A common way of stating the non-cloning theorem -- one of distinguishing characteristics of quantum theory -- is that one cannot make a copy of an arbitrary unknown quantum state. Even though this theorem is an important part of the ongoing discussion of the nature of a quantum state, the role of the theorem in the logical-algebraic approach to quantum theory has not yet been systematically studied. According to the standard point of view (which is in line with the logical tradition), quantum cloning amounts to two classical rules of inference, namely, monotonicity and idempotency of entailment. One can conclude then that the whole of quantum theory should be described through a logic wherein these rules do not hold, which is linear logic. However, in accordance with a supervaluational semantics (that allows one to retain all the theorems of classical logic while admitting `truth-value gaps'), quantum cloning necessitates the permanent loss of the truth values of experimental quantum propositions which violates the unalterability of the past. The present paper demonstrates this.

The nonclassicality of primordial gravitational waves (PGWs) is characterized in terms of sub-Poissonian graviton statistics. The sub-Poissonian statistics are realized when quantum states are squeezed coherent states. In the presence of matter fields, the Universe experiences the squeezed coherent state during inflation. The condition to realize the sub-Poissonian graviton statistics is translated into the frequency range of gravitational waves. If the initial state is the Bunch-Davies vacuum, there is another necessary condition between phases of squeezing and coherent parameters. Here, we extend the initial state to entangled states. We consider $\alpha$-vacua as the initial entangled state that are more general de Sitter invariant vacua than the Bunch-Davies vacuum. We find that, unlike the Bunch-Davies vacuum, PGWs generated in the initial entangled state become sub-Poissonian without requiring the condition between the phases.

Nonlocal advantage of quantum coherence (NAQC) based on coherence complementarity relations is generally viewed as a stronger nonclassical correlation than Bell nonlocality. An arbitrary two-qubit state with NAQC must be an entangled state, which demonstrates that the criterion of NAQC can also be regarded as an entanglement witness. In this paper, we experimentally investigate the NAQC for Bell-diagonal states with high fidelity in an optics-based platform. We perform local measurements on a subsystem in three mutually unbiased bases and reconstruct the density matrices of the measured states by quantum state tomography process. By analyzing characteristic of the $l_1$ norm, relative entropy and skew information of coherence with parameters of quantum states, NAQC for the quantum states is accurately captured, and it shows that our experimental results are well compatible with the theoretical predictions. It is worth mentioning that quantum states with NAQC would have higher entanglement, and thus NAQC could be expected to be a kind of useful physical resource for quantum information processing.

We introduce a new implementation of the coupled cluster method tailored by matrix product states wave functions (DMRG-TCCSD), which employs the local pair natural orbital approach (LPNO). By exploiting locality in the coupled cluster stage of the calculation, we were able to remove some of the limitations that hindered the application of the canonical version of the method to larger systems and/or with larger basis sets. We assessed the accuracy of the approximation using two systems: tetramethyleneethane (TME) and oxo-Mn(Salen). Using the default cut-off parameters, we were able to recover over 99.7% and 99.8% of canonical correlation energy for the triplet and singlet state of TME respectively. In case of oxo-Mn(Salen), we found out that the amount of retrieved canonical correlation energy depends on the size of the active space (CAS) - we retrieved over 99.6% for the larger 27 orbital CAS and over 99.8% for the smaller 22 orbital CAS. The use of LPNO-TCCSD allowed us to perform these calculations up to quadruple-$\zeta$ basis set amounting to 1178 basis functions. Moreover, we examined dependance of the ground state of oxo-Mn(Salen) on CAS composition. We found out that the inclusion of 4d$_{xy}$ orbital plays an important role in stabilizing the singlet state at the DMRG-CASSCF level via double-shell effect. However, by including dynamic correlation the ground state was found to be triplet regardless of the size of the basis set or composition of CAS, which is in agreement with previous findings by canonical DMRG-TCCSD in smaller basis.

We present a scheme for coherently manipulating quantum states of photons by incorporating multiple photonic modes in a system with long-range interactions. The presence of nonlocal photon-photon interactions destroys the energy or momentum matching conditions between distinct propagating polaritons, and consequently gives rise to blockaded effective coupling between the corresponding polaritons. Such a blockade mechanism protects the system from interaction-induced dissipations and enables highly tunable few-photon nonlinearities. Taking Rydberg atomic ensemble as an example, we illustrate several intriguing phenomena based on the proposed scheme, e.g., the deterministic generation of entangled photon pairs, the nonlinear beam splitting, as well as the establishment of a tunable dressed interaction between individual photons.

Qubit memory performance is usually quantified by the 1/e coherence time ($T_{2}^{\ast}$). However, the relevant timescale for fault-tolerant quantum computing is that for which the memory error $\epsilon_m$ remains below a level remediable by quantum error correction techniques. We measure $\epsilon_m$ in the small-error regime for a $^{43}$Ca$^+$ trapped-ion hyperfine qubit, both by direct measurement and by interleaved randomized benchmarking, and find that $\epsilon_m<10^{-4}$ for $t\lesssim50\,\mbox{ms}$, which exceeds gate or measurement times by around 3 orders of magnitude. At $t=1\,\mbox{ms}$, we measure $\epsilon_m=1.2(7)\times 10^{-6}$, more than an order of magnitude below the level extrapolated from $T_{2}^{\ast}$, and limited by instability of the atomic clock reference used to benchmark the qubit. We find no evidence of unusual short-time behaviour that could defeat quantum error correction in this system.

Before global-scale quantum networks become operational, it is important to consider how to evaluate their performance so that they can be suitably built to achieve the desired performance. In this work, we consider three figures of merit for the performance of a quantum network: the average global connection time, the average point-to-point connection time, and the average largest entanglement cluster size. These three quantities are based on the generation of elementary links in a quantum network, which is a crucial initial requirement that must be met before any long-range entanglement distribution can be achieved. We evaluate these figures of merit for a particular class of quantum repeater protocols consisting of repeat-until-success elementary link generation along with entanglement swapping at intermediate nodes in order to achieve long-range entanglement. We obtain lower and upper bounds on these three quantities, which lead to requirements on quantum memory coherence times and other aspects of quantum network implementations. Our bounds are based solely on the inherently probabilistic nature of elementary link generation in quantum networks, and they apply to networks with arbitrary topology.

Probing optical excitations with nanometer resolution is important for understanding their dynamics and interactions down to the atomic scale. Electron microscopes currently offer the unparalleled ability of rendering spatially-resolved electron spectra with combined meV and sub-nm resolution, while the use of ultrafast optical pulses enables fs temporal resolution and exposure of the electrons to ultraintense confined optical fields. Here, we theoretically investigate fundamental aspects of the interaction of fast electrons with localized optical modes that are made possible by these advances. We use a quantum-optics description of the optical field to predict that the resulting electron spectra strongly depend on the statistics of the sample excitations (bosonic or fermionic) and their population (Fock, coherent, or thermal), whose autocorrelation functions are directly retrieved from the ratios of electron gain intensities. We further explore feasible experimental scenarios to probe the quantum characteristics of the sampled excitations and their populations.

Despite significant overhead reductions since its first proposal, magic state distillation is often considered to be a very costly procedure that dominates the resource cost of fault-tolerant quantum computers. The goal of this work is to demonstrate that this is not true. By writing distillation circuits in a form that separates qubits that are capable of error detection from those that are not, most logical qubits used for distillation can be encoded at a very low code distance. This significantly reduces the space-time cost of distillation, as well as the number of qubits. In extreme cases, it can cost less to distill a magic state than to perform a logical Clifford gate on full-distance logical qubits.

A one-dimensional atom -- an atomic system coupled to a single optical mode -- is central for many applications in optical quantum technologies. Here we introduce an effective one-dimensional atom consisting of two interacting quantum emitters coupled to a cavity mode. The dipole-dipole interaction and cavity coupling gives rise to optical resonances of tunable bandwidth with a constant mode coupling. Such versatility, combined with a dynamical control of the system, opens the way to many applications. It can be used to generate single photon light pulses with continuous variable encoding in the time-frequency domain and light states that show sub-Planck features. It can also be exploited to develop a versatile quantum memory of tunable bandwidth, another key ingredient for quantum networks. Our scheme ensures that all above functionalities can be obtained at record high efficiencies. We discuss practical implementation in the most advanced platform for quantum light generation, namely the semiconductor quantum dot system where all the technological tools are in place to bring these new concepts to reality.

A recreational problem from nearly two centuries ago has featured prominently in recent times in the mathematics of designs, codes, and signal processing. The number 15 that is central to the problem coincidentally features in areas of physics, especially in today's field of quantum information, as the number of basic operators of two quantum spins ("qubits"). This affords a 1:1 correspondence that we exploit to use the well-known Pauli spin or Lie-Clifford algebra of those fifteen operators to provide specific constructions as posed in the recreational problem. An algorithm is set up that, working with four basic objects, generates alternative solutions or designs. The choice of four base colors or four basic chords can thus lead to color diagrams or acoustic patterns that correspond to realizations of each design. The Fano Plane of finite projective geometry involving seven points and lines and the tetrahedral three-dimensional simplex of 15 points are key objects that feature in this study.

Correlations in multiparticle systems are constrained by restrictions from quantum mechanics. A prominent example for these restrictions are monogamy relations, limiting the amount of entanglement between pairs of particles in a three-particle system. A powerful tool to study correlation constraints is the notion of sector lengths. These quantify, for different $k$, the amount of $k$-partite correlations in a quantum state in a basis-independent manner. We derive tight bounds on the sector lengths in multi-qubit states and highlight applications of these bounds to entanglement detection, monogamy relations and the $n$-representability problem. For the case of two- and three qubits we characterize the possible sector lengths completely and prove a symmetrized version of strong subadditivity for the linear entropy.

We present a novel tweezer system combining rapid prototyping of user defined microlens arrays with spatial light modulation for site-selective addressing. Using 3D femtosecond direct laser writing we manufacture a microlens array comprising 97 lenslets exhibiting a transition from quadratic to hexagonal patterns. Implemented in our setup we use a digital micromirror device to adapt the light field illuminating the indiviual lenses providing control over each associated tweezer spot.

We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total entropies of the average mixing matrices for some cubic graphs. The trace captures how likely a quantum walk is to revisit the state it started with, and the total entropy measures how close the limiting distribution is to uniform. Our numerical results indicate three relations between quantum walks and graph structures: for the first model, rotation systems with higher genera give lower traces and higher entropies, and for the second model, the symmetric 1-factorizations always give the highest trace.

The causal compatibility question asks whether a given causal structure graph --- possibly involving latent variables --- constitutes a genuinely plausible causal explanation for a given probability distribution over the graph's observed variables. Algorithms predicated on merely necessary constraints for causal compatibility typically suffer from false negatives, i.e. they admit incompatible distributions as apparently compatible with the given graph. In [arXiv:1609.00672], one of us introduced the inflation technique for formulating useful relaxations of the causal compatibility problem in terms of linear programming. In this work, we develop a formal hierarchy of such causal compatibility relaxations. We prove that inflation is asymptotically tight, i.e., that the hierarchy converges to a zero-error test for causal compatibility. In this sense, the inflation technique fulfills a longstanding desideratum in the field of causal inference. We quantify the rate of convergence by showing that any distribution which passes the $n^{th}$-order inflation test must be $O\left(n^{-1/2}\right)$-close in Euclidean norm to some distribution genuinely compatible with the given causal structure. Furthermore, we show that for many causal structures, the (unrelaxed) causal compatibility problem is faithfully formulated already by either the first or second order inflation test.

The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics. The language is sound and complete: one can transform a stabilizer ZX-diagram into another one using the graphical rewrite rules if and only if these two diagrams represent the same quantum evolution or quantum state. We previously showed that the stabilizer ZX-calculus can be simplified by reducing the number of rewrite rules, without losing the property of completeness [Backens, Perdrix & Wang, EPTCS 236:1--20, 2017]. Here, we show that most of the remaining rules of the language are indeed necessary. We do however leave as an open question the necessity of two rules. These include, surprisingly, the bialgebra rule, which is an axiomatisation of complementarity, the cornerstone of the ZX-calculus. Furthermore, we show that a weaker ambient category -- a braided autonomous category instead of the usual compact closed category -- is sufficient to recover the meta rule 'only connectivity matters', even without assuming any symmetries of the generators.

In the standard model of quantum secret sharing, typically, one is interested in minimal authorized sets for the reconstruction of the secret. In such a setting, reconstruction requires the communication of all the shares of the corresponding authorized set. If we allow for non-minimal authorized sets, then we can trade off the size of the authorized sets with the amount of communication required for reconstruction. Based on the staircase codes, proposed by Bitar and El Rouayheb, we propose a class of quantum threshold secret sharing schemes that are also communication efficient. We call them $((k,2k-1,d))$ communication efficient quantum secret sharing schemes where $k\leq d\leq2k-1$. Using the proposed construction, we can recover a secret of $d-k+1$ qudits by communicating $d$ qudits whereas using the standard $((k,2k-1))$ quantum secret sharing requires $k(d-k+1)$ qudits to be communicated. In other words, to share a secret of one qudit, the standard quantum secret sharing requires $k$ qudits whereas the proposed schemes communicate only $\frac{d}{d-k+1}$ qudits per qudit in the communication complexity. Proposed schemes can reduce communication overheads by a factor $O(k)$ with respect to standard schemes, when $d$ equals $2k-1$. Further, we show that our schemes have optimal communication cost for secret reconstruction.

We investigate the formation of trimers in an infinite one-dimensional lattice model with single-particle hopping $t$ and hard-core two-body $U$ and three-body $V$ interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $U \leq- 2t$ and positive $V>0$ a large trimer is stabilized, which persists as $V\rightarrow \infty$, while both attractive $U \leq 0$ and $V \leq 0$ bind a small trimer. Surprisingly, the excited state above this small trimer is also bound and has a large extent; its behavior as $V\rightarrow -\infty$ resembles that of the large ground-state trimer.

Studying a single atomic ion confined in a time-dependent periodic anharmonic potential, we find large amplitude trajectories stable for millions of oscillation periods in the presence of stochastic laser cooling. The competition between energy gain from the time-dependent drive and damping leads to the stabilization of such stochastic limit cycles. Instead of converging to the global minimum of the averaged potential, the steady-state phase-space distribution develops multiple peaks in the regions of phase space where the frequency of the motion is close to a multiple of the periodic drive. Such distinct nonequilibrium behaviour can be observed in realistic radio-frequency traps with laser-cooled ions, suggesting that Paul traps offer a well-controlled test-bed for studying transport and dynamics of microscopically driven systems.

We consider a quantum Brownian particle interacting with two harmonic baths, which is then perturbed by a cubic coupling linking the particle and the baths. This cubic coupling induces non-linear dissipation and noise terms in the influence functional/master equation of the particle. Its effect on the Out-of-Time-Ordered Correlators (OTOCs) of the particle cannot be captured by the conventional Feynman-Vernon formalism.We derive the generalised influence functional which correctly encodes the physics of OTO fluctuations, response, dissipation and decoherence. We examine an example where Markovian approximation is valid for the OTO dynamics. If the original cubic coupling has a definite time-reversal parity, the leading order OTO influence functional is completely determined by the couplings in the usual master equation via OTO generalisation of Onsager-Casimir relations. New OTO fluctuation-dissipation relations connect the non-Gaussianity of the thermal noise to the thermal jitter in the damping constant of the Brownian particle.