It is well known that it is impossible to clone an arbitrary quantum state. However, this inability does not lead directly to no-cloning of quantum coherence. Here, we show that it is impossible to clone the coherence of an arbitrary quantum state which is a stronger statement than the 'no-cloning of quantum state'. In particular, with ancillary system as machine state, we show that it is impossible to clone the coherence of states whose coherence is greater than the coherence of the known states on which the transformations are defined. Also, we characterize the class of states for which coherence cloning will be possible for a given choice of machine. Furthermore, we find the maximum range of states whose coherence can be cloned perfectly. The impossibility proof also holds when we do not include machine states.

Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developing algorithms to calculate the ground state energy of molecules on near-term quantum computers. However, calculating excited state energies has attracted comparatively less attention, and it is currently unclear what the optimal method is. We introduce a low depth, variational quantum algorithm to sequentially calculate the excited states of general Hamiltonians. Incorporating a recently proposed technique, we employ the low depth swap test to energetically penalise the ground state, and transform excited states into ground states of modified Hamiltonians. We use variational imaginary time evolution as a subroutine, which deterministically propagates towards the target eigenstate. We discuss how symmetry measurements can mitigate errors in the swap test step. We numerically test our algorithm on Hamiltonians which encode 3SAT optimisation problems of up to 18 qubits, and the electronic structure of the Lithium Hydride molecule. As our algorithm uses only low depth circuits and variational algorithms, it is suitable for use on near-term quantum hardware.

The models we use, habitually, to describe quantum nonlinear optical processes have been remarkably successful yet, with few exceptions, they each contain a mathematical flaw. We present this flaw, show how it can be fixed and, in the process, suggest why we can continue to use our favoured Hamiltonians.

Entanglement is the key feature of many-body quantum systems, and the development of new tools to probe it in the laboratory is an outstanding challenge. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a new protocol for measuring entropy, based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts - both in the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, applicable to arbitrary quantum states of up to several tens of qubits.

The Janszky representation constructs quantum states of a field mode as a superposition of coherent states on a line in the complex plane. We show that this provides a natural Schr\"{o}dinger picture description of the interference between a pair of modes at a beam splitter.

The mean-field steady states of a generalized model of $N$ two-state systems interacting with one mode of the radiation field in the presence of external driving and dissipation are surveyed as a function of three control parameters: one governs the interaction strength relative to the resonance frequency, thus accessing the Dicke quantum phase transition, a second the relative strength of counter-rotating to rotating-wave interactions, and a third the amplitude of an external field driving the cavity mode. We unify the dissipative extension of the Dicke quantum phase transition with the recently reported breakdown of photon blockade [H.~J.~Carmichael, Phys.\ Rev.\ X {\bf 5}, 031028 (2015)]; key to the unification is a previously unreported phase of the Dicke model and a renormalized critical drive strength in the breakdown of photon blockade. For the simplest case of one two-state system, we complement mean-field results with a full quantum treatment: we derive quasi-energies to recover the renormalized critical drive strength, extend the multi-photon resonances of photon blockade to a counter-rotating interaction, and explore quantum fluctuations through quantum trajectory simulations.

We investigate a quantum annealing approach based on real-time quantum dynamics for graph coloring. In this approach, a driving Hamiltonian is chosen so that constraints are naturally satisfied without penalty terms, and the dimension of the Hilbert space is considerably reduced. The total Hamiltonian, which consists of driving and problem Hamiltonians, resembles a disordered quantum spin chain. The ground state of the problem Hamiltonian for graph coloring is degenerate. This degeneracy is advantageous and is characteristic of this approach. Real-time quantum simulations in a small system demonstrate interesting results and provide some insight into quantum annealing.

We propose a method to verify quantum steering for two qubit states with an arbitrary amount of null measurement outcomes when both steering and steered parties cannot be trusted. We modify a score function that it may depend on the measurement efficiencies of both parties, the number of symmetrically placed measurement settings, and imperfection of the state preparation. The steering bound proposed in a recent work [Phys. Rev. X $2$,031003 (2012)] plays an important role in our score function; thus, similarly, for null measurement outcomes obtained by the steering party with the ratio $1-\eta$, the steering can be verified using the number of different measurement settings larger than $1/\eta$ and maximally steerable states. Furthermore, we show that, for null measurement outcomes at the steered party, the ratio of null measurement outcomes does not affect steerability unless it is $1$. Our result will be helpful to enable loss-tolerant and device-independent steering tasks.

A unit-preserving and completely positive linear map, or a channel, $\Lambda \colon \mathcal{A} \to \mathcal{A}_{\mathrm{in}}$ between $C^\ast$-algebras $\mathcal{A}$ and $\mathcal{A}_{\mathrm{in}}$ is called entanglement-breaking (EB) if $\omega \circ( \Lambda \otimes \mathrm{id}_{\mathcal{B}} ) $ is a separable state for any $C^\ast$-algebra $\mathcal{B}$ and any state $\omega$ on the injective $C^\ast$-tensor product $\mathcal{A}_{\mathrm{in}} \otimes \mathcal{B} .$ In this paper, we establish the equivalence of the following conditions for a channel $\Lambda$ with a quantum input space and with a general outcome $C^\ast$-algebra, generalizing known results in finite dimensions: (i) $\Lambda$ is EB; (ii) $\Lambda$ has a measurement-prepare form (Holevo form); (iii) $n$ copies of $\Lambda$ are compatible for all $2 \leq n < \infty ;$ (iv) countably infinite copies of $\Lambda$ are compatible. By using this equivalence, we also show that the set of randomization-equivalence classes of normal EB channels with a fixed input von Neumann algebra is upper and lower Dedekind-closed, i.e.\ the supremum or infimum of any randomization-increasing or decreasing net of EB channels is also EB.

Collective scattering of spatially coherent radiation by separated point emitters induces inter-particle forces. For particles close to nano-photonic structures as, for example, nano-fibers, hollow core fibers or photonic waveguides, this pair-interaction induced by monochromatic light is periodic and virtually of infinite range. Here we show that the shape and range of the optical interaction potential can be precisely controlled by spectral design of the incoming illumination. If each particle is only weakly coupled to the confined guided modes the forces acting within a particle ensemble can be decomposed to pairwise interactions. These forces can be tailored to almost arbitrary spatial dependence as they are related to Fourier transforms with coefficients controlled by the intensities and frequencies of the illuminating lasers. We demonstrate the versatility of the scheme by highlighting some examples of unconventional pair potentials. Implementing these interactions in a chain of trapped quantum particles could be the basis of a versatile quantum simulator with almost arbitrary all-to-all interaction control.

Nuclear spins in nitrogen-vacancy (NV) centers in diamond are excellent quantum memory for quantum computing and quantum sensing, but are difficult to be initialized due to their weak interactions with the environment. Here we propose and demonstrate a magnetic-field-independent, deterministic and highly efficient polarization scheme by introducing chopped laser pulses into the double-resonance initialization method. With this method, we demonstrate initialization of single-nuclear-spin approaching $98.1\%$ and a $^{14}N$-$^{13}C$ double-nuclear-spin system approaching $96.8\%$ at room temperature. The initialization is limited by a finite illuminated nuclear-spin $T_1$ time. Our approach could be extended to NV systems with more nuclear spins and would be a useful tool in future applications.

We propose definitions and implementations of "supermoney" - virtual tokens designed for high value fast transactions on networks with relativistic or other trusted signalling constraints. Supermoney is more flexible than standard quantum or classical money in the sense that it can solve deterministic summoning tasks that they cannot. It requires networks of agents with classical data storage and communication, but no long term quantum state storage, and is feasible with current technology. User privacy can be incorporated by secure bit commitment and zero knowledge proof protocols. The level of privacy feasible in given scenarios depends on efficiency and composable security questions that remain to be systematically addressed.

The fundamental process limiting the coherence of quantum-dot based single-photon sources is the interaction with phonons. We study the effect of phonon decoherence on the indistinguishability of single photons emitted from a quantum dot embedded in a suspended nanobeam waveguide. At low temperatures, the indistinguishability is limited by the coupling between the quantum dot and the fundamental vibrational modes of the waveguide and is sensitive to the quantum-dot position within the nanobeam cross-section. We show that this decoherence channel can be efficiently suppressed by clamping the waveguide with a low refractive index cladding material deposited on the waveguide. With only a few microns of cladding material, the coherence of the emitted single photons is drastically improved. We show that the degree of indistinguishability can reach near unity and become independent of the quantum-dot position. We finally show that the cladding material may serve dual purposes since it can also be applied as a means to efficiently outcouple single photons from the nanophotonic waveguide into an optical fiber. Our proposal paves the way for a highly efficient fiber-coupled source of indistinguishable single photons based on a planar nanophotonic platform.

We study the probability that a horizon appears when concentric shells of matter collide, by computing the horizon wave-function of the system. We mostly consider the collision of two ultra-relativistic shells, both shrinking and expanding, at the moment their radii are equal, and find a probability that the system is a black hole which is in qualitative agreement with what one would expect according to the hoop conjecture and the uncertainty principle of quantum physics, and parallels the results obtained for simpler sources. One new feature however emerges, in that this probability shows a modulation with the momenta of the shells and the radius at which the shells collide, as a manifestation of quantum mechanical interference. Finally, we also consider the case of one light shell collapsing into a larger central mass.

The distribution of the ratios of nearest neighbor level spacings has become a popular indicator of spectral fluctuations in complex quantum systems like interacting many-body localized and thermalization phases, quantum chaotic systems, and also in atomic and nuclear physics. In contrast to the level spacing distribution, which requires the cumbersome and at times ambiguous unfolding procedure, the ratios of spacings do not require unfolding and are easier to compute. In this work, for the class of Wigner-Dyson random matrices with nearest neighbor spacing ratios $r$ distributed as $P_{\beta}(r)$ for the three ensembles indexed by $\beta=1,2, 4$, their $k-$th order spacing ratio distributions are shown to be identical to $P_{\beta'}(r)$, where $\beta'$, an integer, is a function of $\beta$ and $k$. This result is shown for Gaussian and circular ensembles of random matrix theory and for several physical systems such as spin chains, chaotic billiards, Floquet systems and measured nuclear resonances.

A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. We discuss static memory materials based on Ising spins that realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical spins can account for the entanglement of quantum spins. An arbitrary unitary evolution for an arbitrary number of quantum spins can be described by static memory materials for an infinite number of Ising spins. We discuss discrete subsets of unitary operations realized by a finite number of Ising spins. They may be useful for new computational structures. We suggest that features of quantum computation or more general probabilistic computation may be realized by neural networks, neuromorphic computing or the brain. We propose a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases.

Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection between tensor networks and probabilistic graphical models, and show that it motivates the definition of generalized tensor networks where information from a tensor can be copied and reused in other parts of the network. We discuss the relationship between generalized tensor network architectures used in quantum physics, such as String-Bond States and Entangled Plaquette States, and architectures commonly used in machine learning. We provide an algorithm to train these networks in a supervised learning context and show that they overcome the limitations of regular tensor networks in higher dimensions, while keeping the computation efficient. A method to combine neural networks and tensor networks as part of a common deep learning architecture is also introduced. We benchmark our algorithm for several generalized tensor network architectures on the task of classifying images and sounds, and show that they outperform previously introduced tensor network algorithms. Some of the models we consider can be realized on a quantum computer and may guide the development of near-term quantum machine learning architectures.

An open question in experimental physics is the characterization of gravitational effects in quantum regimes. We propose an experimental set-up that uses well-tested techniques in cavity optomechanics to observe the effects of the gravitational interaction between two micro-mechanical oscillators on the interference of the cavity photons through the shifts in the visibility of interfering photons. The gravitational coupling leads to a shift in the period and magnitude of the visibility whose observability is within reach of current technology. We discuss the feasibility of the set-up as well as the effects on entanglement due to gravitational interaction.

This paper shows a novel way of simulating a Markov process by a quantum computer. The main purpose of the paper is to show a particular application of quantum computing in the field of stochastic processes analysis. Using a Quantum computer, the process could be superposed, where the random variables of the Markov chain are represented by entangled qubit states, which gives the great opportunity of having all the possible scenarios at once.

We introduce a class of quantum channels called passive-environment bosonic channels. These channels are relevant from a quantum thermodynamical viewpoint because they correspond to the energy-preserving linear coupling of a bosonic system with a bosonic environment that is in a passive state (no energy can be extracted from it by using a unitary transformation) followed by discarding the environment. The Fock-majorization relation defined in [New J. Phys. 18, 073047 (2016)] happens to be especially useful in this context as, unlike regular majorization, it connects the disorder of a state together with its energy. Our main result here is the preservation of Fock majorization across all passive-environment bosonic channels. This implies a similar preservation property for regular majorization over the set of passive states, and it also extends to passive-environment channels whose Stinespring dilation involves an active Gaussian unitary. Beyond bosonic systems, the introduced class of passive environment operations naturally generalizes thermal operations and is expected to provide new insights into the thermodynamics of quantum systems.