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International Journal of Scientific Research in Science Engineering and Technology

Quantum Clocks with Double Audit and Relations with Gravity

Harsh Jindal, Jagdeep Kaur

Published Apr 14, 2021• 0 citations
Publisher

Abstract

In this paper, a non-repeating quantum algorithm is introduced that depends on detectable Byzantine’s quantum solution that attains Clk synchronization in the arbitrary faultier processes’ presence through utilizing a double quantum system only. Precisely, it has been shown that general relativistic mass–energy equivalences intimate gravitational relation among Clks, however, energy’s quantum mechanical superposition resulted in a non-fixed metric background. Depending only on assumptions that gravitational principles held in such conditions, it has been shown that the Clks essentially gets involve over time dilation effect that ultimately results in a double Clk coherence loss. Therefore, the measured time through a double Clk is not defined precisely. Although, the time’s general relativistic notion is recuperated in the Clks conventional limits.

DOI
10.32628/ijsrset218276

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In this paper, a non-repeating quantum algorithm is introduced that depends on detectable Byzantine’s quantum solution that attains Clk synchronization in the arbitrary faultier processes’ presence through utilizing a double quantum system only. Precisely, it has been shown that general relativistic mass–energy equivalences intimate gravitational relation among Clks, however, energy’s quantum mechanical superposition resulted in a non-fixed metric background. Depending only on assumptions that gravitational principles held in such conditions, it has been shown that the Clks essentially gets involve over time dilation effect that ultimately results in a double Clk coherence loss. Therefore, the measured time through a double Clk is not defined precisely. Although, the time’s general relativistic notion is recuperated in the Clks conventional limits.
In this paper, a non-repeating quantum algorithm is introduced that depends on detectable Byzantine’s quantum solution that attains Clk synchronization in the arbitrary faultier processes’ presence through utilizing a double quantum system only. Precisely, it has been shown that general relativistic mass–energy equivalences intimate gravitational relation among Clks, however, energy’s quantum mechanical superposition resulted in a non-fixed metric background. Depending only on assumptions that gravitational principles held in such conditions, it has been shown that the Clks essentially gets involve over time dilation effect that ultimately results in a double Clk coherence loss. Therefore, the measured time through a double Clk is not defined precisely. Although, the time’s general relativistic notion is recuperated in the Clks conventional limits.
In general relativity, the picture of space-time assigns an ideal clock to each world line. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of clocks along nearby world lines. However, if time is defined operationally, as a pointer position of a physical clock that obeys the principles of general relativity and quantum mechanics, such a picture is, at most, a convenient fiction. Specifically, we show that the general relativistic mass-energy equivalence implies gravitational interaction between the clocks, whereas the quantum mechanical superposition of energy eigenstates leads to a nonfixed metric background. Based only on the assumption that both principles hold in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well defined. However, the general relativistic notion of time is recovered in the classical limit of clocks.
In general relativity, the picture of spacetime assigns an ideal clock to each spacetime point. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of surrounding clocks. However, if time is defined operationally, as a pointer position of a physical clock that obeys the laws of quantum mechanics and general relativity, such a picture is at most a convenient fiction. We show that the mass-energy equivalence implies gravitational interaction between the clocks, while the superposition of energy eigenstates leads to a non-fixed metric background. Based only on the assumption that both quantum mechanics and general relativity are valid in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well-defined. However, the general relativistic notion of time is recovered in the classical limit of clocks.
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.
Abstract It has recently been reported that, under an operational definition of time, quantum clocks would get entangled through gravitational effects. Here, an alternative scenario is studied: The clocks have different masses and energy gaps, which would produce time differences via gravitational interaction. The proposal of quantum clock synchronization (QCS) for the gravity‐induced time difference is discussed. It is illustrated how the stability of measurement probability in the QCS proposal is influenced by the gravitational interaction induced by the clocks themselves. It is found that the precision of clock synchronization depends on the energy gaps of the clocks and the improvement of precision in quantum metrology is in fact an indicator of entanglement generation. The quantum enhanced estimation of time difference is also presented and it is found that the quantum Fisher information is very sensitive to the distance between the clocks.
The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when matter behaves quantum mechanically. Here, we develop a framework to operationally define events and their localisation with respect to a quantum clock reference frame, also in the presence of gravitating quantum systems. We find that, when clocks interact gravitationally, the time localisability of events becomes relative, depending on the reference frame. This relativity ia a signature of an indefinite metric, where events can occur in an indefinite causal order. Even if the metric is indefinite, for any event we can find a reference frame where local quantum operations take their standard unitary dilation form. This form is preserved when changing clock reference frames, yielding physics covariant with respect to quantum reference frame transformations.