Entropy of quantum states: Ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.

Evolution of quantum discord and its stability in two-qubit NMR systems

We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.

Quantum entropy for the fuzzy sphere and its monopoles

Using generalized bosons, we construct the fuzzy sphere S-F(2) and monopoles on S-F(2) in a reducible representation of SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent nonabelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.

Ancilla-assisted measurements on quantum ensembles: general protocols and applications in NMR quantum information processing

Quantum ensembles form easily accessible architectures for studying various phenomena in quantum physics, quantum information science and spectroscopy. Here we review some recent protocols for measurements in quantum ensembles by utilizing ancillary systems. We also illustrate these protocols experimentally via nuclear magnetic resonance techniques. In particular, we shall review noninvasive measurements, extracting expectation values of various operators, characterizations of quantum states and quantum processes, and finally quantum noise engineering.

Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin bath

Avoiding the loss of coherence of quantum mechanical states is an important prerequisite for quantum information processing. Dynamical decoupling (DD) is one of the most effective experimental methods for maintaining coherence, especially when one can access only the qubit system and not its environment (bath). It involves the application of pulses to the system whose net effect is a reversal of the system-environment interaction. In any real system, however, the environment is not static, and therefore the reversal of the system-environment interaction becomes imperfect if the spacing between refocusing pulses becomes comparable to or longer than the correlation time of the environment. The efficiency of the refocusing improves therefore if the spacing between the pulses is reduced. Here, we quantify the efficiency of different DD sequences in preserving different quantum states. We use C-13 nuclear spins as qubits and an environment of H-1 nuclear spins as the environment, which couples to the qubit via magnetic dipole-dipole couplings. Strong dipole-dipole couplings between the proton spins result in a rapidly fluctuating environment with a correlation time of the order of 100 mu s. Our experimental results show that short delays between the pulses yield better performance if they are compared with the bath correlation time. However, as the pulse spacing becomes shorter than the bath correlation time, an optimum is reached. For even shorter delays, the pulse imperfections dominate over the decoherence losses and cause the quantum state to decay.

Negative differential capacitance in n-GaN/p-Si heterojunctions

Negative differential capacitance (NDC) has been observed in n-GaN/p-Si heterojunctions grown by plasma assisted molecular beam epitaxy (PAMBE). The NDC is observed at low frequencies 1 and 10 kilohertz (kHz) and disappeared at a higher testing frequency of 100 kHz. The NDC is also studied with temperature and found that it has disappeared above 323 degrees C. Current-Voltage (I-V) characteristics of n-GaN /p-Si heterojunction were measured at different temperatures and are attributed to the space-charge-limited current (SCLC). A simple model involving two quantum states is proposed to explain the observed NDC behavior. (C) 2010 Elsevier Ltd. All rights reserved.

Direct Observation of Valley Hybridization and Universal Symmetry of Graphene with Mesoscopic Conductance Fluctuations

In graphene, the valleys represent spinlike quantities and can act as a physical resource in valley-based electronics to produce novel quantum computation schemes. Here we demonstrate a direct route to tune and read the valley quantum states of disordered graphene by measuring the mesoscopic conductance fluctuations. We show that the conductance fluctuations in graphene at low temperatures are reduced by a factor of 4 when valley triplet states are gapped in the presence of short-range potential scatterers at high carrier densities. We also show that this implies a gate tunable universal symmetry class that outlines a fundamental feature arising from graphene's unique crystal structure.

Universal Conductance Fluctuations as a direct probe to valley coherence and universality class of disordered graphene

We demonstrate that the universal conductance fluctuations (UCF) can be used as a direct probe to study the valley quantum states in disordered graphene. The UCF magnitude in graphene is suppressed by a factor of four at high carrier densities where the short-range disorder essentially breaks the valley degeneracy of the K and K' valleys, leading to a density dependent crossover of symmetry class from symplectic near the Dirac point to orthogonal at high densities.

Probing the Neutral Edge Modes in Transport across a Point Contact via Thermal Effects in the Read-Rezayi Non-Abelian Quantum Hall States

Non-Abelian quantum Hall states are characterized by the simultaneous appearance of charge and neutral gapless edge modes, with the structure of the latter being intricately related to the existence of bulk quasiparticle excitations obeying non-Abelian statistics. Here we propose a scenario for detecting the neutral modes by having two point contacts in series separated by a distance set by the thermal equilibration length of the charge mode. We show that by using the first point contact as a heating device, the excess charge noise measured at the second point contact carries a nontrivial signature of the presence of the neutral mode. We also obtain explicit expressions for the thermal conductance and corresponding Lorentz number for transport across a quantum point contact between two edges held at different temperatures and chemical potentials.

Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states

A general analysis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4, R). Within the framework of the unitary (metaplectic) representation of this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving squeezing transformations is made. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two-mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) elements can be reproduced are briefly described.

Quantum-confinement effects on the ordering of the lowest-lying excited states in conjugated chains

The symmetrized density-matrix renormalization-group approach is applied within the extended Hubbard-Peierls model (with parameters U/t, V/t, and bond alternation delta) to study the ordering of the lowest one-photon (1(1)B(u)(-)) and two-photon (2(1)A(g)(+)) states in one-dimensional conjugated systems with chain lengths N up to N = 80 sites. Three different types of crossovers are studied, as a function of U/t, delta, and N. The ''U crossover'' emphasizes the larger ionic character of the 2A(g) state compared to the lowest triplet excitation. The ''delta crossover'' shows strong dependence on both N and U/t. the ''N crossover'' illustrates the more localized nature of the 2A(g) excitation relative to the 1B(u) excitation at intermediate correlation strengths.

Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin Hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground-state configuration of all the members of the family on a periodic chain. The ground state is twofold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh Hamiltonian with a twofold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.

Electronic energy transfer between long-range resonance states of 3-mercaptopropionic acid capped CdTe quantum dots in aqueous media

We demonstrate electronic energy transfer between resonance states of 2 and 2.8 nm CdTe quantum dots in aqueous media using steady-state photoluminescence spectroscopy without using any external linker molecule. With increasing concentration of larger dots, there is subsequent quenching of luminescence in smaller dots accompanied by the enhancement of luminescence in larger dots. Our experimental evidence suggests that there is long-range resonance energy transfer among electronic excitations, specifically from the electronically confined states of the smaller dots to the higher excited states of the larger dots.

Tailoring local density of optical states to control emission intensity and anisotropy of quantum dots in hybrid photonic-plasmonic templates

We report results of controlled tuning of the local density of states (LDOS) in versatile, flexible, and hierarchical self assembled plasmonic templates. Using 5 nm diameter gold (Au) spherical nanoantenna within a polymer template randomly dispersed with quantum dots, we show how the photoluminescence intensity and lifetime anisotropy of these dots can be significantly enhanced through LDOS tuning. Finite difference time domain simulations corroborate the experimental observations and extend the regime of enhancement to a wider range of geometric and spectral parameters bringing out the versatility of these functional plasmonic templates. It is also demonstrated how the templates act as plasmonic resonators for effectively engineer giant enhancement of the scattering efficiency of these nano antenna embedded in the templates. Our work provides an alternative method to achieve spontaneous emission intensity and anisotropy enhancement with true nanoscale plasmon resonators. (C) 2015 AIP Publishing LLC.

Quantum entanglement in a noncommutative system

We explore the effect of two-dimensional position-space noncommutativity on the bipartite entanglement of continuous-variable systems. We first extend the standard symplectic framework for studying entanglement of Gaussian states of commutative systems to the case of noncommutative systems residing in two dimensions. Using the positive partial transpose criterion for separability of bipartite states, we derive a condition on the separability of a noncommutative system that is dependent on the noncommutative parameter theta. We then consider the specific example of a bipartite Gaussian state and show the quantitative reduction in entanglement originating from noncommutative dynamics. We show that such a reduction in entanglement for a noncommutative system arising from the modification of the variances of the phase-space variables (uncertainty relations) is clearly manifested between two particles that are separated by small distances.