nodes. We find analytical expressions for the average node degree, the expected number of edges, and the Landau and Helmholtz free energies, as a function of the temperature and number of nodes. We show that the network's temperature is a parameter that controls the average node degree in the whole network and the transition from unconnected graphs to a power-law degree (scale-free) and random graphs. With increasing temperature, the degree distribution is changed from power-law degree distribution, for lower temperatures, to a Poisson-like distribution for high temperatures. We also show that phase transition in the so-called Type A networks leads to fundamental structural changes in the network topology. Below the critical temperature, the graph is completely disconnected. Above the critical temperature, the graph becomes connected, and a giant component appears.

Categories: Journals, Physics