We characterize the set of shared quantum states which contain a cryptographically private key. This allows us to recast the theory of privacy as a paradigm closely related to that used in entanglement manipulation. It is shown that one can distill an arbitrarily secure key from bound entangled states. There are also states that have less distillable private keys than the entanglement cost of the state. In general, the amount of distillable key is bounded from above by the relative entropy of entanglement. Relationships between distillability and distinguishability are found for a class of states which have Bell states correlated to separable hiding states. We also describe a technique for finding states exhibiting irreversibility in entanglement distillation.

We construct a device that can unambiguously discriminate between two unknown quantum states. The unknown states are provided as inputs, or programs, for the program registers, and a third system, which is guaranteed to be prepared in one of the states stored in the program registers, is fed into the data register of the device. The device will then, with some probability of success, tell us whether the unknown state in the data register matches the state stored in the first or the second program register. We show that the optimal device, i.e., the one that maximizes the probability of success, is universal. It does not depend on the actual unknown states that we wish to discriminate.

We show that a Bose-condensed gas, under extreme rotation in a 2D anisotropic trap, forms a novel elongated quantum fluid which has a roton-maxon excitation spectrum. For a sufficiently large interaction strength, the roton energy reaches zero and the system undergoes a second order quantum transition to the state with a periodic structure—rows of vortices. The number of rows increases with the interaction, and the vortices eventually form a triangular Abrikosov lattice.

We consider the storage and transmission of a Gaussian distributed set of coherent states of continuous variable systems. We prove a limit on the average fidelity achievable when the states are transmitted or stored by a classical channel, i.e., a measure and repreparation scheme which sends or stores classical information only. The obtained bound is tight and serves as a benchmark which has to be surpassed by quantum channels in order to outperform any classical strategy. The success in experimental demonstrations of quantum memories as well as quantum teleportation has to be judged on this footing.

It is experimentally demonstrated that an arbitrary quantum state of a single spin $1/2$, $a|\uparrow ⟩+b|\downarrow ⟩$, can be converted into a superposition of the two ferromagnetic states of a spin cluster: $a|\uparrow \uparrow \cdots \uparrow \uparrow ⟩+b|\downarrow \downarrow \cdots \downarrow \downarrow ⟩$. The physical system is a cluster of seven dipolar-coupled nuclear spins of single-labeled ${}^{13}\mathrm{C}$-benzene molecules in a liquid-crystalline matrix. In this complex system, the pseudopure ground state and the required controlled unitary transformations have been implemented. The experimental scheme can be considered as an explicit model of quantum measurement.

We present a simple, robust, and efficient method for varying the parameters in a many-body wave function to optimize the expectation value of the energy. The effectiveness of the method is demonstrated by optimizing the parameters in flexible Jastrow factors that include 3-body electron-electron-nucleus correlation terms for the ${\mathrm{NO}}_2$ and decapentaene (${\mathrm{C}}_{10}{\mathrm{H}}_{12}$) molecules. The basic idea is to add terms to the straightforward expression for the Hessian of the energy that have zero expectation value, but that cancel much of the statistical fluctuations for a finite Monte Carlo sample. The method is compared to what is currently the most popular method for optimizing many-body wave functions, namely, minimization of the variance of the local energy. The most efficient wave function is obtained by optimizing a linear combination of the energy and the variance.

We report free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13 km. It is shown that the desired entanglement can still survive after both entangled photons have passed through the noisy ground atmosphere with a distance beyond the effective thickness of the aerosphere. This is confirmed by observing a spacelike separated violation of Bell inequality of $2.45\pm 0.09$. On this basis, we exploit the distributed entangled photon source to demonstrate the Bennett-Brassard 1984 quantum cryptography scheme. The distribution distance of entangled photon pairs achieved in the experiment is for the first time well beyond the effective thickness of the aerosphere, hence presenting a significant step towards satellite-based global quantum communication.

We experimentally demonstrate the first remote state preparation of arbitrary single-qubit states, encoded in the polarization of photons generated by spontaneous parametric down-conversion. Utilizing degenerate and nondegenerate wavelength entangled sources, we remotely prepare arbitrary states at two wavelengths. Further, we derive theoretical bounds on the states that may be remotely prepared for given two-qubit resources.

We propose a protocol for deterministic communication that does not make use of entanglement. It exploits nonorthogonal states in a two-way quantum channel to attain unconditional security and high efficiency of the transmission. We explicitly show the scheme is secure against a class of individual attacks regardless of the noise on the channel. Its experimental realization is feasible with current technology.

We construct a general renormalization-group transformation on quantum states, independent of any Hamiltonian dynamics of the system. We illustrate this procedure for translational invariant matrix product states in one dimension and show that product, Greenberger-Horne-Zeilinger, $W$, and domain wall states are special cases of an emerging classification of the fixed points of this coarse-graining transformation.

The concept of a geometric phase (Berry’s phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry’s phases. Our results are demonstrated with a nonlinear two-level model.

In order to clarify the structure of a singly quantized vortex in a superfluid fermion gas near the Feshbach resonance, we numerically solve the generalized Bogoliubov–de Gennes equation in the boson-fermion model. The superfluid gap, which contains contributions from both condensed fermion pairs and condensed bosons, is self-consistently determined, and the quasiparticle excitation levels bound in the vortex core are explicitly shown. We find that the boson condensate contributes to enhance the matter density depletion and the discreteness of localized quasiparticle spectrum inside the core. It is predicted that the matter density depletion and the discrete core levels are detectable in the vicinity of the BCS–Bose-Einstein condensation crossover point.

We analyze finite temperature effects in the generation of bright solitons in condensates in optical lattices. We show that even in the presence of strong phase fluctuations solitonic structures with a well defined phase profile can be created. We propose a novel family of variational functions which describe well the properties of these solitons and account for the nonlinear effects in the band structure. We discuss also the mobility and collisions of these localized wave packets.

Our realistic numerical results show that the fundamental and higher-order quantum resonances of the $\delta$-kicked rotor are observable in state-of-the-art experiments with a Bose condensate in a shallow harmonic trap, kicked by a spatially periodic optical lattice. For stronger confinement, interaction-induced destruction of the resonant motion of the kicked harmonic oscillator is predicted.

Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information processing. We report the implementation of a concatenated quantum error-correcting code able to correct phase errors with a strong correlated component. The experiment was performed using liquid-state nuclear magnetic resonance techniques on a four spin subsystem of labeled crotonic acid. Our results show that concatenation between active and passive quantum error correction is a practical tool to handle realistic noise involving both independent and correlated errors.

We derive the order parameter of the chiral Potts model, using the method of Jimbo et al. The result agrees with previous conjectures.

The concept of indistinguishability is the key element in quantum statistics. But, are particles really either indistinguishable or distinguishable? Most works begin with the premise that all the particles, for example, in a quantum gas, are indistinguishable. Can we vary the degree of distinguishability in some controlled, continuous manner and see how it affects the behavior of the quantum gas, such as Bose-Einstein condensation (BEC)? We have found a complex parameter with a definite phase that does just that. As it deviates from zero, a gas mixture of originally indistinguishable bosons would divide into several distinct species that undergo BEC individually. Each species is found to be in a new type of atomic state whose spin structure adapts itself to the prevailing densities of the gases in the mixture.

The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultracold atomic Bose-Einstein condensates to condensed matter, biology, and even astrophysics. Here we demonstrate a conceptually simple method of determining the regime of validity of stochastic simulations of unitary quantum dynamics by employing a time-reversal test. We apply this test to a simulation of the evolution of a quantum anharmonic oscillator with up to $6.022\times {10}^{23}$ (Avogadro’s number) of particles. This system is realizable as a Bose-Einstein condensate in an optical lattice, for which the time-reversal procedure could be implemented experimentally.

A gas of interacting atoms confined by a three dimensional anisotropic harmonic potential is studied. It is shown that there appear “new” thermodynamic variables instead of the usual pressure and volume: the latter is replaced by (the inverse of) the cube of the geometric average of the oscillator frequencies of the trap, and the former by the harmonic pressure responsible for the mechanical equilibrium of the fluid in the trap. We discuss the origin and physical meaning of these quantities and show that the equation of state of the gas is given in terms of these variables. The equation of state of a cold gas of interacting Bose atoms in the Hartree-Fock approximation is presented. We indicate how the harmonic pressure can be measured in current experiments.

We report the observation of strongly damped dipole oscillations of a quantum degenerate 1D atomic Bose gas in a combined harmonic and optical lattice potential. Damping is significant for very shallow axial lattices (0.25 photon recoil energies), and increases dramatically with increasing lattice depth, such that the gas becomes nearly immobile for times an order of magnitude longer than the single-particle tunneling time. Surprisingly, we see no broadening of the atomic quasimomentum distribution after damped motion. Recent theoretical work suggests that quantum fluctuations can strongly damp dipole oscillations of a 1D atomic Bose gas, providing a possible explanation for our observations.