Coherent superposition is a key feature of quantum mechanics that underlies the advantage of quantum technologies over their classical counterparts. Recently, coherence has been recast as a resource theory in an attempt to identify and quantify it in an operationally well-defined manner. Here we study how the coherence present in a state can be used to implement a quantum channel via incoherent operations and, in turn, to assess its degree of coherence. We introduce the robustness of coherence of a quantum channel---which reduces to the homonymous measure for states when computed on constant-output channels---and prove that: i) it quantifies the minimal rank of a maximally coherent state required to implement the channel; ii) its logarithm quantifies the amortized cost of implementing the channel provided some coherence is recovered at the output; iii) its logarithm also quantifies the zero-error asymptotic cost of implementation of many independent copies of a channel. We also consider the generalized problem of imperfect implementation with arbitrary resource states. Using the robustness of coherence, we find that in general a quantum channel can be implemented without employing a maximally coherent resource state. In fact, we prove that \textit{every} pure coherent state in dimension larger than $2$, however weakly so, turns out to be a valuable resource to implement \textit{some} coherent unitary channel. We illustrate our findings for the case of single-qubit unitary channels.

The permutational invariance of identical two-level systems allows for an exponential reduction in the computational resources required to study the Lindblad dynamics of coupled spin-boson ensembles evolving under the effect of both local and collective noise. Here we take advantage of this speedup to study several important physical phenomena in the presence of local incoherent processes, in which each degree of freedom couples to its own reservoir. Assessing the robustness of collective effects against local dissipation is paramount to predict their presence in different physical implementations. We have developed an open-source library in Python, the Permutational-Invariant Quantum Solver (PIQS), which we use to study a variety of phenomena in driven-dissipative open quantum systems. We consider both local and collective incoherent processes in the weak, strong, and ultrastrong-coupling regimes. Using PIQS, we reproduced a series of known physical results concerning collective quantum effects and extended their study to the local driven-dissipative scenario \cite{Johansson12,Johansson13}. Our work addresses the robustness of various collective phenomena, e.g., spin squeezing, superradiance, quantum phase transitions, against local dissipation processes.

The issue of time travel can be reduced in quantum theory to an appropriate Hilbert-space description of feedback loops. I show how to do it in a way that automatically eliminates problems with chronology protection, provided all input-output relations are given by unitary maps. Examples of elementary loops and a two-loop time machine illustrate the construction.

The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The contributions of this work are threefold. First of all, we build upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes. Together with our classification we also provide lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects. Our work thus provides an explicit toy model that will help to better understand the abstract theory of domain walls. Secondly, we discover a number of interesting new applications of the cataloged objects for quantum information protocols. These include improved methods for performing quantum computations by code deformation, a new four-qubit error-detecting code, as well as families of new quantum error-correcting codes we call stellated color codes, which encode logical qubits at the same distance as the next best color code, but using approximately half the number of physical qubits. To the best of our knowledge, our new topological codes have the highest encoding rate of local stabilizer codes with bounded-weight stabilizers in two dimensions. Finally, we show how the boundaries and twist defects of the color code are represented by multiple copies of other phases. Indeed, in addition to the well studied comparison between the color code and two copies of the surface code, we also compare the color code to two copies of the three-fermion model. In particular, we find that this analogy offers a very clear lens through which we can view the symmetries of the color code which gives rise to its multitude of domain walls.

The classical and quantum mechanical correspondence for constant mass settings is used, along with some point canonical transformation, to find the position-dependent mass (PDM) classical and quantum Hamiltonians. The comparison between the resulting quantum PDM-Hamiltonian and the von Roos PDM-Hamiltonian implied that the ordering ambiguity parameters of von Roos are strictly determined. Eliminating, in effect, the ordering ambiguity associated with the von Roos PDM-Hamiltonian. This, consequently, played a vital role in the construction and identification of the PDM-momentum operator. The same recipe is followed to identify the form of the minimal coupling of electromagnetic interactions for the classical and quantum PDM-Hamiltonians. It turned out that whilst the minimal coupling may very well inherit the usual form in classical mechanics, it admits a necessarily different and vital form in quantum mechanics. Under our point transformation settings, only one of the two commonly used vector potentialsis found eligible and is considered for our Illustrative examples.

We describe the design and implementation of a stable high-power 1064 nm laser system to generate optical lattices for experiments with ultracold quantum gases. The system is based on a low-noise laser amplified by an array of four heavily modified, high-power fiber amplifiers. The beam intensity is stabilized and controlled with a nonlinear feedback loop. Using real-time monitoring of the resulting optical lattice, we find the stability of the lattice site positions to be well below the lattice spacing for several hours. The pointing stability of the optical lattice beams is around one lattice spacing and the long-term (six month) relative stability of the lattice spacing itself is 0.5% RMS.

Full quantum capability devices can provide secure communications, but they are challenging to make portable given the current technology. Besides, classical portable devices are unable to construct communication channels resistant to quantum computers. Hence, communication security on portable devices cannot be guaranteed. Semi-Quantum Key Distribution (SQKD) and Semi-Quantum Direct Communication (SQDC) attempt to break the quandary by lowering the receiver's required quantum capability so that secure communications can be implemented on a portable device. However, all SQKD and SQDC protocols have low qubit efficiency and complex hardware implementations. The protocols involving quantum entanglement require linear Entanglement Preservation Time (EPT) and linear quregister size. In this paper, we propose two new no-key SQDC protocols that address the aforementioned weaknesses. They are named Economic No-key SQDC (ENKSQDC) and Rate Estimation ENKSQDC (RENKSQDC). They achieve theoretically constant minimal EPT and quregister size, regardless of message length. We show that the new protocols, with low overhead, can detect Measure and Replay Attacks (MRAs). RENKSQDC is tolerant to transmission impairments and environmental perturbations. The protocols are based on a new quantum message transmission operation termed Tele-Conjure. Like QKD, their strength depends on physical principles rather than mathematical complexity.

The performance enhancements observed in various models of continuous quantum thermal machines have been linked to the buildup of coherences in a preferred basis. But, is this connection always an evidence of 'quantum-thermodynamic supremacy'? By force of example, we show that this is not the case. In particular, we compare a power-driven three-level quantum refrigerator with a four-level combined cycle, partly driven by power and partly by heat. We focus on the weak driving regime and find the four-level model to be superior since it can operate in parameter regimes in which the three-level model cannot, it may exhibit a larger cooling rate, and, simultaneously, a better coefficient of performance. Furthermore, we find that the improvement in the cooling rate matches the increase in the stationary quantum coherences exactly. Crucially, though, we also show that the thermodynamic variables for both models follow from a classical representation based on graph theory. This implies that we can build incoherent stochastic-thermodynamic models with the same steady-state operation or, equivalently, that both coherent refrigerators can be simulated classically. More generally, we prove this for any $ N $-level weakly driven device with a 'cyclic' pattern of transitions. Therefore, even if coherence is present in a thermal machine, it is often unnecessary for the underlying energy conversion process.

Quantum simulation of complex quantum systems and their properties often requires the ability to prepare initial states in an eigenstate of the Hamiltonian to be simulated. In addition, to compute the eigenvalues of a Hamiltonian is in general a non-trivial problem. Here, we propose a hybrid quantum-classical probabilistic method to compute eigenvalues and prepare eigenstates of Hamiltonians which are simulatable with a trapped-ion quantum processor.

Scalable quantum computing relies crucially on high-fidelity entangling operations. Here we demonstrate that four coupled qubits can operate as a high-fidelity two-qubit entangling gate that swaps two target qubits and adds a relative sign on the $\lvert 11 \rangle$ state (ZSWAP). The gate operation is controlled by the state of two ancilla (control) qubits. The system is readily implementable with superconducting qubits, using capacitively coupled qubits arranged in a diamond-shaped architecture. By using realistic device and noise parameters from state-of-the-art superconducting qubits, we show that the conditional ZSWAP operation can be implemented with a fidelity above 0.99 in a time $t_g \sim 65$ ns.

Most Quantum Key Distribution protocols use a two-dimensional basis such as HV polarization as first proposed by Bennett and Brassard in 1984. These protocols are consequently limited to a key generation density of 1 bit per photon. We increase this key density by encoding information in the transverse spatial displacement of the used photons. Employing this higher-dimensional Hilbert space together with modern single-photon-detecting cameras, we demonstrate experimentally large-alphabet Quantum Key Distribution with 1024 symbols and a shared information between sender and receiver of 7 bit per photon.

We provide a unified and strengthened framework for the product form and the sum form variance-based uncertainty relations by constructing a unified uncertainty relation. In the unified framework, we deduce that the uncertainties of the incompatible observables are bounded by not only the commutator of themselves, but also the quantities related with the other operator. This operator can provide information so that we can capture the uncertainty of the measurement result more accurately, and thus is named as the information operator. The introduction of the information operator can fix the deficiencies in both the product form and the sum form uncertainty relations, and provides a more accurate description of the quantum uncertainty relation. The unified framework also proposes a new interpretation of the uncertainty relation for non-Hermitian operators; i.e., the "observable" second-order origin moments of the non-Hermitian operators cannot be arbitrarily small at the same time when they are generalized-incompatible on the new definition of the generalized commutator.

We consider an algorithm to approximate complex-valued periodic functions $f(e^{i\theta})$ as a matrix element of a product of $SU(2)$-valued functions, which underlies so-called quantum signal processing. We prove that the algorithm runs in time $\mathcal O(N^3 \mathrm{polylog}(N/\epsilon))$ under the random-access memory model of computation where $N$ is the degree of the polynomial that approximates $f$ with accuracy $\epsilon$; previous efficiency claim assumed a strong arithmetic model of computation and lacked numerical stability analysis.

Weak values have been shown to be helpful especially when considering them as the outcomes of weak measurements. In this paper we show that in principle, the real and imaginary parts of the weak value of any operator may be elucidated from expectation values of suitably defined density, flux and hermitian commutator operators. Expectation values are the outcomes of strong (projective) measurements implying that weak values are general properties of operators in association with pre- and post-selection and they need not be preferentially associated with weak measurements. They should be considered as an important measurable property which provides added information as compared with the "standard" diagonal expectation value of an operator. As a first specific example we consider the determination of the real and imaginary parts of the weak value of the momentum operator employing projective time of flight experiments. Then the results are analyzed from the point of view of Bohmian mechanics. Finally we consider recent neutron interferometry experiments used to determine the weak values of the neutron spin.

Author(s): Paul A. Knott, Tommaso Tufarelli, Marco Piani, and Gerardo Adesso

Quantum Darwinism posits that information becomes objective whenever multiple observers indirectly probe a quantum system by each measuring a fraction of the environment. It was recently shown that objectivity of observables emerges generically from the mathematical structure of quantum mechanics, w...

[Phys. Rev. Lett. 121, 160401] Published Wed Oct 17, 2018

Author(s): Felix Leditzky, Debbie Leung, and Graeme Smith

The quantum capacity of a quantum channel captures its capability for noiseless quantum communication. It lies at the heart of quantum information theory. Unfortunately, our poor understanding of nonadditivity of coherent information makes it hard to understand the quantum capacity of all but very s...

[Phys. Rev. Lett. 121, 160501] Published Wed Oct 17, 2018

Author(s): Luca Mancino, Vasco Cavina, Antonella De Pasquale, Marco Sbroscia, Robert I. Booth, Emanuele Roccia, Ilaria Gianani, Vittorio Giovannetti, and Marco Barbieri

Theoretical bounds on irreversible entropy production in a thermalizing quantum system are supported by experiments simulating the thermalization of a qubit using a quantum photonic architecture.

[Phys. Rev. Lett. 121, 160602] Published Wed Oct 17, 2018

Author(s): Jacopo De Nardis, Denis Bernard, and Benjamin Doyon

We show that hydrodynamic diffusion is generically present in many-body, one-dimensional interacting quantum and classical integrable models. We extend the recently developed generalized hydrodynamic (GHD) to include terms of Navier-Stokes type, which leads to positive entropy production and diffusi...

[Phys. Rev. Lett. 121, 160603] Published Wed Oct 17, 2018

Author(s): M. Brunelli, L. Fusco, R. Landig, W. Wieczorek, J. Hoelscher-Obermaier, G. Landi, F. L. Semião, A. Ferraro, N. Kiesel, T. Donner, G. De Chiara, and M. Paternostro

Physicists observe entropy production in two intermediate-scale quantum systems, indicating that the systems have undergone an irreversible process.

[Phys. Rev. Lett. 121, 160604] Published Wed Oct 17, 2018

Author(s): Y. B. Band, Y. Avishai, and Alexander Shnirman

An analysis of a single-domain magnetic needle (MN) in the presence of an external magnetic field B is carried out with the aim of achieving a high-precision magnetometer. We determine the uncertainty ΔB of such a device due to Gilbert dissipation and the associated internal magnetic field fluctuati...

[Phys. Rev. Lett. 121, 160801] Published Wed Oct 17, 2018