We present a thermodynamic framework for the refined weak coupling limit. In this limit the interaction between system and environment is weak, but not negligible. As a result, the system dynamics becomes non-Markovian breaking divisibility conditions. Nevertheless, we propose a derivation of the first and second law just in terms of the reduced system dynamics. To this end, we extend the refined weak coupling limit for allowing slow-varying external drivings, and reconsider the definition of internal energy due to the non-negligible interaction.

Knowledge of the nitrogen-vacancy center formation kinetics in diamond is critical to engineering sensors and quantum information devices based on this defect. Here we utilize the longitudinal tracking of single NV centers to elucidate NV defect kinetics during high-temperature annealing from 800-1100 $^\circ$C in high-purity chemical-vapor-deposition diamond. We observe three phenomena which can coexist: NV formation, NV quenching, and NV orientation changes. Of relevance to NV-based applications, a 6 to 24-fold enhancement in the NV density, in the absence of sample irradiation, is observed by annealing at 980 $^\circ$C, and NV orientation changes are observed at 1050 $^\circ$C. With respect to the fundamental understanding of defect kinetics in ultra-pure diamond, our results indicate a significant vacancy source can be activated for NV creation between 950-980 $^\circ$C and suggests that native hydrogen from NVH$_y$ complexes plays a dominant role in NV quenching, in agreement with recent {\it ab initio} calculations. Finally, the direct observation of orientation changes allows us to estimate an NV diffusion barrier of 5.1~eV.

We present a derivation of the holographic dual of logarithmic negativity in $AdS_3/CFT_2$ that was recently conjectured in [Phys. Rev. D 99, 106014 (2019)]. This is given by the area of an extremal cosmic brane that terminates on the boundary of the entanglement wedge. The derivation consists of relating the recently introduced R\'enyi reflected entropy to the logarithmic negativity in holographic conformal field theories. Furthermore, we clarify previously mysterious aspects of negativity at large central charge seen in conformal blocks and comment on generalizations to generic dimensions, dynamical settings, and quantum corrections.

We introduce a formalism that exploits the many-input many-output nature of nodes in quantum circuits. There is a diagrammatic and an algebraic version, the latter similar to the spinor formalism of general relativity. This allows us to work in truly basis independent ways, clarifying and simplifying many aspects of quantum state processing. The narrative is at times interrupted by antics of characters from quantum age fairy tales.

Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in a multitude of quantum algorithms. Simultaneously measuring sets of operators allows for fewer measurements and an overall speedup of the measurement process. We investigate the task of partitioning a random subset of Pauli operators into simultaneously-measurable parts. Using heuristics from coloring random graphs, we give an upper bound for the expected number of parts in our partition. We go on to conjecture that allowing arbitrary Clifford operators before measurement, rather than single-qubit operations, leads to a decrease in the number of parts which is linear with respect to the lengths of the operators. We give evidence to confirm this conjecture and comment on the importance of this result for a specific near-term application: speeding up the measurement process of the variational quantum eigensolver.

Resonant soft x-ray scattering (RSXS) is a leading probe of valence band order in materials best known for establishing the existence of charge density wave order in the copper-oxide superconductors. One of the biggest limitations on the RSXS technique is the presence of a severe fluorescence background which, like the RSXS cross section itself, is enhanced under resonance conditions. This background prevents the study of weak signals such as diffuse scattering from glassy or fluctuating order that is spread widely over momentum space. Recent advances in superconducting transition edge sensor (TES) detectors have led to major improvements in resolution and detection efficiency in the soft x-ray range. Here, we perform a RSXS study of stripe-ordered La$_{2-x}$Ba$_x$CuO$_4$ at the Cu $L_{3/2}$ edge (932.2 eV) using a TES detector with 1.5 eV resolution, to evaluate its utility for mitigating the fluorescence background problem. We find that, for suitable degree of detuning from the resonance, the TES could be used to reject the fluorescence background, leading to a 5 to 10 times improvement in the statistical quality of the data compared to an equivalent, energy-integrated measurement. We conclude that a TES presents a promising approach to reducing background in RSXS studies and may lead to new discoveries in materials exhibiting valence band order that is fluctuating or glassy.

High-dimensional entangled states of light provide novel possibilities for quantum information, from fundamental tests of quantum mechanics to enhanced computation and communication protocols. In this context, the frequency degree of freedom combines the assets of robustness to propagation and easy handling with standard telecommunication components. Here we use an integrated semiconductor chip to engineer the wavefunction and exchange statistics of frequency-entangled photon pairs directly at the generation stage, without post-manipulation. Tuning the spatial properties of the pump beam allows to generate frequency-anticorrelated, correlated and separable states, and to control the symmetry of the spectral wavefunction to induce either bosonic or fermionic behaviors. These results, supported by analytical and numerical calculations, open promising perspectives for the quantum simulation of fermionic problems with photons on an integrated platform, as well as for communication and computation protocols exploiting antisymmetric high-dimensional quantum states.

It is well known that the Schmidt decomposition exists for all pure states of a two-party quantum system. We demonstrate that there are two ways to obtain an analogous decomposition for arbitrary rank-1 operators acting on states of a bipartite finite-dimensional Hilbert space. These methods amount to joint Schmidt-type decompositions of two pure states where the two sets of coefficients and local bases depend on the properties of either state, however, at the expense of the local bases not all being orthonormal and in one case the complex-valuedness of the coefficients. With these results we derive several generally valid purity-type formulae for one-party reductions of rank-1 operators, and we point out relevant relations between the Schmidt decomposition and the Bloch representation of bipartite pure states.

Synchronisation is a collective phenomenon widely investigated in classical oscillators and, more recently, in quantum systems. However, it remains unclear what features distinguish synchronous behaviour in these two scenarios. Recent works have shown that investigating the dynamics of synchronisation in open quantum systems can give insight into this issue. Here we study transient synchronisation in a bio-inspired vibronic dimer, where the dynamics of electronic excitation is mediated by coherent interactions with intramolecular vibrational modes. We show that the synchronisation dynamics of the displacement of these local modes exhibit a rich behaviour which arises directly from the distinct time-evolutions of different vibronic quantum coherences. Furthermore, our study shows that coherent energy transport in this bio-inspired system is concomitant with the emergence of positive synchronisation between mode displacements. Our work provides further understanding of the relations between quantum coherence and synchronisation in open quantum systems and suggests an interesting role for coherence in biomolecules, that is promoting the synchronisation of vibrational motions driven out of thermal equilibrium.

We exploit the nonlinearity arising from the spin-photon interaction in an InAs quantum dot to demonstrate phase shifts of scattered light pulses at the single-photon level. Photon phase shifts of close to 90 degrees are achieved using a charged quantum dot in a micropillar cavity. We also demonstrate a photon phase switch by using a spin-pumping mechanism through Raman transitions in an in-plane magnetic field. The experimental findings are supported by a theoretical model which explores the dynamics of the system. Our results demonstrate the potential of quantum dot-induced nonlinearities for quantum information processing.

We demonstrate homodyne detection of quantum states originating from a genuinely spatially and temporally singlemode parametric downconversion source in non-linear waveguides. By using single photon subtraction, we implement the distillation of squeezed states witnessing an improvement of 0.1 dB from an initial squeezing value of 1.62 +/- 0.01 dB, while achieving a purity of 0.58, and confirm the non-Gaussianity of the distilled state via the higher order cumulants. With this we demonstrate the source's suitability for scalable hybrid quantum network applications.

Critical to the construction of large scale quantum networks, i.e. a quantum internet, is the development of fast algorithms for managing entanglement present in the network. One fundamental building block for a quantum internet is the distribution of Bell pairs between distant nodes in the network. Here we focus on the problem of transforming multipartite entangled states into the tensor product of bipartite Bell pairs between specific nodes using only a certain class of local operations and classical communication. In particular we study the problem of deciding whether a given graph state, and in general a stabilizer state, can be transformed into a set of Bell pairs on specific vertices using only single-qubit Clifford operations, single-qubit Pauli measurements and classical communication. We prove that this problem is NP-Complete.

The complexity of experimental quantum information processing devices is increasing rapidly, requiring new approaches to control them. In this paper, we address the problems of practically modeling and controlling an integrated optical waveguide array chip, a technology expected to have many applications in telecommunications and optical quantum information processing. This photonic circuit can be electrically reconfigured, but only the output optical signal can be monitored. As a result, the conventional control methods cannot be naively applied. Characterizing such a chip is challenging for three reasons. First, there are uncertainties associated with the Hamiltonian describing the chip. Second, we expect distortions of the control voltages caused by the chip's electrical response, which cannot be directly observed. Finally, there are imperfections in the measurements caused by losses from coupling the chip externally to optical fibers. We developed a deep neural network approach to solve these problems. The architecture is designed specifically to overcome the aforementioned challenges using a Gated Recurrent Unit (GRU)-based network as the central component. The Hamiltonian is estimated as a blackbox, while the rules of quantum mechanics such as state evolution is embedded in the structure as a whitebox. The resulting overall graybox model of the chip shows good performance both quantitatively in terms of the mean square error and qualitatively in terms of the predicted waveforms. We use this neural network to solve a classical and a quantum control problem. In the classical application we find a control sequence to approximately realize a time-dependent output power distribution. For the quantum application we obtain the control voltages to realize a target set of quantum gates. The proposed method is generic and can be applied to other systems that can only be probed indirectly.

Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are equivalent up to single-qubit Clifford operations is known to be decidable in polynomial time and have been studied both in the context of producing certain required states in a quantum network but also in relation to stabilizer codes. The reason for the latter this is that single-qubit Clifford equivalent graph states exactly corresponds to equivalent stabilizer codes. We here consider the computational complexity of, given a graph state |G>, counting the number of graph states, single-qubit Clifford equivalent to |G>. We show that this problem is #P-Complete. To prove our main result we make use of the notion of isotropic systems in graph theory. We review the definition of isotropic systems and point out their strong relation to graph states. We believe that these isotropic systems can be useful beyond the results presented in this paper.

Trapped ions are among the most promising candidates for performing quantum information processing tasks. Recently, it was demonstrated how the properties of geometric phases can be used to implement an entangling two qubit phase gate with significantly reduced operation time while having a built-in resistance against certain types of errors. In this article, we investigate the influence of dissipation on the geometric phase in the Markov regime. We show that additional environmentally induced phases as well as a loss of coherence result from the non-unitary evolution and connect these effects to the associated dynamical and geometrical phases. This suggests a strategy to compensate the detrimental environmental influences and restore some of the properties of the ideal implementation. In particular, we present a way to construct forces for the geometric phase gate which compensate the dissipative effects and leave the produced phase as well as the final motional state identical to the isolated case. Finally, we examine the effects of dissipation on the fidelity and the robustness of a two qubit phase gate against certain error types.

Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the properties and existing calculation techniques of QFIM for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology. On the other hand, as the main application of QFIM, the second part of this paper reviews the quantum multiparameter Cram\'{e}r-Rao bound, its attainability condition and the associated optimal measurements. Moreover, recent developments in a few typical scenarios of quantum multiparameter estimation and the quantum advantages are also thoroughly discussed in this part.

In this article, the dynamics of an unbalanced two-ion crystal comprising the 'target' and the 'sensor' ions confined in a Penning trap has been studied. First, the low amplitude regime is addressed. In this regime, the overall potential including the Coulomb repulsion between the ions can be considered harmonic and the axial, magnetron and reduced-cyclotron modes split up into the so-called 'stretch' and 'common' modes, that are generalizations of the well-known 'breathing' and 'center-of-mass' motions of a balanced crystal made of two ions. By measuring the frequency modes of the crystal and the sensor ion eigenfrequencies using optical detection, it will be possible to determine the target ion's free-cyclotron frequency. The measurement scheme is described and the non-harmonicity of the Coulomb interaction is discussed since this might cause large systematic effects.

It is promising to achieve quantum supremacy with boson sampling given the rapid development of physical implementations. However, the sample loss issue, which exists in both the physical experiments and classical simulation, has a strong impact on where the frontier of quantum supremacy is. Addressing this, we present Sample Caching Markov Chain Monte Carlo (SC-MCMC), a sampling method that can generate samples without loss. SC-MCMC can reduce the estimated time for a 50-photon sample in ~10 days to <100 minutes with state-of-the-art classical computing platform. Further, our results indicate that to experimentally approach quantum supremacy, reducing sample loss within an experimental setup is an important and effective method.

For a quantum system in a macroscopically large volume $V$, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system $v\ll V$ is almost surely totally mixing. We show that the fluctuations around this limiting value, evaluated according to the invariant measure of these unitary flows, are captured by the Gaussian unitary ensemble (GUE) of random matrix theory. An extension of this statement, applicable when the unitary transformations conserve the energy but are maximally noisy or ergodic on any energy shell, allows to decipher the fluctuations around canonical typicality. According to typicality, if the large system is prepared in a generic pure state in a given energy shell, the reduced density matrix of the sub-system is almost surely the canonical Gibbs state of that sub-system. We show that the fluctuations around the Gibbs state are encoded in a deformation of the GUE whose covariance is specified by the Gibbs state. Contact with the eigenstate thermal hypothesis (ETH) is discussed.

A simpler quantum counting algorithm based on consecutive measurements is presented. This algorithm terminates within log(sqrt(N/M)) measurement steps, where M is the number of marked states and N is the total number of states in the search space, and is followed by a classical post processing. This algorithm is bounded by O(sqrt(N/M)) calls to the controlled-Grover operator. This simpler algorithm requires less quantum resources in terms of the width and depth of the quantum circuit, and runs significantly faster than the phase estimation-based quantum counting algorithm when the ratio M/N is small. We compare these two quantum counting algorithms by simulating various cases with a different M/N ratio, such as M/N > 0.125 or M/N < 0.001.