Search Results (41)

We propose a scheme to enhance the range and precision of ultra-low temperature measurements by employing a probe qubit coupled to a chain of ancilla qubits. Specifically, we analyze a qubit chain governed by Heisenberg $XX$ and Dzyaloshinskii–Moriya (DM) interactions. The precision limits of temperature measurements are characterized by evaluating quantum Fisher information (QFI). Our findings demonstrate that the achievable precision bounds, as well as the number of peaks in the QFI as a function of temperature, can be controlled by adjusting the number of ancilla qubits and the system’s model parameters. These results are interpreted in terms of the influence of energy transitions on the range and the number of QFI peaks as a function of temperature. This study highlights the potential of the probe qubit–ancilla chain system as a powerful and precise tool for quantum thermometry in the ultra-low temperature regime. Full article

The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to $\sqrt{K}$, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the $\sqrt{K}$ gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional $\sqrt{K}$ gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of $\mathsf{\pi }/\mathrm{N}$ in resolution. Full article

In order to achieve time–frequency superresolution in comparison to the conventional Wigner distribution (WD), this study generalizes the well-known $\tau$-Wigner distribution ($\tau$-WD) with only one parameter $\tau$ to the multiple-parameter matrix-Wigner distribution (M-WD) with the parameter matrix $\mathcal{M}$. According to operator theory, we construct Heisenberg’s inequalities on the uncertainty product in M-WD domains and formulate two kinds of attainable lower bounds dependent on $\mathcal{M}$. We solve the problem of lower bound minimization and obtain the optimality condition of $\mathcal{M}$, under which the M-WD achieves superior time–frequency resolution. It turns out that the M-WD breaks through the limitation of the $\tau$-WD and gives birth to some novel distributions other than the WD that could generate the highest time–frequency resolution. As an example, the two-dimensional linear frequency-modulated signal is carried out to demonstrate the time–frequency concentration superiority of the M-WD over the short-time Fourier transform and wavelet transform. Full article

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum–optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations. Full article

The relation between de Broglie’s double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie’s theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with a view to reformulating and studying de Broglie’s double-solution program in the modern language of classical field theory. Notably, the entire family is local and Lorentz-invariant, follows from a variational principle, and exhibits time-invariant, two-way coupling between particle and pilot-wave field. We first introduce a variational framework for generic pilot-wave systems, including a derivation of particle-wave exchange of Noether currents. We then focus on a particular limit of our system, in which the particle is propelled by the local gradient of its pilot wave. In this case, we see that the Compton-scale oscillations proposed by de Broglie emerge naturally in the form of particle vibrations, and that the vibration modes dynamically adjust to match the Compton frequency in the rest frame of the particle. The underlying field dynamically changes its radiation patterns in order to satisfy the de Broglie relation $p=\hslash k$ at the particle’s position, even as the particle momentum p changes. The wave form and frequency thus evolve so as to conform to de Broglie’s harmony of phases, even for unsteady particle motion. We show that the particle is always dressed with a Compton-scale Yukawa wavepacket, independent of its trajectory, and that the associated energy imparts a constant increase to the particle’s inertial mass. Finally, we see that the particle’s wave-induced Compton-scale oscillation gives rise to a classical version of the Heisenberg uncertainty principle. Full article

We are looking at an aggregation of matter into granules. Diffusion plays a pivotal role here. When going down to the nanometer scale (the so-called nanoscale quantum-size effect limit), quantum mechanics, and the Heisenberg uncertainty relation, may take over the role of classical diffusion, as viewed typically in the mesoscopic/stochastic limit. A d-dimensional entropy-production aggregation of the granules-involving matter in the granule-size space is considered in terms of a (sub)diffusive realization. It turns out that when taking a full d-dimensional pathway of the aggregation toward the nanoscale, one is capable of disclosing a Heisenberg-type (diffusional) relation, setting up an upper uncertainty bound for the (sub)diffusive, very slow granules-including environment that, within the granule-size analogy invoked, matches the quantum limit of h/2πμ (μ—average mass of a granule; h—the Planck’s constant) for the diffusion coefficient of the aggregation, first proposed by Fürth in 1933 and qualitatively foreseen by Schrödinger some years before, with both in the context of a diffusing particle. The classical quantum passage uncovered here, also termed insightfully as the quantum-size effect (as borrowed from the quantum dots’ parlance), works properly for the three-dimensional (d = 3) case, making use of a substantial physical fact that the (nano)granules interact readily via their surfaces with the also-granular surroundings in which they are immersed. This natural observation is embodied in the basic averaging construction of the diffusion coefficient of the entropy-productive (nano)aggregation of interest. Full article

The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size L is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, $T_h$ and $T_l$ ($T_h>T_l$), respectively. These particles at the extremities of the chain are subjected to standard Langevin dynamics, whereas all remaining rotators ($i=2,\cdots ,L-1$) interact by means of nearest-neighbor ferromagnetic couplings and evolve in time following their own equations of motion, being investigated numerically through molecular-dynamics numerical simulations. Fourier’s law for the heat flux is verified numerically, with the thermal conductivity becoming independent of the lattice size in the limit $L\to \infty$, scaling with the temperature, as $\kappa \left(T\right)\sim T^{-2.25}$, where $T=(T_h+T_l)/2$. Moreover, the thermal conductance, $\sigma (L,T)\equiv \kappa \left(T\right)/L$, is well-fitted by a function, which is typical of nonextensive statistical mechanics, according to $\sigma (L,T)=A{exp}_q(-B{x}^{\eta })$, where A and B are constants, $x=L^{0.475}T$, $q=2.28\pm 0.04$, and $\eta =2.88\pm 0.04$. Full article

In this contribution, motivated by the quest to understand cosmic acceleration, based on the theory of Hořava–Lifshitz and on the branch-cut gravitation, we investigate the effects of non-commutativity of a mini-superspace of variables obeying the Poisson algebra on the structure of the branch-cut scale factor and on the acceleration of the Universe. We follow the guiding lines of a previous approach, which we complement to allow a symmetrical treatment of the Poisson algebraic variables and eliminate ambiguities in the ordering of quantum operators. On this line of investigation, we propose a phase-space transformation that generates a super-Hamiltonian, expressed in terms of new variables, which describes the behavior of a Wheeler–DeWitt wave function of the Universe within a non-commutative algebraic quantum gravity formulation. The formal structure of the super-Hamiltonian allows us to identify one of the new variables with a modified branch-cut quantum scale factor, which incorporates, as a result of the imposed variable transformations, in an underlying way, elements of the non-commutative algebra. Due to its structural character, this algebraic structure allows the identification of the other variable as the dual quantum counterpart of the modified branch-cut scale factor, with both quantities scanning reciprocal spaces. Using the iterative Range–Kutta–Fehlberg numerical analysis for solving differential equations, without resorting to computational approximations, we obtained numerical solutions, with the boundary conditions of the wave function of the Universe based on the Bekenstein criterion, which provides an upper limit for entropy. Our results indicate the acceleration of the early Universe in the context of the non-commutative branch-cut gravity formulation. These results have implications when confronted with information theory; so to accommodate gravitational effects close to the Planck scale, a formulation à la Heisenberg’s Generalized Uncertainty Principle in Quantum Mechanics involving the energy and entropy of the primordial Universe is proposed. Full article

We analyze the (dynamical) classic limit of a special semiclassical system. We describe the interaction of a quantum system with a classical one. This limit has been well studied before as a function of a constant of motion linked to the Heisenberg principle. In this paper, we investigate the existence of the mentioned limit, but with reference to the total energy of the system. Additionally, we find an attractive result regarding the border of the transition. Full article

After a brief introduction of Born’s reciprocal relativity theory is presented, we review the construction of the $deformed$ quaplectic group that is given by the semi-direct product of $U(1,3)$ with the $deformed$ (noncommutative) Weyl–Heisenberg group corresponding to $noncommutative$ fiber coordinates and momenta $[X_a,X_b]\ne 0$; $[P_a,P_b]\ne 0$. This construction leads to more general algebras given by a two-parameter family of deformations of the quaplectic algebra, and to further algebraic extensions involving antisymmetric tensor coordinates and momenta of higher ranks $[X_{a_1{a}_2\cdots a_n},X_{b_1{b}_2\cdots b_n}]\ne 0$; $[P_{a_1{a}_2\cdots a_n},P_{b_1{b}_2\cdots b_n}]\ne 0$. We continue by examining algebraic extensions of the Yang algebra in extended noncommutative phase spaces and compare them with the above extensions of the deformed quaplectic algebra. A solution is found for the exact analytical mapping of the noncommuting $x^{\mu },p^{\mu }$ operator variables (associated to an 8D curved phase space) to the canonical $Y^A,{\mathsf{\Pi }}^A$ operator variables of a flat 12D phase space. We explore the geometrical implications of this mapping which provides, in the $classical$ limit, the embedding functions $Y^A(x,p),{\mathsf{\Pi }}^A(x,p)$ of an 8D curved phase space into a flat 12D phase space background. The latter embedding functions determine the functional forms of the base spacetime metric $g_{\mu \nu }(x,p)$, the fiber metric of the vertical space $h^{ab}(x,p)$, and the nonlinear connection $N_{a\mu }(x,p)$ associated with the 8D cotangent space of the 4D spacetime. Consequently, we find a direct link between noncommutative curved phase spaces in lower dimensions and commutative flat phase spaces in higher dimensions. Full article

Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferromagnetic (HAF) of the spin S chain is that the half-integer and the integer S chain have gapless and gapped energy spectrums, respectively. The ground state (gs) of the HAF spin-1/2 and spin-1 chains have a quasi-long-range and short-range correlation, respectively. We study the effect of the exchange interaction between an HAF spin-1/2 and an HAF spin-1 chain forming a normal ladder system and its gs properties. The inter-chain exchange interaction $J_{\perp }$ can be either ferromagnetic (FM) or antiferromagnetic (AFM). Using the density matrix renormalization group method, we show that in the weak AFM/FM coupling limit of $J_{\perp }$, the system behaves like two decoupled chains. However, in the large AFM $J_{\perp }$ limit, the whole system can be visualized as weakly coupled spin-1/2 and spin-1 pairs which behave like an effective spin-1/2 HAF chain. In the large FM $J_{\perp }$ limit, coupled spin-1/2 and spin-1 pairs can form pseudo spin-3/2 and the whole system behaves like an effective spin-3/2 HAF chain. We also derive the effective model Hamiltonian in both strong FM and AFM rung exchange coupling limits. Full article

The emergence of a minimal length at the Planck scale is consistent with modern developments in quantum gravity. This is taken into account by transforming the Heisenberg uncertainty principle into the generalized uncertainty principle. Here, the position-momentum commutator is modified accordingly. In this paper, majorization uncertainty relations within the generalized uncertainty principle are considered. Dealing with observables with continuous spectra, each of the axes of interest is divided into a set of non-intersecting bins. Such formulation is consistent with real experiments with a necessarily limited precision. On the other hand, the majorization approach is mainly indicative for high-resolution measurements with sufficiently small bins. Indeed, the effects of the uncertainty principle are brightly manifested just in this case. The current study aims to reveal how the generalized uncertainty principle affects the leading terms of the majorization bound for position and momentum measurements. Interrelations with entropic formulations of this principle are briefly discussed. Full article

A universal upper limit on the entropy contained in a localized quantum system of a given size and total energy is expressed by the so-called Bekenstein bound. In a previous paper [Buoninfante, L. et al. 2022], on the basis of general thermodynamic arguments, and in regimes where the equipartition theorem still holds, the Bekenstein bound has been proved practically equivalent to the Heisenberg uncertainty relation. The smooth transition between the Bekenstein bound and the holographic bound suggests a new pair of canonical non-commutative variables, which could be thought to hold in strong gravity regimes. Full article

Electro-optical sampling of Terahertz fields with ultrashort pulsed probes is a well-established approach for directly measuring the electric field of THz radiation. This technique usually relies on balanced detection to record the optical phase shift brought by THz-induced birefringence. The sensitivity of electro-optical sampling is, therefore, limited by the shot noise of the probe pulse, and improvements could be achieved using quantum metrology approaches using, e.g., NOON states for Heisenberg-limited phase estimation. We report on our experiments on THz electro-optical sampling using single-photon detectors and a weak squeezed vacuum field as the optical probe. Our approach achieves field sensitivity limited by the probe state statistical properties using phase-locked single-photon detectors and paves the way for further studies targeting quantum-enhanced THz sensing. Full article

An uncertainty relation for the Rényi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form $\mathrm{RMSE}\ge f\left(\alpha \right)/(⟨N⟩+\frac{1}{2})$, bounding the root mean square error of any estimate of a random optical phase shift in terms of average photon number, where $f\left(\alpha \right)$ is maximised for non-Shannon entropies. Related simple yet strong uncertainty relations linking phase uncertainty to the photon number distribution, such as $\Delta \Phi \ge {max}_n{p}_n$, are also obtained. These results are significantly strengthened via upper and lower bounds on the Rényi mutual information of quantum communication channels, related to asymmetry and convolution, and applied to the estimation (with prior information) of unitary shift parameters such as rotation angle and time, and to obtain strong bounds on measures of coherence. Sharper Rényi entropic uncertainty relations are also obtained, including time-energy uncertainty relations for Hamiltonians with discrete spectra. In the latter case almost-periodic Rényi entropies are introduced for nonperiodic systems. Full article