Quantum Clock Research Articles

Demonstration and Comparison of Different Entanglement Fabrication Approaches

Quantum entanglement is the most representative feature of quantum mechanics to classical mechanics. It is the delocalization, non-classical strong correlation among multiple quantum system. It has been developed for nearly one hundred years and a lot of methods of production and applications have been proposed. Aiming at the generation mode of quantum entanglement, this study presents two general preparation methods of quantum entanglement sources, including spontaneous parametric down-conversion (SPDC) and the preparation of quantum entanglement sources based on the four-wave mixing (FWM) effect. The principle, advantages and disadvantages of quantum entanglement sources are analyzed respectively. Finally, the research and application direction of the preparation method of quantum entanglement source are prospected. With the ability of preparation of quantum entanglement source, the application of quantum entanglement developed quickly, (e.g., quantum teleportation, entanglement swapping, quantum key distribution and quantum dense coding in the area of communication), and other area such as quantum computer, quantum imaging, quantum ranging and quantum clock synchronization. These results shed light on guiding further exploration of entanglement fabrication.

Local Predecoder to Reduce the Bandwidth and Latency of Quantum Error Correction

A fault-tolerant quantum computer will be supported by a classical decoding system interfacing with quantum hardware to perform quantum error correction. It is important that the decoder can keep pace with the quantum clock speed, within the limitations on communication that are imposed by the physical architecture. To this end, we propose a local ``predecoder,'' which makes greedy corrections to reduce the amount of syndrome data sent to a standard matching decoder. We study these classical overheads for the surface code under a phenomenological phase-flip noise model with imperfect measurements. We find substantial improvements in the run time of the global decoder and the communication bandwidth by using the predecoder. For instance, to achieve a logical-failure probability of $f={10}^{\ensuremath{-}15}$ using qubits with physical error rate $p={10}^{\ensuremath{-}3}$ and a distance $d=22$ code, we find that the bandwidth cost is reduced by a factor of 1000 and that the time taken by a matching decoder is sped up by a factor of 200. To achieve this target failure probability, the predecoding approach requires a 50% increase in the qubit count compared with the optimal decoder.

Universality-of-clock-rates test using atom interferometry with T3 scaling

Metric descriptions of gravitation, among them general relativity as today's established theory, are founded on assumptions summarized by the Einstein equivalence principle (EEP). Its violation would hint at unknown physics and could be a leverage for the development of quantum gravity. Atomic clocks are excellent systems to probe aspects of EEP connected to (proper) time and have evolved into a working horse for tests of local position invariance (LPI). Even though the operational definition of time requires localized and idealized clocks, quantum systems like atoms allow for spatial superpositions that are inherently delocalized. While quantum experiments have tested other aspects of EEP, no competitive test of LPI has been performed or proposed allowing for an intrinsic delocalization. We extend the concepts for tests of the universality of clock rates (one facet of LPI) to atom interferometry generating delocalized quantum clocks. The proposed test depends on proper time with a favorable scaling and is, in contrast to fountain clocks, robust against initial conditions and recoil effects. It enables optical frequencies so that the projected sensitivity exceeds the one of state-of-the-art localized clocks. These results extend our notion of time, detached from classical and localized philosophies.

Towards global time distribution via satellite-based sources of entangled photons

We propose a satellite-based scheme to perform clock synchronization between ground stations spread across the globe using quantum resources. We refer to this as a quantum clock synchronization (QCS) network. Through detailed numerical simulations, we assess the feasibility and capabilities of a near-term implementation of this scheme. We consider a small constellation of nanosatellites equipped only with modest resources. These include quantum devices such as spontaneous parametric down conversion (SPDC) sources, avalanche photo-detectors (APDs), and moderately stable on-board clocks such as chip scale atomic clocks (CSACs). In our simulations, the various performance parameters describing the hardware have been chosen such that they are either already commercially available, or require only moderate advances. We conclude that with such a scheme establishing a global network of ground based clocks synchronized to sub-nanosecond level (up to a few picoseconds) of precision, would be feasible. Such QCS satellite constellations would form the infrastructure for a future quantum network, able to serve as a globally accessible entanglement resource. At the same time, our clock synchronization protocol, provides the sub-nanosecond level synchronization required for many quantum networking protocols, and thus, can be seen as adding an extra layer of utility to quantum technologies in the space domain designed for other purposes.

Autonomous Quantum Devices: When Are They Realizable without Additional Thermodynamic Costs?

The resource theory of quantum thermodynamics has been a very successful theory and has generated much follow-up work in the community. It requires energy-preserving unitary operations to be implemented over a system, bath, and catalyst as part of its paradigm. So far, such unitary operations have been considered a "free" resource in the theory. However, this is only an idealization of a necessarily inexact process. Here, we include an additional auxiliary control system which can autonomously implement the unitary by turning an interaction "on or off". However, the control system will inevitably be degraded by the backaction caused by the implementation of the unitary. We derive conditions on the quality of the control device so that the laws of thermodynamics do not change and prove - by utilizing a good quantum clock - that the laws of quantum mechanics allow the backreaction to be small enough so that these conditions are satisfiable. Our inclusion of nonidealized control into the resource framework also raises interesting prospects, which were absent when considering idealized control. Among other things, the emergence of a third law without the need for the assumption of a light cone. Our results and framework unify the field of autonomous thermal machines with the thermodynamic quantum resource-theoretic one, and lay the groundwork for all quantum processing devices to be unified with fully autonomous machines.

Quantum memories for fundamental science in space

Investigating and verifying the connections between the foundations of quantum mechanics and general relativity will require extremely sensitive quantum experiments. To provide ultimate insight into this fascinating area of physics, the realization of dedicated experiments in space will sooner or later become a necessity. Quantum technologies, and among them quantum memories in particular, are providing novel approaches to reach conclusive experimental results due to their advanced state of development backed by decades of progress. Storing quantum states for prolonged time will make it possible to study Bell tests on astronomical baselines, to increase measurement precision for investigations of gravitational effects on quantum systems, or enable distributed networks of quantum sensors and clocks. We here promote the case of exploiting quantum memories for fundamental physics in space, and discuss both distinct experiments as well as potential quantum memory platforms and their performance.

Gravitational time dilation in extended quantum systems: The case of light clocks in Schwarzschild spacetime

The precision of optical atomic clocks is approaching a regime where they resolve gravitational time dilation on smaller scales than their own extensions. Hence, an accurate description of quantum clocks has to take their spatial extension into account. In this article, as a first step toward a fully relativistic description of extended quantum clocks, we investigate a quantized version of Einstein's light clock fixed at a constant distance from a large massive object like the Earth. The model consists of a quantum light field in a one-dimensional cavity in Schwarzschild spacetime, where the distance between the mirrors is fixed by a rigid rod. By comparing a vertical and a horizontal clock, we propose an operational way to define the clock time when the clock resolves gravitational time dilation on scales smaller than its extension. In particular, we show that the time measured by the vertical light clock is equivalent to the proper time defined at its center. We also derive fundamental bounds on the precision of these clocks for measurements of proper time and the Schwarzschild radius.

Method of relativistic syntonization of quantum clocks: experimental studies

Method of relativistic syntonization of quantum clocks: experimental studies

Quantum clocks, gravitational time dilation, and quantum interference

A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order to investigate whether the weak equivalence principle holds for quantum matter. We find that for general quantum states the quantum time dilation in a weak gravitational field obeys a similar gravitational time dilation found in classical relativity. However, unlike the special relativistic case, the time dilation involves the external time (a background coordinate time at the observer on the Earth) as well as the proper times of two clocks. We also investigate a quantum time dilation effect induced by a clock in a superposition of wave packets localized in momentum space or in position space and propose the setup to observe the gravitational effect in the quantum interference effect in the time dilation.

Entanglement-Asymmetry Correspondence for Internal Quantum Reference Frames.

In the quantization of gauge theories and quantum gravity, it is crucial to treat reference frames such as rods or clocks not as idealized external classical relata, but as internal quantum subsystems. In the Page-Wootters formalism, for example, evolution of a quantum system S is described by a stationary joint state of S and a quantum clock, where time dependence of S arises from conditioning on the value of the clock. Here, we consider (possibly imperfect) internal quantum reference frames R for arbitrary compact symmetry groups, and show that there is an exact quantitative correspondence between the amount of entanglement in the invariant state on RS and the amount of asymmetry in the corresponding conditional state on S. Surprisingly, this duality holds exactly regardless of the choice of coherent state system used to condition on the reference frame. Averaging asymmetry over all conditional states, we obtain a simple representation-theoretic expression that admits the study of the quality of imperfect quantum reference frames, quantum speed limits for imperfect clocks, and typicality of asymmetry in a unified way. Our results shed light on the role of entanglement for establishing asymmetry in a fully symmetric quantum world.

Postselection and quantum energetics

We investigate the anomalous energy change of the measurement apparatus when a qubit is measured in bases that do not commute with energy. We model two possible measurement implementations: one is a quantum clock model with a completely time-independent Hamiltonian, while the other is a Jaynes-Cummings model which is time-dependent but conserves the total excitation number. We look at the mean energy change of the measurement apparatus in both models, conditioned on the qubit post-selection, and find that this change can be much greater than the level spacing of the qubit, like an anomalous weak value. In the clock model, the expression for the apparatus energy shift explicitly contains the weak value of the qubit Hamiltonian. However, in our case, no explicit weak measurements are carried out. Our two models give different results, which we explain to be a consequence of the non-degenerate spectrum of the Jaynes-Cummings model. We compare our calculations in the Jaynes-Cummings model with the experimental data of [J. Stevens, et al, arXiv:2109.09648 (2021)] and find good agreement when the conditions of our derivation are valid.

Non-inertial quantum clock frames lead to non-Hermitian dynamics

The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend the notion of proper time to quantum mechanics within a relational framework. Here, we use similar ideas combined with the relativistic mass-energy equivalence to study an accelerating massive quantum particle with an internal clock system. We show that the ensuing evolution from the perspective of the particle’s internal clock is non-Hermitian. This result does not rely on specific implementations of the clock. As a particular consequence, we prove that the effective Hamiltonian of two gravitationally interacting particles is non-Hermitian from the perspective of the clock of either particle.

A model of quantum spacetime

We consider a global quantum system (the “Universe”) satisfying a double constraint, both on total energy and total momentum. Generalizing the Page and Wootters quantum clock formalism, we provide a model of 3 + 1 dimensional, non-relativistic, quantum spacetime emerging from entanglement among different subsystems in a globally “timeless” and “positionless” Universe.

QuCTS—Single-Flux Quantum Clock Tree Synthesis

Superconductive rapid single-flux quantum (RSFQ) is an emerging cryogenic technology, promising a significant boost in performance and ultralow power consumption. The operating frequency achieved by RSFQ digital integrated circuits is several orders of magnitude greater than traditional CMOS circuits. The fundamental difference of RSFQ circuits, however, renders traditional clocking techniques appropriate for CMOS unsuitable for RSFQ technology. Most RSFQ logic gates, such as AND and OR, are sequential in nature. The number of pipeline stages is therefore significantly greater in RSFQ as compared to CMOS, complicating the clock distribution network design process. This issue is further exacerbated with the need for splitters to achieve a fanout greater than one and the need for transmission lines rather than ordinary metallic wires as in CMOS. In this work, QuCTS—single-flux Quantum (SFQ) Clock Tree Synthesis—is presented. QuCTS utilizes a two-stage framework for synthesizing clock networks. In the clock skew scheduling stage, the clock signal arrival time of each gate is chosen to maximize the robustness of the circuit to timing variations. In the clock tree synthesis stage, the layout of the clock distribution network is generated based on a novel delay equilibration technique. QuCTS is the first clock tree synthesis tool for RSFQ circuits utilizing useful clock skew. The synthesized network satisfies the clock arrival time requirements while minimizing the associated overhead, such as the interconnect length and number of delay elements. The tool is validated on a set of benchmark circuits. In a prototypical case study, a clock tree is generated for the AMD2901 with 1049 clock sinks in 53 min while satisfying the clock arrival time.

Sensitivity to Mass Changes of Lakes, Subsurface Hydrology and Glaciers of the Quantum Technology Gravity Gradients and Time Observations of Satellite MOCAST+

The quantum technology absolute gravimeters, gradiometers, and clocks are at the forefront of the instrumentation to be exploited in a future gravity mission (the QSG mission concept). Apart from the quantum payload, the mission design defines the choice of the number of satellites and the satellite orbit constellation, with the goal of optimizing the observation of the earth’s gravity field and reducing aliasing phenomena. Our goal is to define the realistic gravity field changes generated by glaciers and lakes and define the sensitivity of the quantum gravity mission for the detection of hydrologic and cryospheric mass changes. The analysis focuses on mass changes in the high mountains of Asia and the South American continent. The mass changes are based on terrestrial and satellite observations and are of a climatic origin. We show that compared to the existing GRACE-FO mission, a quantum gravity mission significantly improves the detection of the climatic mass gain of lakes and mass loss of glaciers, allowing for smaller mass features to be distinguished, and smaller mass losses to be detected. The greater signal is the seasonal signal with a yearly period, which would be detected at the 10 Gt level for areas > 8000 km2. The yearly mass loss of the Patagonian glaciers can be detected at the 5 Gt/yr level, an improvement from the 10 Gt/yr detectable by GRACE-FO. Spatial resolution would also be improved, with an increase of about 50% in spatial frequency for the detection of the mass change rate of lakes and glaciers in Tibet. The improved spatial resolution enables an improved localization of the lakes and glaciers affected by climatic mass change. The results will contribute to defining the user requirements of the future QSG missions.

Continuous quantum clock with high precision and long recurrence time

Continuous clocks, i.e., clocks that measure time in a continuous manner, are regarded as an essential component of sensing technology. Precision and recurrence time are two basic features of continuous clocks. In this paper, in the framework of quantum estimation theory various models for continuous quantum clocks are proposed, and all tools of quantum estimation theory are employed to seek the characteristics of clocks with high precision and long recurrence time. Then, in a resource-based approach, the performances of the proposed models are compared. It is shown that quantum clocks based on an $n$ two-qubit system not only can have better precision than quantum clocks based on a $2n$ one-qubit system but also support long recurrence time. Finally, it is shown that while employing $n$ entangled qubits improves the precision of clocks by a factor of $1/\sqrt{n}$, it inevitably worsens the recurrence time of the clock.

Evaluation of the systematic shifts of a $${}^{40}\text {Ca}^{+}$$–$${}^{27}\text {Al}^{+}$$ optical clock

Quantum-logic-based ${}^{27}\textrm{Al}^+$ optical clock has been demonstrated in several schemes as there are different choices of the auxiliary ion species. In this paper, we present the first detailed evaluation of the systematic shift and the total uncertainty of an ${}^{27}\textrm{Al}^+$ optical clock sympathetically cooled by a ${}^{40}\textrm{Ca}^+$ ion. The total systematic uncertainty of the ${}^{40}\textrm{Ca}^+ - {}^{27}\textrm{Al}^+$ quantum logic clock has been estimated to be $7.9 \times 10^{-18}$, which was mainly limited by the uncertainty of the quadratic Zeeman shift. By comparing the frequency of two counter-propagating clock beams on the same ion, we measured the frequency stability to be $3.7 \times 10^{-14} /\sqrt{\tau}$.

Demonstration of 50 Km Fiber-Optic Two-Way Quantum Clock Synchronization

Fiber-optic Quantum clock synchronization has been proposed and experimentally demonstrated for its potential enhancements in precision and better guarantee of security. To further prove its advantage in practical applications, it is necessary to test its synchronization performance between clocks apart for at least intracity optical fiber distance. In this paper, we report a fiber-optic two-way quantum clock synchronization experiment with the distance reaching 50 km. With the common reference clock, a synchronization stability of 54.6 fs at 57300 s and an accuracy of 1.3 ps±36.6 ps have been achieved. With independent reference clocks, comparable performance has also been achieved combined with the microwave frequency transfer technology, which shows a stability of 89.5 fs at 57300 s. These results nicely showcase the feasibility of the two-way quantum clock synchronization to provide femtosecond-scale synchronization precision over intracity optical fiber links.

Time and Quantum Clocks: A Review of Recent Developments

In this review we present the problem of time in quantum physics, including a short history of the problem and the known objections about considering time as a quantum observable. The need to deal with time as an observable is elaborated through some unresolved problems. The lack of a consistent theory of time is currently hindering the formulation of a full-fledged theory of quantum gravity. It is argued that the proposal set forth by several authors of considering an intrinsic measurement of quantum time, besides having the conventional external time, is compelling. Recently several suggestions have been put forward to revive the proposal of Page and Wootters (1983), elaborating and resolving some of the main ambiguities of the original proposal and opening new scope for understanding its content. The approach followed in these new contributions exposes the need to go beyond the limitations enforced by the conventional approach of quantum physics. The attitude of covariant loop quantum gravity, in which it is called to completely ignore time, is also discussed. This review could be a step forward in an endeavour to reform our outlook of the unification of the theory of relativity and quantum physics by furnishing the conceptual ground needed for this goal. Intentionally, some technical details are avoided since we aim to present the approaches to resolve the problem in a simple way with the clearest possible outlook. These can be looked up in the original references provided.

The use of a random number generator to develop a technique for predicting the departure of quantum clocks

The issues related to the development of models for predicting the divergence of scales of spatially dispersed quantum clocks are considered. The graphs of discrepancies between the scales of the onboard clocks of navigation satellites (NS) GLONASS and GPS relative to the scale of the central synchronizer are given. Mathematical models are proposed for predicting the departure of the onboard clock scales from the CA scale, consisting of three analytical components and an autoregression equation. The first two components analytically define linear and parabolic trends in the divergence of the scales. The third component is represented by a trigonometric polynomial with non-multiple harmonics. The parameters of all three components are estimated using the least squares method (OLS) based on the data of discrepancies in the NS clock scales individually for each NS. The forecast of residual stochastic changes is made using the autoregression equation. To work out forecasting models, it is proposed to use a software simulator of the instability process of quantum clocks.