We propose a generalisation of the Leggett-Garg conditions for macrorealistic behaviour. Our proposal relies on relaxing the postulate of non-invasive measurability with that of retrievability of information. This leads to a strictly broader class of hidden variable theories than those having a macrorealistic description. Crucially, whereas quantum mechanical tests of macrorealism require one to optimise over all possible state updates, for retrievability of information it suffices to use the basic L\"uders state update, which is present in every quantum measurement. We show that in qubit systems the optimal retrieving protocols further relate to the fundamental precision limit of quantum theory given by Busch-Lahti-Werner error-disturbance uncertainty relations. We implement an optimal protocol using a photonic setting, and report an experimental violation of the proposed generalisation of macrorealism.

Inevitable interactions with the reservoir largely degrade the performance of non-local gates, which hinders practical quantum computation from coming into existence. Here we experimentally demonstrate a 99.920(7)\%-fidelity controlled-NOT gate by suppressing the complicated noise in a solid-state spin system at room temperature. We found that the fidelity limited at 99\% in previous works results from only considering static noise, and thus, in this work, time-dependent noise and quantum noise are also included. All noises are dynamically corrected by an exquisitely designed shaped pulse, giving the resulting error below $10^{-4}$. The residual gate error is mainly originated from the longitudinal relaxation and the waveform distortion that can both be further reduced technically. Our noise-resistant method is universal, and will benefit other solid-state spin systems.

This paper presents three classes of metalinear structures that abstract some of the properties of Hilbert spaces. Those structures include a binary relation that expresses orthogonality between elements and enables the definition of an operation that generalizes the projection operation in Hilbert spaces. The logic defined by the most general class has a unitary connective and two dual binary connectives that are neither commutative nor associative. It is a substructural logic of sequents in which the Exchange rule is extremely limited and Weakening is also restricted. This provides a logic for quantum measurements whose proof theory is attractive. A completeness result is proved. An additional property of the binary relation ensures that the structure satisfies the MacLane-Steinitz exchange property and is some kind of matroid. Preliminary results on richer structures based on a sort of real inner product that generalizes the Born factor of Quantum Physics are also presented.

Revealing the properties of single spin defects in solids is essential for quantum applications based on solid-state systems. However, it is intractable to investigate the temperature-dependent properties of single defects, due to the low precision for single-defect measurements in contrast to defect ensembles. Here we report that the temperature dependence of the Hamiltonian parameters for single negatively charged nitrogen-vacancy (NV$^{-}$) centers in diamond is precisely measured, and the results find a reasonable agreement with first-principles calculations. Particularly, the hyperfine interactions with randomly distributed $^{13}$C nuclear spins are clearly observed to vary with temperature, and the relevant coefficients are measured with Hz-level precision. The temperature-dependent behaviors are attributed to both thermal expansion and lattice vibrations by first-principles calculations. Our results pave the way for taking nuclear spins as more stable thermometers at nanoscale. The methods developed here for high-precision measurements and first-principles calculations can be further extended to other solid-state spin defects.

In the field of cavity nano-optomechanics, the nanoresonator-in-the-middle approach consists in inserting a sub-wavelength sized deformable resonator, here a nanowire, in the small mode volume of a fiber microcavity. Internal resonances in the nanowire enhance the light nanowire interaction which provide giant coupling strengthes -- sufficient to enter the single photon regime of cavity optomechanics -- at the condition to precisely position the nanowire within the cavity field. Here we expose a theoretical description that combines an analytical formulation of the Mie-scattering of the intracavity light by the nanowire and an input-output formalism describing the dynamics of the intracavity optical eigenmodes. We investigate both facets of the optomechanical interaction describing the position dependent parametric and dissipative optomechanical coupling strengths, as well as the optomechanical force field experienced by the nanowire. We find a quantitative agreement with recent experimental realization. We discuss the specific phenomenology of the optomechanical interaction which acquires a vectorial character since the nanowire can identically vibrate along both transverse directions: the optomechanical force field presents a non-zero rotational, while anomalous positive cavity shifts are expected. Taking advantage of the large Kerr-like non linearity, this work opens perspectives in the field of quantum optics with nanoresonator with for instance broadband squeezing of the outgoing cavity fields close to the single photon level.

Entanglement distribution in multi-node networks can become the backbone for a future quantum internet. It will become a widely accepted phenomenon as quantum repeater networks become increasingly efficient. Graph theoretical approaches to make a feasible multi-node quantum network for secure communication and distributed quantum computation are exciting, as the classical internet was built on such theories. Unlike today's classical internet, a quantum internet will likely rely on more than one path between the source and destination. This multi-path routing paradigm allows the user-pair to send their Bell-pairs through pathways other than the shortest one and still get a single high-fidelity Bell-pair at the end via entanglement purification. This study encompasses a quintessential comparative analysis of having more than the minimum required edges in networks to support multi-path routing with quantum memories. We explain the benefits of having redundant edges in tree networks by adding rings of edges at each level and comparing cost distances with that of lattice networks. Our analysis provides an understanding of fidelity-efficiency trade-offs in the context of user competition and path-finding probabilities. We argue that network topologies are essential in serving the entanglement distribution. To show the deployability of large-scale quantum communication networks, we present a $14$-node network in Islamabad in two fibre-optic-based networks. One is the minimal spanning tree topology that costs around $\$61,370.00$, and the other is a complete graph topology, which costs about $\$1.1\text{Mil}$. It shows that the network topologies can significantly improve key generation rates, even when memory is unavailable.

In a class of non-Hermitian quantum walk in lossy lattices with open boundary conditions, an unexpected peak in the distribution of the decay probabilities appears at the edge, dubbed edge burst. It is proposed that the edge burst is originated jointly from the non-Hermitian skin effect (NHSE) and the imaginary gaplessness of the spectrum [Wen-Tan Xue et al., Phys. Rev. Lett. 128, 120401 (2022)]. Using a particular one-dimensional lossy lattice with a nonuniform loss rate, we show that the edge burst can occur even in the absence of NHSE. Furthermore, we discuss that the edge burst may not appear if the spectrum satisfies the imaginary gaplesness condition. Aside from its fundamental importance, by removing the restrictions on observing the edge burst effect, our results open the door to broader design space for future applications of the edge burst effect.

The stipulation that no measurable quantity could have an infinite value is indispensable in physics. At the same time, in mathematics, the possibility of considering an infinite procedure as a whole is usually taken for granted. However, not only does such possibility run counter to computational feasibleness, but it also leads to the most serious problem in modern physics, to wit, the emergence of infinities in calculated physical quantities. Particularly, having agreed on the axiom of infinity for set theory -- the backbone of the theoretical foundations of calculus integrated in every branch of physics -- one could no longer rule out the existence of a classical field theory which is not quantizable, let alone renormalizable. By contrast, the present paper shows that negating the axiom of infinity results in physics acting in a finite geometry where it is ensured that all classical field theories are quantizable.

Dynamical phases are obtained for a quantum thermal engine, whose working medium is a single harmonic oscillator. The dynamics of this engine is obtained by using four steps where in two steps the time dependent frequency is changing. In the other two steps, the thermal engine is coupled alternatively to hot and cold heat baths. Similar dynamical phases are obtained in a quantum thermal engine whose working medium is spin 1/2 system. The role of times durations of such steps in the quantum engines for getting maximal efficiency is analyzed. The dynamic of charge pumping in a quantum dot coupled to two reservoirs is studied. The effects of many modulation parameters including their fluctuations for getting geometric phases are analyzed. Since the separate steps in thermal engines describe non-cyclic circuits, we propose to use a special method for measuring geometric phases in thermal engines for non-cyclic circuits which is gauge invariant.

The quantum interference of two wavelength-entangled photons overlapping at a beamsplitter results in an oscillating interference pattern. The frequency of this interference pattern is dependent on the wavelength separation of the entangled photons, but is robust to wavelength scale perturbations that can limit the practicality of standard interferometry. Here we use two-colour entanglement interferometry to demonstrate 3D imaging of a semi-transparent sample with sub-${\mu}$m precision. The axial precision and the dynamic range of the microscope is actively controlled by detuning the wavelength separation of the entangled photon pairs. Sub-${\mu}$m precision is reported using up to 16 nm of detuning with an average in the order of 10^3 photon pairs for each pixel.

Reflecting the increasing interest in quantum computing, the variational quantum eigensolver (VQE) has attracted much attentions as a possible application of near-term quantum computers. Although the VQE has often been applied to quantum chemistry, high computational cost is required for reliable results because infinitely many measurements are needed to obtain an accurate expectation value and the expectation value is calculated many times to minimize a cost function in the variational optimization procedure. Therefore, it is necessary to reduce the computational cost of the VQE for a practical task such as estimating the potential energy surfaces (PESs) with chemical accuracy, which is of particular importance for the analysis of molecular structures and chemical reaction dynamics. A hybrid quantum-classical neural network has recently been proposed for surrogate modeling of the VQE [Xia $et\ al$, Entropy 22, 828 (2020)]. Using the model, the ground state energies of a simple molecule such as H2 can be inferred accurately without the variational optimization procedure. In this study, we have extended the model by using the subspace-search variational quantum eigensolver procedure so that the PESs of the both ground and excited state can be inferred with chemical accuracy. We also demonstrate the effects of sampling noise on performance of the pre-trained model by using IBM's QASM backend.

The hybridization between light and matter forms the basis to achieve cavity control over quantum materials. In this work we investigate a cavity coupled to an XXZ quantum chain of interacting spinless fermions by numerically exact solutions and perturbative analytical expansions. We find two important effects: (i) Specific quantum fluctuations of the matter system play a pivotal role in achieving entanglement between light and matter; and (ii) in turn, light-matter entanglement is the key ingredient to modify electronic properties by the cavity. We hypothesize that quantum fluctuations of those matter operators to which the cavity modes couple are a general prerequisite for light-matter entanglement in the groundstate. Implications of our findings for light-matter-entangled phases, cavity-modified phase transitions in correlated systems, and measurement of light-matter entanglement through Kubo response functions are discussed.

Given a renormalization scheme, we show how to formulate a tractable convex relaxation of the set of feasible local density matrices of a many-body quantum system. The relaxation is obtained by introducing a hierarchy of constraints between the reduced states of ever-growing sets of lattice sites. The coarse-graining maps of the underlying renormalization procedure serve to eliminate a vast number of those constraints, such that the remaining ones can be enforced with reasonable computational means. This can be used to obtain rigorous lower bounds on the ground state energy of arbitrary local Hamiltonians, by performing a linear optimization over the resulting convex relaxation of reduced quantum states. The quality of the bounds crucially depends on the particular renormalization scheme, which must be tailored to the target Hamiltonian. We apply our method to 1D translation-invariant spin models, obtaining energy bounds comparable to those attained by optimizing over locally translation-invariant states of $n\gtrsim 100$ spins. Beyond this demonstration, the general method can be applied to a wide range of other problems, such as spin systems in higher spatial dimensions, electronic structure problems, and various other many-body optimization problems, such as entanglement and nonlocality detection.

This paper presents a new method for quantum identity authentication (QIA) protocols. The logic of classical zero-knowledge proofs (ZKPs) due to Schnorr is applied in quantum circuits and algorithms. This novel approach gives an exact way with which a prover $P$ can prove they know some secret without transmitting that directly to a verifier $V$ by means of a quantum channel - allowing for a ZKP wherein an eavesdropper or manipulation can be detected with a `fail safe' design. With the anticipated advent of a `quantum internet', such protocols and ideas may soon have utility and execution in the real world.

Defect-free atom arrays have emerged as a powerful platform for quantum simulation and computation with high programmability and promising scalability. Defect-free arrays can be prepared by rearranging atoms from an initial partially loaded array to the target sites. However, it is challenging to achieve large-size defect-free arrays due to atom loss during atom rearrangement and the vaccum-limited lifetime which is inversely proportional to the array size. It is crucial to rearrange atoms in fast algorithms with minimized time cost and atom loss. Here we propose a novel parallel compression algorithm which utilizes multiple mobile tweezers to transfer the atoms in parallel. The total time cost of atom rearrangement could be reduced to scale linearly with the number of target sites. The algorithm can be readily implemented in current experimental setups.

I expose nonrelativistic quantum electrodynamics in the Weyl-Wigner representation. Hence I prove that an approximation to first order in Planck constant has formal analogy with stochastic electrodynamics (SED), that is classical electrodynamics of charged particles immersed in a random radiation filling space. The analogy elucidates why SED agrees with quantum theory for particle Hamiltonians quadratic in coordinates and momenta, but fails otherwise.

The functioning of the human brain, nervous system and heart is based on the conduction of electrical signals. These electrical signals also create magnetic fields which extend outside the human body. Highly sensitive magnetometers, such as superconducting quantum interference device magnetometers or optically pumped magnetometers, placed outside the human body can detect these biomagnetic fields and provide non-invasive measurements of e.g. brain activity, nerve impulses, and cardiac activity. Animal models are used widely in medical research, including for disease diagnostics and for drugs testing. We review the topic of biomagnetic recordings on animal models using optically pumped magnetometers, and present our experiments on detecting nerve impulses in the frog sciatic nerve and the heart beat in an isolated guinea pig heart.

Taking the Hydrogen atom as an example it is shown that if the symmetry of the three-dimensional system is $O(2) \oplus Z_2$, the variables $(r, \rho, \varphi)$ allow a separation of variable $\varphi$ and the eigenfunctions define a new family of orthogonal polynomials in two variables, $(r, \rho^2)$. These polynomials are related with the finite-dimensional representations of the algebra $gl(2) \ltimes {\it R}^3 \in g^{(2)}$, which occurs as the hidden algebra of the $G_2$ rational integrable system of 3 bodies on the line (the Wolfes model). Namely, those polynomials occur in the study of the Zeeman effect on Hydrogen atom.

This study examines the possibility of finding perfect entanglers for a Hamiltonian which corresponds to several quantum information platforms of interest at the present time. However, in this study, we use a superconducting circuit that stands out from other quantum-computing devices, especially because Transmon qubits can be coupled via capacitors or microwave cavities, which enable us to combine high coherence, fast gates, and high flexibility in its design parameters. There are currently two factors limiting the performance of superconducting processors: timing mismatch and the limitation of entangling gates to two qubits. In this work, we present a two-qubit SWAP and a three-qubit Fredkin gate, additionally, we also demonstrate a perfect adiabatic entanglement generation between two and three programmable superconducting qubits. Furthermore, in this study, we also demonstrate the impact of random dephasing, emission, and absorption noises on the quantum gates and entanglement. It is demonstrated by numerical simulation that the CSWAP gate and $W$-state generation can be achieved perfectly in one step with high reliability under weak coupling conditions. Hence, our scheme could contribute to quantum teleportation, quantum communication, and some other areas of quantum information processing.

Time-dependent driving holds the promise of realizing dynamical phenomenon absent in static systems. Here, we introduce a correlated random driving protocol to realize a spatiotemporal order that cannot be achieved even by periodic driving, thereby extending the discussion of time translation symmetry breaking to randomly driven systems. We find a combination of temporally disordered micro-motion with prethermal stroboscopic spatiotemporal long-range order. This spatiotemporal order remains robust against generic perturbations, with an algebraically long prethermal lifetime where the scaling exponent strongly depends on the symmetry of the perturbation, which we account for analytically.