We derive several entanglement criteria for bipartite continuous variable quantum systems based on the Shannon entropy. These criteria are more sensitive than those involving only second-order moments, and are equivalent to well-known variance product tests in the case of Gaussian states. Furthermore, they involve only a pair of quadrature measurements, and will thus prove extremely useful in the experimental identification of entanglement.

We report repeated single-shot measurements of the two-electron spin state in a GaAs double quantum dot. The readout allows measurement with a fidelity above 90% with a $\sim 7\mu \mathrm{s}$ cycle time. Hyperfine-induced precession between singlet and triplet states of the two-electron system are directly observed, as nuclear Overhauser fields are quasistatic on the time scale of the measurement cycle. Repeated measurements on millisecond to second time scales reveal the evolution of the nuclear environment.

We introduce variants of relative entropy of entanglement based on the optimal distinguishability from unentangled states by means of restricted measurements. In this way we are able to prove that the standard regularized entropy of entanglement is strictly positive for all multipartite entangled states. This implies that the asymptotic creation of a multipartite entangled state by means of local operations and classical communication always requires the consumption of a nonlocal resource at a strictly positive rate.

We create a six-qubit linear cluster state by transforming a two-photon hyperentangled state in which three qubits are encoded in each particle, one in the polarization and two in the linear momentum degrees of freedom. For this state, we demonstrate genuine six-qubit entanglement, persistency of entanglement against the loss of qubits, and higher violation than in previous experiments on Bell inequalities of the Mermin type.

Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which, in principle, can be used for topological quantum computation. We present a prescription for efficiently finding braids which can be used to carry out a universal set of quantum gates on encoded qubits based on anyons of the Read-Rezayi states with $k>2$, $k\ne 4$. This work extends previous results which only applied to the case $k=3$ (Fibonacci) and clarifies why, in that case, gate constructions are simpler than for a generic Read-Rezayi state.

How fast a quantum state can evolve has attracted considerable attention in connection with quantum measurement and information processing. A lower bound on the orthogonalization time, based on the energy spread $\Delta E$, was found by Mandelstam and Tamm. Another bound, based on the average energy $E$, was established by Margolus and Levitin. The bounds coincide and can be attained by certain initial states if $\Delta E=E$. Yet, the problem remained open when $\Delta E\ne E$. We consider the unified bound that involves both $\Delta E$ and $E$. We prove that there exist no initial states that saturate the bound if $\Delta E\ne E$. However, the bound remains tight: for any values of $\Delta E$ and $E$, there exists a one-parameter family of initial states that can approach the bound arbitrarily close when the parameter approaches its limit. These results establish the fundamental limit of the operation rate of any information processing system.

We propose a second renormalization group method to handle the tensor-network states or models. This method dramatically reduces the truncation error of the tensor renormalization group. It allows physical quantities of classical tensor-network models or tensor-network ground states of quantum systems to be accurately and efficiently determined.

The very small size of optical nonlinearities places strict restrictions on the types of novel physics one can explore. This work describes how a single artificial multilevel Cooper pair box molecule, interacting with a superconducting microwave coplanar resonator, when suitably driven, can generate extremely large optical nonlinearities at microwave frequencies, with no associated absorption. We describe how the giant self-Kerr effect can be detected by measuring the second-order correlation function and quadrature squeezing spectrum.

We investigate the propagation of spin impurity atoms through a strongly interacting one-dimensional Bose gas. The initially well localized impurities are accelerated by a constant force, very much analogous to electrons subject to a bias voltage, and propagate as a one-dimensional impurity spin wave packet. We follow the motion of the impurities in situ and characterize the interaction induced dynamics. We observe a very complex nonequilibrium dynamics, including the emergence of large density fluctuations in the remaining Bose gas, and multiple scattering events leading to dissipation of the impurity’s motion.

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix $A$ and a vector $\overrightarrow{b}$, find a vector $\overrightarrow{x}$ such that $A\overrightarrow{x}=\overrightarrow{b}$. We consider the case where one does not need to know the solution $\overrightarrow{x}$ itself, but rather an approximation of the expectation value of some operator associated with $\overrightarrow{x}$, e.g., ${\overrightarrow{x}}^{†}M\overrightarrow{x}$ for some matrix $M$. In this case, when $A$ is sparse, $N\times N$ and has condition number $\kappa$, the fastest known classical algorithms can find $\overrightarrow{x}$ and estimate ${\overrightarrow{x}}^{†}M\overrightarrow{x}$ in time scaling roughly as $N\sqrt{\kappa }$. Here, we exhibit a quantum algorithm for estimating ${\overrightarrow{x}}^{†}M\overrightarrow{x}$ whose runtime is a polynomial of $\log (N)$ and $\kappa$. Indeed, for small values of $\kappa$ [i.e., $\mathrm{poly}\log (N)$], we prove (using some common complexity-theoretic assumptions) that any classical algorithm for this problem generically requires exponentially more time than our quantum algorithm.

Quantum multiphoton interferometry has now reached the six-photon stage. Thus far, the observed fidelities of entangled states never reached $2/3$. We report a high fidelity (estimated at 88%) experiment in which six-qubit singlet correlations were observed. With such a high fidelity we are able to demonstrate the central property of these “singlet” correlations, their “rotational invariance,” by performing a full set of measurements in three complementary polarization bases. The patterns are almost indistinguishable. The data reveal genuine six-photon entanglement. We also study several five-photon states, which result upon detection of one of the photons. Multiphoton singlet states survive some types of depolarization and are thus important in quantum communication schemes.

We present the experimental realization of a scheme, based on single-photon interference, for implementing superpositions of distinct quantum operations. Its application to a thermal light field (a well-categorized classical entity) illustrates quantum superposition from a new standpoint and provides a direct and quantitative verification of the bosonic commutation relation between creation and annihilation operators. By shifting the focus towards operator superpositions, this result opens interesting alternative perspectives for manipulating quantum states.

We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong interaction and relatively low temperature. Using the new formulation, we discuss the qualitative features of finite-temperature crossover and make quantitative predictions on the density profiles in traps. We propose a practical two-stage scheme to achieve accurate thermometry for a trapped spin-imbalanced Fermi gas.

Inspired by experiments on Bose-Einstein condensates in optical lattices, we study the quantum evolution of dark soliton initial conditions in the context of the Bose-Hubbard Hamiltonian. An extensive set of quantum measures is utilized in our analysis, including von Neumann and generalized quantum entropies, quantum depletion, and the pair correlation function. We find that quantum effects cause the soliton to fill in. Moreover, soliton-soliton collisions become inelastic, in strong contrast to the predictions of mean-field theory. These features show that the lifetime and collision properties of dark solitons in optical lattices provide clear signals of quantum effects.

Quantum phase transitions occur at zero temperature, when the ground state of a Hamiltonian undergoes a qualitative change as a function of a control parameter. We consider a particularly interesting system with competing one-, two-, and three-body interactions. Depending on the relative strength of these interactions, the ground state of the system can be a product state, or it can exhibit genuine tripartite entanglement. We experimentally simulate such a system in a NMR quantum simulator and observe the different ground states. By adiabatically changing the strength of one coupling constant, we push the system from one ground state to a qualitatively different ground state. We show that these ground states can be distinguished and the transitions between them observed by measuring correlations between the spins or the expectation values of suitable entanglement witnesses.

We compute exactly the mean perimeter and area of the convex hull of $N$ independent planar Brownian paths each of duration $T$, both for open and closed paths. We show that the mean perimeter $⟨L_N⟩={\alpha }_N\sqrt{T}$ and the mean area $⟨A_N⟩={\beta }_{N}T$ for all $T$. The prefactors ${\alpha }_N$ and ${\beta }_N$, computed exactly for all $N$, increase very slowly (logarithmically) with increasing $N$. This slow growth is a consequence of extreme value statistics and has interesting implications in an ecological context in estimating the home range of a herd of animals with a population size $N$.

We investigate experimentally the entropy transfer between two distinguishable atomic quantum gases at ultralow temperatures. Exploiting a species-selective trapping potential, we are able to control the entropy of one target gas in presence of a second auxiliary gas. With this method, we drive the target gas into the degenerate regime in conditions of controlled temperature by transferring entropy to the auxiliary gas. We envision that our method could be useful both to achieve the low entropies required to realize new quantum phases and to measure the temperature of atoms in deep optical lattices. We verified the thermalization of the two species in a 1D lattice.

We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove the compressibility of the system on the superfluid–insulator critical line and in its neighborhood. These conclusions follow from a general theorem of inclusions, which states that for any transition in a disordered system, one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for the nature of the Mott insulator to Bose glass phase transition: the critical disorder bound ${\Delta }_c$ corresponding to the onset of disorder-induced superfluidity, satisfies the relation ${\Delta }_c>E_{g/2}$, with $E_{g/2}$ the half-width of the Mott gap in the pure system.

We illustrate that open quantum systems composed of neutral, ultracold atoms in one-dimensional optical lattices can exhibit behavior analogous to semiconductor electronic circuits. A correspondence is demonstrated for bosonic atoms, and the experimental requirements to realize these devices are established. The analysis follows from a derivation of a quantum master equation for this general class of open quantum systems.

We report on residual-gas damping of the motion of a macroscopic test mass enclosed in a nearby housing in the molecular flow regime. The damping coefficient, and thus the associated thermal force noise, is found to increase significantly when the distance between the test mass and surrounding walls is smaller than the test mass itself. The effect has been investigated with two torsion pendulums of different geometry and has been modeled in a numerical simulation whose predictions are in good agreement with the measurements. Relevant to a wide variety of small-force experiments, the residual-gas force noise power for the test masses in the LISA gravitational wave observatory is roughly a factor 15 larger than in an infinite gas volume, though still compatible with the target acceleration noise of $3\mathrm{fm}{\mathrm{s}}^{-2}{\mathrm{Hz}}^{-1/2}$ at the foreseen pressure below ${10}^{-6}\mathrm{Pa}$.