We consider the general measurement scenario in which the ensemble average of an operator is determined via suitable data processing of the outcomes of a quantum measurement described by a positive operator-valued measure. We determine the optimal processing that minimizes the statistical error of the estimation.

Secret sharing is a multiparty cryptographic task in which some secret information is split into several pieces which are distributed among the participants such that only an authorized set of participants can reconstruct the original secret. Similar to quantum key distribution, in quantum secret sharing, the secrecy of the shared information relies not on computational assumptions, but on laws of quantum physics. Here, we present an experimental demonstration of four-party quantum secret sharing via the resource of four-photon entanglement.

Collisions between bright solitary waves in the 1D Gross-Pitaevskii equation with a harmonic potential, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. A particle analogy for the solitary waves is formulated and shown to be integrable for a two-particle system. The extension to three particles is shown to support chaotic regimes. Good agreement is found between the particle model and simulations of the full wave dynamics, suggesting that the dynamics can be described in terms of solitons both in regular and chaotic regimes, presenting a paradigm for chaos in wave mechanics.

By requiring general-coordinate and conformal invariance of the hydrodynamic equations, we show that the unitary Fermi gas has zero bulk viscosity, $\zeta =0$, in the normal phase. In the superfluid phase, two of the bulk viscosities have to vanish, ${\zeta }_1={\zeta }_2=0$, while the third one ${\zeta }_3$ is allowed to be nonzero.

We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal $X(t)$. As an application, we compute the persistence exponent associated with the probability that the process remains below a nonzero level $M$. When $X(t)$ is a Gaussian process, our results are expressed explicitly in terms of the two-time correlation function, $f(t)=⟨X(0)X(t)⟩$.

We study and characterize a new dynamical regime of underdamped particles in a tilted washboard potential. We find that for small friction in a finite range of forces the particles move essentially nondispersively, that is, coherently, over long intervals of time. The associated distribution of the particle positions moves at an essentially constant velocity and is far from Gaussian-like. This new regime is complementary to, and entirely different from, well-known nonlinear response and large dispersion regimes observed for other values of the external force.

We derive generalized two-superfluid continuity equations for the BEC-BCS crossover in the presence of a Feshbach resonance at $T=0$. In addition, we calculate the velocity of sound throughout both BCS and Bose-Einstein condensation (BEC) regimes.

How important is fast measurement for fault-tolerant quantum computation? Using a combination of existing and new ideas, we argue that measurement times as long as even 1000 gate times or more have a very minimal effect on the quantum accuracy threshold. This shows that slow measurement, which appears to be unavoidable in many implementations of quantum computing, poses no essential obstacle to scalability.

We provide a simple security proof for prepare and measure quantum key distribution protocols employing noisy processing and one-way postprocessing of the key. This is achieved by showing that the security of such a protocol is equivalent to that of an associated key distribution protocol in which, instead of the usual maximally entangled states, a more general private state is distilled. In addition to a more general target state, the usual entanglement distillation tools are employed (in particular, Calderbank-Shor-Steane–like codes), with the crucial difference that noisy processing allows some phase errors to be left uncorrected without compromising the privacy of the key.

We present a method of measuring the quantum state of a harmonic oscillator through instantaneous probe-system selective interactions of the Jaynes-Cummings type. We prove that this scheme is robust to general decoherence mechanisms, allowing the possibility of measuring fast-decaying systems in the weak-coupling regime. This method could be applied to different setups: motional states of trapped ions, microwave fields in cavity or circuit QED, and even intracavity optical fields.

The theoretical existence of photon-number-splitting attacks creates a security loophole for most quantum key distribution (QKD) demonstrations that use a highly attenuated laser source. Using ultralow-noise, high-efficiency transition-edge sensor photodetectors, we have implemented the first version of a decoy-state protocol that incorporates finite statistics without the use of Gaussian approximations in a one-way QKD system, enabling the creation of secure keys immune to photon-number-splitting attacks and highly resistant to Trojan horse attacks over 107 km of optical fiber.

We report on the experimental implementation of a Bennett-Brassard 1984 (BB84) protocol type quantum key distribution over a 144 km free-space link using weak coherent laser pulses. Optimization of the link transmission was achieved with bidirectional active telescope tracking, and the security was ensured by employing decoy-state analysis. This enabled us to distribute a secure key at a rate of $12.8\mathrm{bit}/\mathrm{s}$ at an attenuation of about 35 dB. Utilizing a simple transmitter setup and an optical ground station capable of tracking a spacecraft in low earth orbit, this outdoor experiment demonstrates the feasibility of global key distribution via satellites.

We demonstrate the decoy-state quantum key distribution (QKD) with one-way quantum communication in polarization space over 102 km. Further, we simplify the experimental setup and use only one detector to implement the one-way decoy-state QKD over 75 km, with the advantage to overcome the security loopholes due to the efficiency mismatch of detectors. Our experimental implementation can really offer the unconditionally secure final keys. We use 3 different intensities of 0, 0.2, and 0.6 for the light sources in our experiment. In order to eliminate the influences of polarization mode dispersion in the long-distance single-mode optical fiber, an automatic polarization compensation system is utilized to implement the active compensation.

We propose to use the recently predicted two-dimensional “weak-pairing” $p_x+i{p}_y$ superfluid state of fermionic cold atoms as a platform for topological quantum computation. In the core of a vortex, this state supports a zero-energy Majorana mode, which moves to finite energy in the corresponding topologically trivial “strong-pairing” state. By braiding vortices in the “weak-pairing” state, unitary quantum gates can be applied to the Hilbert space of Majorana zero modes. For readout of the topological qubits, we propose realistic schemes suitable for atomic superfluids.

We introduce a hierarchy of conditions necessarily satisfied by any distribution $P_{\alpha \beta }$ representing the probabilities for two separate observers to obtain outcomes $\alpha$ and $\beta$ when making local measurements on a shared quantum state. Each condition in this hierarchy is formulated as a semidefinite program. Among other applications, our approach can be used to obtain upper bounds on the quantum violation of an arbitrary Bell inequality. It yields, for instance, tight bounds for the violations of the Collins et al. inequalities.

The Particle Data Group gives an upper bound on the photon mass $m<2\times {10}^{-16}\mathrm{eV}$ from a laboratory experiment and lists, but does not adopt, an astronomical bound $m<3\times {10}^{-27}\mathrm{eV}$, both of which are based on the plausible assumption of large galactic vector potential. We argue that the interpretations of these experiments should be changed, which alters significantly the bounds on $m$. If $m$ arises from a Higgs effect, both limits are invalid because the Proca vector potential of the galactic magnetic field may be neutralized by vortices giving a large-scale magnetic field that is effectively Maxwellian. If, on the other hand, the galactic magnetic field is in the Proca regime, the very existence of the observed large-scale magnetic field gives $m^{-1}\gtrsim 1\mathrm{kpc}$, or $m\lesssim {10}^{-26}\mathrm{eV}$.

We present a Hamiltonian that can be used for amplifying the signal from a quantum state, enabling the measurement of a macroscopic observable to determine the state of a single spin. We prove a general mapping between this Hamiltonian and an exchange Hamiltonian for arbitrary coupling strengths and local magnetic fields. This facilitates the use of existing schemes for perfect state transfer to give perfect amplification. We further prove a link between the evolution of this fixed Hamiltonian and classical cellular automata, thereby unifying previous approaches to this amplification task. Finally, we show how to use the new Hamiltonian for perfect state transfer in the scenario where total spin is not conserved during the evolution, and demonstrate that this yields a significantly different response in the presence of decoherence.

It is possible to achieve an arbitrary amount of entanglement between two atoms using only spontaneously emitted photons, linear optics, single-photon sources, and projective measurements. This is in contrast to all current experimental proposals for entangling two atoms, which are fundamentally restricted to one entanglement bit or “ebit.”

We provide a complete analysis of mixed three-qubit states composed of a Greenberger-Horne-Zeilinger state and a $W$ state orthogonal to the former. We present optimal decompositions and convex roofs for the three-tangle. Further, we provide an analytical method to decide whether or not an arbitrary rank-2 state of three qubits has vanishing three-tangle. These results highlight intriguing differences compared to the properties of two-qubit mixed states, and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states. By studying the Coffman-Kundu-Wootters inequality we find that, while the amounts of inequivalent entanglement types strictly add up for pure states, this “monogamy” can be lifted for mixed states by virtue of vanishing tangle measures.

The density matrix renormalization group approach is arguably the most successful method to numerically find ground states of quantum spin chains. It amounts to iteratively locally optimizing matrix-product states, aiming at better and better approximating the true ground state. To date, both a proof of convergence to the globally best approximation and an assessment of its complexity are lacking. Here we establish a result on the computational complexity of an approximation with matrix-product states: The surprising result is that when one globally optimizes over several sites of local Hamiltonians, avoiding local optima, one encounters in the worst case a computationally difficult NP-hard problem (hard even in approximation). The proof exploits a novel way of relating it to binary quadratic programming. We discuss intriguing ramifications on the difficulty of describing quantum many-body systems.