We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space. This enhancement is robust with respect to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition principle in Fock space. It is a genuine quantum many-body effect that lies beyond the reach of any mean-field approach. Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss their relevance in the context of many-body thermalization.

Observations in quantum mechanics are subject to complex restrictions arising from the principle of energy conservation. Determining such restrictions, however, has been so far an elusive task, and only partial results are known. In this Letter, we discuss how constraints on the energy spectrum of a measurement device translate into limitations on the measurements which we can effect on a target system with a nonconstant energy operator. We provide efficient algorithms to characterize such limitations and, in case the target is a two-level quantum system, we quantify them exactly. Our Letter, thus, identifies the boundaries between what is possible or impossible to measure, i.e., between what we can see or not, when energy conservation is at stake.

An important problem in quantum information processing is the certification of the dimension of quantum systems without making assumptions about the devices used to prepare and measure them, that is, in a device-independent manner. A crucial question is whether such certification is experimentally feasible for high-dimensional quantum systems. Here we experimentally witness in a device-independent manner the generation of six-dimensional quantum systems encoded in the orbital angular momentum of single photons and show that the same method can be scaled, at least, up to dimension 13.

We address the problem of compiling quantum operations into braid representations for non-Abelian quasiparticles described by the Fibonacci anyon model. We classify the single-qubit unitaries that can be represented exactly by Fibonacci anyon braids and use the classification to develop a probabilistically polynomial algorithm that approximates any given single-qubit unitary to a desired precision by an asymptotically depth-optimal braid pattern. We extend our algorithm in two directions: to produce braids that allow only single-strand movement, called weaves, and to produce depth-optimal approximations of two-qubit gates. Our compiled braid patterns have depths that are 20 to 1000 times shorter than those output by prior state-of-the-art methods, for precisions ranging between $10^{-10}$ and $10^{-30}$.

We use a relationship between response and correlation function in nonequilibrium systems to establish a connection between the heat production and the deviations from the equilibrium fluctuation-dissipation theorem. This scheme extends the Harada-Sasa formulation [Phys. Rev. Lett. 95, 130602 (2005)], obtained for Langevin equations in steady states, as it also holds for transient regimes and for discrete jump processes involving small entropic changes. Moreover, a general formulation includes two times and the new concepts of two-time work, kinetic energy, and of a two-time heat exchange that can be related to a nonequilibrium “effective temperature.” Numerical simulations of a chain of anharmonic oscillators and of a model for a molecular motor driven by adenosine triphosphate hydrolysis illustrate these points.

We report on an experimental test of classical and quantum dimension. We have used a dimension witness that can distinguish between quantum and classical systems of dimensions two, three, and four and performed the experiment for all five cases. The witness we have chosen is a base of semi-device-independent cryptographic and randomness expansion protocols. Therefore, the part of the experiment in which qubits were used is a realization of these protocols. In our work we also present an analytic method for finding the maximum quantum value of the witness along with corresponding measurements and preparations. This method is quite general and can be applied to any linear dimension witness.

Separability criteria are typically of the necessary, but not sufficient, variety, in that satisfying some separability criterion, such as positivity of eigenvalues under partial transpose, does not strictly imply separability. Certifying separability amounts to proving the existence of a decomposition of a target mixed state into some convex combination of separable states; determining the existence of such a decomposition is “hard.” We show that it is effective to ask, instead, if the target mixed state “fits” some preconstructed separable form, in that one can generate a sufficient separability criterion relevant to all target states in some family by ensuring enough degrees of freedom in the preconstructed separable form. We demonstrate this technique by inducing a sufficient criterion for “diagonally symmetric” states of $N$ qubits. A sufficient separability criterion opens the door to study precisely how entanglement is (not) formed; we use ours to prove that, counterintuitively, entanglement is not generated in idealized Dicke model superradiance despite its exemplification of many-body effects. We introduce a quantification of the extent to which a given preconstructed parametrization comprises the set of all separable states; for “diagonally symmetric” states our preconstruction is shown to be fully complete. This implies that our criterion is necessary in addition to sufficient, among other ramifications which we explore.

In quantum mechanics, observing is not a passive act. Consider a system of two quantum particles $A$ and $B$: if a measurement apparatus $M$ is used to make an observation on $B$, the overall state of the system $AB$ will typically be altered. When this happens, no matter which local measurement is performed, the two objects $A$ and $B$ are revealed to possess peculiar correlations known as quantum discord. Here, we demonstrate experimentally that the very act of local observation gives rise to an activation protocol which converts discord into distillable entanglement, a stronger and more useful form of quantum correlations, between the apparatus $M$ and the composite system $AB$. We adopt a flexible two-photon setup to realize a three-qubit system ($A$, $B$, $M$) with programmable degrees of initial correlations, measurement interaction, and characterization processes. Our experiment demonstrates the fundamental mechanism underpinning the ubiquitous act of observing the quantum world and establishes the potential of discord in entanglement generation.

Machines are only Carnot efficient if they are reversible, but then their power output is vanishingly small. Here we ask, what is the maximum efficiency of an irreversible device with finite power output? We use a nonlinear scattering theory to answer this question for thermoelectric quantum systems, heat engines or refrigerators consisting of nanostructures or molecules that exhibit a Peltier effect. We find that quantum mechanics places an upper bound on both power output and on the efficiency at any finite power. The upper bound on efficiency equals Carnot efficiency at zero power output but decays with increasing power output. It is intrinsically quantum (wavelength dependent), unlike Carnot efficiency. This maximum efficiency occurs when the system lets through all particles in a certain energy window, but none at other energies. A physical implementation of this is discussed, as is the suppression of efficiency by a phonon heat flow.

Bender et al. [Phys. Rev. Lett. 80, 5243 (1998)] have developed $\mathcal{P}\mathcal{T}$-symmetric quantum theory as an extension of quantum theory to non-Hermitian Hamiltonians. We show that when this model has a local $\mathcal{P}\mathcal{T}$ symmetry acting on composite systems, it violates the nonsignaling principle of relativity. Since the case of global $\mathcal{P}\mathcal{T}$ symmetry is known to reduce to standard quantum mechanics A. Mostafazadeh [J. Math. Phys. 43, 205 (2001)], this shows that the $\mathcal{P}\mathcal{T}$-symmetric theory is either a trivial extension or likely false as a fundamental theory.

We introduce the Uhlmann geometric phase as a tool to characterize symmetry-protected topological phases in one-dimensional fermion systems, such as topological insulators and superconductors. Since this phase is formulated for general mixed quantum states, it provides a way to extend topological properties to finite temperature situations. We illustrate these ideas with some paradigmatic models and find that there exists a critical temperature $T_c$ at which the Uhlmann phase goes discontinuously and abruptly to zero. This stands as a borderline between two different topological phases as a function of the temperature. Furthermore, at small temperatures we recover the usual notion of topological phase in fermion systems.

In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide an explicit algorithm for estimating parameters of physical models given access to a simulator which is only capable of producing sample outcomes. Since our algorithm does not require that a simulator be able to efficiently compute exact probabilities, it is able to exponentially outperform standard algorithms based on exact computation. In this way, our algorithm opens the door for the application of new insights and resources to the problem of characterizing large quantum systems, which is exponentially intractable using standard simulation resources.

In the ongoing discussion on thermalization in closed quantum many-body systems, the eigenstate thermalization hypothesis has recently been proposed as a universal concept and has attracted considerable attention. So far this concept is, as the name states, hypothetical. The majority of attempts to overcome this hypothetical character are based on exact diagonalization, which implies for, e.g., spin systems a limitation of roughly 15 spins. In this Letter we present an approach that pushes this limit up to system sizes of roughly 35 spins, thereby going significantly beyond what is possible with exact diagonalization. A concrete application to a Heisenberg spin ladder which yields conclusive results is demonstrated.

We demonstrate a client-server quantum key distribution (QKD) scheme. Large resources such as laser and detectors are situated at the server side, which is accessible via telecom fiber to a client requiring only an on-chip polarization rotator, which may be integrated into a handheld device. The detrimental effects of unstable fiber birefringence are overcome by employing the reference-frame-independent QKD protocol for polarization qubits in polarization maintaining fiber, where standard QKD protocols fail, as we show for comparison. This opens the way for quantum enhanced secure communications between companies and members of the general public equipped with handheld mobile devices, via telecom-fiber tethering.

Deterministic quantum computation with one quantum bit (DQC1) [E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)] is a model of quantum computing where the input is restricted to containing a single qubit in a pure state and has all other qubits in a completely mixed state. Only the single pure qubit is measured at the end of the computation. While it is known that DQC1 can efficiently solve several problems for which no known classical efficient algorithms exist, the question of whether DQC1 is really more powerful than classical computation remains open. In this Letter, we introduce a slightly modified version of DQC1, which we call $\mathrm{DQC}{1}_k$, where $k$ output qubits are measured, and show that $\mathrm{DQC}{1}_k$ cannot be classically efficiently simulated for any $k\ge 3$ unless the polynomial hierarchy collapses at the third level.

We present the complete result for the $\mathcal{O}({\alpha }^7{m}_e)$ one photon annihilation contribution to the hyperfine splitting of the ground state energy levels in positronium. Numerically it increases the prediction of quantum electrodynamics by $217\pm 1\mathrm{kHz}$.

Comprehensive no-go theorems show that information encoded over local two-dimensional topologically ordered systems cannot support macroscopic energy barriers, and hence will not maintain stable quantum information at finite temperatures for macroscopic time scales. However, it is still well motivated to study low-dimensional quantum memories due to their experimental amenability. Here we introduce a grid of defect lines to Kitaev’s quantum double model where different anyonic excitations carry different masses. This setting produces a complex energy landscape which entropically suppresses the diffusion of excitations that cause logical errors. We show numerically that entropically suppressed errors give rise to superexponential inverse temperature scaling and polynomial system size scaling for small system sizes over a low-temperature regime. Curiously, these entropic effects are not present below a certain low temperature. We show that we can vary the system to modify this bound and potentially extend the described effects to zero temperature.