Localized Quantum States Research Articles

Interpreting the macroscopic pointer by analysing the elements of reality of a Schrödinger cat

We examine Einstein–Podolsky–Rosen’s (EPR) steering nonlocality for two realisable Schrödinger cat-type states where a meso/macroscopic system (called the ‘cat’-system) is entangled with a microscopic spin- system. We follow EPR’s argument and derive the predictions for ‘elements of reality’ that would exist to describe the cat-system, under the assumption of EPR’s local realism. By showing that those predictions cannot be replicated by any local quantum state description of the cat-system, we demonstrate the EPR-steering of the cat-system. For large cat-systems, we find that a local hidden state model is near-satisfied, meaning that a local quantum state description exists (for the cat) whose predictions differ from those of the elements of reality by a vanishingly small amount. For such a local hidden state model, the EPR-steering of the cat vanishes, and the cat-system can be regarded as being in a mixture of ‘dead’ and ‘alive’ states despite it being entangled with the spin system. We therefore propose that a rigorous signature of the Schrödinger cat-type paradox is the EPR-steering of the cat-system and provide two experimental signatures. This leads to a hybrid quantum/classical interpretation of the macroscopic pointer of a measurement device and suggests that many Schrödinger cat-type paradoxes may be explained by microscopic nonlocality.

Erratum: Effect of relativistic acceleration on localized two-mode Gaussian quantum states [Phys. Rev. D 93 , 124031 (2016)

Received 1 March 2017DOI:https://doi.org/10.1103/PhysRevD.95.069903© 2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGeneral relativityQuantum entanglementQuantum fields in curved spacetimeQuantum InformationInterdisciplinary PhysicsGravitation, Cosmology & Astrophysics

Localization of quantum states and landscape functions

Eigenfunctions in inhomogeneous media can have strong localization properties. Filoche and Mayboroda showed that the function u u solving ( − Δ + V ) u = 1 (-\Delta + V)u = 1 controls the behavior of eigenfunctions ( − Δ + V ) ϕ = λ ϕ (-\Delta + V)\phi = \lambda \phi via the inequality \[ | ϕ ( x ) | ≤ λ u ( x ) ‖ ϕ ‖ L ∞ . |\phi (x)| \leq \lambda u(x) \|\phi \|_{L^{\infty }}. \] This inequality has proven to be remarkably effective in predicting localization and recently Arnold, David, Jerison, Mayboroda and Filoche connected 1 / u 1/u to decay properties of eigenfunctions. We aim to clarify properties of the landscape: the main ingredient is a localized variation estimate obtained from writing ϕ ( x ) \phi (x) as an average over Brownian motion ω ( ⋅ ) \omega (\cdot ) started in x x \[ ϕ ( x ) = E x ( ϕ ( ω ( t ) ) e λ t − ∫ 0 t V ( ω ( z ) ) d z ) . \phi (x) = \mathbb {E}_{x}\left (\phi (\omega (t)) e^{\lambda t-\int _{0}^{t}{V(\omega (z))dz}} \right ). \] This variation estimate will guarantee that ϕ \phi has to change at least by a factor of 2 in a small ball, which implicitly creates a landscape whose relationship with 1 / u 1/u we discuss.

Activation of the Violation of Svetlichny Inequality for a Broad Class of States

The fact that several copies of a local quantum state — when processed together — can generate a nonlocal correlation, i.e. the superactivation of quantum nonlocality, is a well-known feature of quantum mechanics. Most of research results focused strongly on the bipartite scenario. In this paper we show that the activation of violation of Svetlichny inequality, reported for the first time in our previous paper, is not an exceptional phenomenon but holds for a broad class of quantum states as well for pure as for mixed, noisy ones.

Two-qubit quantum cloning machine and quantum correlation broadcasting

Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: "Is there an optimal quantum cloning machine?" Buzek and Hillery answer to this question and construct their famous B-H quantum cloning machine. The B-H machine clones state of an arbitrary single qubit in optimal manner and hence it is universal. Generalizing this machine for two-qubit system is straightforward, but this procedure does not preserve quantum correlation existing in bipartite state in optimal manner and also, during this procedure, this machine loses its universality and becomes a state-dependent cloning machine. In this paper we propose an optimal universal local quantum state cloner for two qubit systems. Also we present two classes of state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement and quantum discord defined, respectively, within the entanglement-separability paradigm and from an information-theoretic perspective. The results show that although quantum correlation is in general very fragile during broadcasting procedure, quantum discord is broadcasted more robustly than quantum entanglement.

Multiple magnetization plateaus and magnetic structures in theS=12Heisenberg model on the checkerboard lattice

We study the ground state of $S = 1/2$ Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group (DMRG) method with the sine-square deformation. We obtain magnetization plateaus at $M/M_{\rm sat}=$0, 1/4, 3/8, 1/2, and 3/4 where $M_{\rm sat}$ is the saturated magnetization. The obtained 3/4 plateau state is consistent with the exact result, and the 1/2 plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the 1/3 plateau of the kagome lattice. Different four-spin loop structures are obtained in the 1/4 and 3/8 plateaus but no corresponding states exist in the kagome lattice. The 3/8 plateau has a unique magnetic structure of three types of four-spin local quantum states in a $4\sqrt{2}\times2\sqrt{2}$ magnetic unit cell with a 16-fold degeneracy.

Effect of relativistic acceleration on localized two-mode Gaussian quantum states

We study how an arbitrary Gaussian state of two localized wave packets, prepared in an inertial frame of reference, is described by a pair of uniformly accelerated observers. We explicitly compute the resulting state for arbitrarily chosen proper accelerations of the observers and independently tuned distance between them. To do so, we introduce a generalized Rindler frame of reference and analytically derive the corresponding state transformation as a Gaussian channel. Our approach provides several new insights into the phenomenon of vacuum entanglement such as the highly non-trivial effect of spatial separation between the observers including sudden death of entanglement. We also calculate the fidelity of the two-mode channel for non-vacuum Gaussian states and obtain bounds on classical and quantum capacities of a single-mode channel. Our framework can be directly applied to any continuous variable quantum information protocol in which the effects of acceleration or gravity cannot be neglected.

Multiparticle entanglement as an emergent phenomenon

The question whether global entanglement of a multiparticle quantum system can be inferred from local properties is of great relevance for the theory of quantum correlations as well as for experimental implementations. We present a method to systematically find quantum states, for which the two- or three-body marginals do not contain any entanglement, nevertheless, the knowledge of these reduced states is sufficient to prove genuine multiparticle entanglement of the global state. With this, we show that the emergence of global entanglement from separable local quantum states occurs frequently and for an arbitrary number of particles. We discuss various extensions of the phenomenon and present examples where global entanglement can be proven from marginals, even if entanglement cannot be localized in the marginals with measurements on the other parties.

Effective Confining Potential of Quantum States in Disordered Media.

The amplitude of localized quantum states in random or disordered media may exhibit long-range exponential decay. We present here a theory that unveils the existence of an effective potential which finely governs the confinement of these states. In this picture, the boundaries of the localization subregions for low energy eigenfunctions correspond to the barriers of this effective potential, and the long-range exponential decay characteristic of Anderson localization is explained as the consequence of multiple tunneling in the dense network of barriers created by this effective potential. Finally, we show that Weyl's formula based on this potential turns out to be a remarkable approximation of the density of states for a large variety of one-dimensional systems, periodic or random.

Manipulating quantum wave packets via time-dependent absorption

A pulse of matter waves may dramatically change its shape when traversing an absorbing barrier with time-dependent transparency. Here we show that this effect can be utilized for controlled manipulation of spatially localized quantum states. In particular, in the context of atom-optics experiments, we explicitly demonstrate how the proposed approach can be used to generate spatially shifted, split, squeezed, and cooled atomic wave packets. We expect our work to be useful in devising new interference experiments with atoms and molecules and, more generally, to enable new ways of coherent control of matter waves.

80 years of steering and the Einstein–Podolsky–Rosen paradox: introduction

The year 2015 marks 80 years since Einstein, Podolsky, and Rosen argued for the incompleteness of quantum mechanics, in the process describing one of the most counterintuitive characteristics of quantum mechanics: distant measurements can influence the character of local quantum states. This led to reactions from Schrodinger, Bohr, and John Bell. This issue shows that these developments are still well under way, with new foundational insights on the history of steering and Bell-nonlocality, new directions in the mathematical characterization of EPR-steering, demonstrations in quantum optical experiments, and further connections with quantum information processing.

Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements.

A single quantum particle can be described by a wavefunction that spreads over arbitrarily large distances; however, it is never detected in two (or more) places. This strange phenomenon is explained in the quantum theory by what Einstein repudiated as 'spooky action at a distance': the instantaneous nonlocal collapse of the wavefunction to wherever the particle is detected. Here we demonstrate this single-particle spooky action, with no efficiency loophole, by splitting a single photon between two laboratories and experimentally testing whether the choice of measurement in one laboratory really causes a change in the local quantum state in the other laboratory. To this end, we use homodyne measurements with six different measurement settings and quantitatively verify Einstein's spooky action by violating an Einstein-Podolsky-Rosen-steering inequality by 0.042±0.006. Our experiment also verifies the entanglement of the split single photon even when one side is untrusted.

Local decoherence-resistant quantum states of large systems

We identify a class of quantum states, each consisting of a microscopic and a macroscopic section, that are effectively decoherence-free when each particle is locally passed through a quantum channel. In particular, and in contrast to other macroscopic quantum states like the Greenberger-Horne-Zeilinger state, the content of entanglement and other quantum correlations in the microscopic to macroscopic partition of this class of states is independent of the number of particles in their macroscopic sectors, when all the particles suffer passage through local amplitude and phase damping channels. Decay of quantum correlations -- entanglement as well as quantum discord -- of this class of states in the microscopic to macroscopic partition is also much lower in the case of all the local quantum channels, as compared to the other macroscopic superposition states. The macroscopic sections of the states are formed, in each case, by using a Dicke state and an orthogonal product state, which are macroscopically distinct in terms of markedly different amounts of violation of Bell inequality.

Exact quantum dynamics of yrast states in the finite 1D Bose gas

We demonstrate that the quantum dynamics of yrast states in the one-dimensional (1D) Bose gas gives an illustrative example to equilibration of an isolated quantum many-body system. We first formulate the energy spectrum of yrast states in terms of the dressed energy by applying the method of finite-size corrections. We then review the exact time evolution of quantum states constructed from yrast states shown by the Bethe ansatz. In time evolution the density profile of an initially localized quantum state constructed from yrast states collapses into a flat profile in the case of a large particle number such as N = 1000, while recurrence of the localized state occurs in the case of a small particle number such as N = 20. We suggest that the dynamical relaxation behavior for the large N case is consistent with the viewpoint of typicality for generic quantum states: the expectation values of local operators evaluated in most of quantum states are very close to those of the micro-canonical ensemble.

Fano effect and bound state in continuum in electron transport through an armchair graphene nanoribbon with line defect

Electron transport properties in an armchair graphene nanoribbon are theoretically investigated by considering the presence of line defect. It is found that the line defect causes the abundant Fano effects and bound state in continuum (BIC) in the electron transport process, which are tightly dependent on the width of the nanoribbon. By plotting the spectra of the density of electron states of the line defect, we see that the line defect induces some localized quantum states around the Dirac point and that the different localizations of these states lead to these two kinds of transport results. Next, the Fano effect and BIC phenomenon are detailedly described via the analysis about the influence of the structure parameters. According to the numerical results, we propose such a structure to be a promising candidate for graphene nanoswitch.PACS81.05.Uw, 71.55.-i, 73.23.-b, 73.25.+i

Line-defect–induced Fano interference in an armchair graphene nanoribbon

Electron transport through a metallic armchair graphene nanoribbon is theoretically investigated by considering the presence of line defect. The line defect is formed by the staggered stacking of the pentagons and heptagons. Our calculation results show that the line defect mainly destroys the electron transport in the conduction-band region by inducing the abundant Fano effects in the electron transport process. Moreover, the properties of the Fano effects are tightly dependent on the width M of the nanoribbon, and the results of are completely different from those of M > 17. The spectra of the density of electron states illustrate that the line defect induces some localized quantum states, and that the different localizations of these states lead to the distinct transport results. By analyzing the influence of the structure parameters, the Fano effects are described in detail. All the results demonstrate that such a structure can be a promising candidate for electron manipulation in graphene nanoribbon.

A graphene quantum dot realized by an armchair graphene nanoribbon with line defect

AbstractThe electron transport in a semiconducting armchair graphene nanoribbon with line defect is theoretically investigated, by coupling it to two normal metallic leads. It is found that the line defect induces a new localized quantum state near the Dirac point, and that the coupling between this state and the leads provides a channel for the resonant tunneling. This means that such a finite‐size nanoribbon can be viewed as a quantum dot. When two line defects are present simultaneously, a coupled quantum dot forms, leading to the splitting of the conductance peaks. With these results, we propose such a structure to be a promising candidate of an electron transistor. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Fano effects in electron transport through an armchair graphene nanoribbon with one line defect

Electron transport in an armchair graphene nanoribbon is theoretically investigated by considering the presence of one line defect. It is found that different-property Fano effects occur in electron transport through such a structure, which are determined by the nanoribbon width and the coupling manner between the line defect and the nanoribbon. The spectra of the density of electron states show that the line defect induces some localized quantum states around the Dirac point, and that the different localizations of these states lead to the abundant transport results. By analyzing the influence of the structure parameters, the Fano effects are described in detail. With the obtained results, we consider such a structure to be a promising candidate for nanoswitch.

Quantum metamaterial without local control

A quantum metamaterial can be implemented as a quantum coherent one-dimensional array of qubits placed in a transmission line. The properties of quantum metamaterials are determined by the local quantum state of the system. Here we show that a spatially periodic quantum state of such a system can be realized without direct control of the constituent qubits, by their interaction with the initializing (``priming'') pulses sent through the system in opposite directions. The properties of the resulting quantum photonic crystal are determined by the choice of the priming pulses. This proposal can be readily generalized to other implementations of quantum metamaterials.

Features of the time evolution of localized quantum states in graphene

In the Heisenberg representation, the phenomena of the interference of quantum states of the conduction and valence bands of graphene, arising for localized electron wave packets are analyzed. The interference leads to temporal oscillations in the values of the average physical quantities.