We study two quantum versions of the Eddington clock-synchronization protocol in the presence of decoherence. The first protocol uses maximally entangled states to achieve the Heisenberg limit for clock synchronization. The second protocol achieves the limit without using entanglement. We show the equivalence of the two protocols under any single-qubit decoherence model that does not itself provide synchronization information.
The clock synchronization problem is to determine the time difference $Δ$ between two spatially separated clocks. When message delivery times between the two clocks are uncertain, $O(2^{2n})$ classical messages must be exchanged between the clocks to determine $n$ digits of $Δ$. On the other hand, as we show, there exists a quantum algorithm to obtain $n$ digits of $Δ$ while communicating only O(n) quantum messages.
I consider quantum protocols for clock synchronization, and investigate in particular whether entanglement distillation or quantum error-correcting codes can improve the robustness of these protocols. I also draw attention to some unanswered questions about the relativistic theory of quantum measurement. This paper is based on a talk given at the NASA-DoD Workshop on Quantum Information and Clock Synchronization for Space Applications (QuICSSA), September 25-26, 2000.
Clock synchronization procedures are analyzed in the presence of imperfect communications. In this context we show that there are physical limitations which prevent one from synchronizing distant clocks when the intervening medium is completely dephasing, as in the case of a rapidly varying dispersive medium.
We present a multi-party quantum clock synchronization protocol that utilizes shared prior entanglement and broadcast of classical information to synchronize spatially separated clocks. Notably, it is necessary only for any one party to publish classical information. Consequently, the efficacy of the method is independent of the relative location of the parties. The suggested protocol is robust and does not require precise sequencing of procedural steps.
We report a proof-of-principle experiment on distant clock synchronization. Besides the achievement of picosecond resolution at 3 kilometer distance, this experiment demonstrated a novel concept for high accuracy non-local timing and positioning based on the quantum feature of entangled states.
A multi-party protocol for distributed quantum clock synchronization has been claimed to provide universal limits on the clock accuracy, viz. that accuracy monotonically decreases with the number n of party members. But, this is only true for synchronization when one limits oneself to W-states. This work shows that usage of Zen-states, a generalization of W-states, results in improved accuracy, having a maximum when \lfloor n/2 \rfloor of its members have their qubits with a |1> value.
Recently a protocol for Quantum Clock Synchronization (QCS) of remote clocks using quantum entanglement was proposed by Jozsa et al. This method has the goal of eliminating the random noise present in classical synchronization techniques. However, as stated QCS depends on the two members of each entangled pair undergoing the same unitary evolution even while being transported to different locations. This is essentially equivalent to a perfect Eddington Slow Clock Transfer protocol and thus, not an improvement over classical techniques. We will discuss this and suggest ways in which QCS may sti…
The quantum clock synchronization algorithm proposed by I. L. Chuang (Phys. Rev. Lett, 85, 2006(2000)) has been implemented in a three qubit nuclear magnetic resonance quantum system. The effective-pure state is prepared by the spatial averaging approach. The time difference between two separated clocks can be determined by reading out directly through the NMR spectra.
We demonstrate a point-to-point clock synchronization protocol based on bidirectionally propagating photons generated in a single spontaneous parametric down-conversion (SPDC) source. Tight timing correlations between photon pairs are used to determine the single and round-trip times measured by two separate clocks, providing sufficient information for distance-independent absolute synchronization secure against symmetric delay attacks. We show that the coincidence signature useful for determining the round-trip time of a synchronization channel, established using a 10\,km telecommunications f…
We demonstrate that two spatially separated parties (Alice and Bob) can utilize shared prior quantum entanglement, and classical communications, to establish a synchronized pair of atomic clocks. In contrast to classical synchronization schemes, the accuracy of our protocol is independent of Alice or Bob's knowledge of their relative locations or of the properties of the intervening medium.
We demonstrate an attack on a clock synchronization protocol that attempts to detect tampering of the synchronization channel using polarization-entangled photon pairs. The protocol relies on a symmetrical channel, where propagation delays do not depend on propagation direction, for correctly deducing the offset between clocks -- a condition that could be manipulated with optical circulators, which rely on static magnetic fields to break the reciprocity of propagating electromagnetic fields. Despite the polarization transformation induced within a set of circulators, our attack creates an erro…
The two-way quantum clock synchronization has been shown not only providing femtosecond-level synchronization capability but also security against symmetric delay attacks, thus becoming a prospective method to compare and synchronize distant clocks with both enhanced precision and security. In this letter, a field test of two-way quantum synchronization between a H-maser and a Rb clock linked by a 7 km-long deployed fiber was implemented. Limited by the frequency stability of the Rb clock, the achieved time stability at 30 s was measured as 32 ps. By applying a fiber-optic microwave frequency …
We present an algorithm for synchronizing two clocks based on second-order quantum interference between entangled photons generated by parametric down-conversion. The procedure is distinct from the standard Einstein two-way clock synchronization method in that photon correlations are used to define simultaneous events in the frame of reference of a Hong-Ou-Mandel (HOM) interferometer. Once the HOM interferometer is balanced, by use of an adjustable optical delay in one arm, arrival times of simultaneously generated photons are recorded by each clock. Classical information on the arrival times …
Clock synchronization for nonfaulty processes in multiprocess networks is indispensable for a variety of technologies. A reliable system must be able to resynchronize the nonfaulty processes upon some components failing causing the distribution of incorrect or conflicting information in the network. The task of synchronizing such networks is related to detectable Byzantine agreement (DBA), which can classically be solved using recursive algorithms if and only if less than one-third of the processes are faulty. Here we introduce a nonrecursive quantum algorithm that solves the DBA and achieves …
The ability to measure, hold and distribute time with high precision and accuracy is a foundational capability for scientific exploration. Beyond fundamental science, time synchronization is an indispensable feature of public and private communication, navigation and ranging, and distributed sensing, amongst others technological applications. We propose the implementation of a quantum network of satellite- and ground-based clocks with the ability to implement Quantum Clock Synchronization to picosecond accuracy. Implementation of the proposed QCS network offers a double advantage: (1) a more a…
We present an algorithm to detect the time and frequency difference of independent clocks based on observation of time-correlated photon pairs. This enables remote coincidence identification in entanglement-based quantum key distribution schemes without dedicated coincidence hardware, pulsed sources with a timing structure or very stable reference clocks. We discuss the method for typical operating conditions, and show that the requirement in reference clock accuracy can be relaxed by about 5 orders of magnitude in comparison with previous schemes.
We introduce methods for clock synchronization that make use of the adiabatic exchange of nondegenerate two-level quantum systems: ticking qubits. Schemes involving the exchange of N independent qubits with frequency $ω$ give a synchronization accuracy that scales as $(ω\sqrt{N})^{-1}$, i.e., as the standard quantum limit. We introduce a protocol that makes use of N coherent exchanges of a single qubit at frequency $ω$, leading to an accuracy that scales as $(ωN)^{-1}\log N$. This protocol beats the standard quantum limit without the use of entanglement, and we argue that this scaling is the f…
We propose a multi party quantum clock synchronization protocol that makes optimal use of the maximal multipartite entanglement of GHZ-type states. To realize the protocol, different versions of maximally entangled eigenstates of collective energy are generated by local transformations that distinguish between different groupings of the parties. The maximal sensitivity of the entangled states to time differences between the local clocks can then be accessed if all parties share the results of their local time dependent measurements. The efficiency of the protocol is evaluated in terms of the s…
Quantum key distribution (QKD) systems provide a method for two users to exchange a provably secure key. Synchronizing the users' clocks is an essential step before a secure key can be distilled. Qubit-based synchronization protocols directly use the transmitted quantum states to achieve synchronization and thus avoid the need for additional classical synchronization hardware. Previous qubit-based synchronization protocols sacrifice secure key either directly or indirectly, and all known qubit-based synchronization protocols do not efficiently use all publicly available information published b…
We present a novel quantum clock synchronization(QCS) scheme of multiple parties which uses operation as the trigger to start the evolution of the initial state, where existing QCS protocols use measurement to start the evolution. Since the trigger is the unitary operation, we have protected entanglement of remote nodes, and after concentration of the qubits to the center node, general measurements of the total state is possible. We show that our protocol links the QCS problem to a multiple phase estimation problem. We use the Fisher information to give the precision of the synchronization, an…
The ultimate stability of atomic clocks is limited by the quantum noise of the atoms. To reduce this noise it has been suggested to use entangled atomic ensembles with reduced atomic noise. Potentially this can push the stability all the way to the limit allowed by the Heisenberg uncertainty relation, which is denoted the Heisenberg limit. In practice, however, entangled states are often more prone to decoherence, which may prevent reaching this performance. Here we present an adaptive measurement protocol that in the presence of a realistic source of decoherence enables us to get near Heisenb…
The dispersion cancellation feature of pulses which are entangled in frequency is employed to synchronize clocks of distant parties. The proposed protocol is insensitive to the pulse distortion caused by transit through a dispersive medium. Since there is cancellation to all orders, also the effects of slowly fluctuating dispersive media are compensated. The experimental setup can be realized with currently available technology, at least for a proof of principle.
Recent work has raised the possibility that quantum information theory techniques can be used to synchronize atomic clocks nonlocally. One of the proposed algorithms for quantum clock synchronization (QCS) requires distribution of entangled pure singlets to the synchronizing parties. Such remote entanglement distribution normally creates a relative phase error in the distributed singlet state which then needs to be purified asynchronously. We present a fully relativistic analysis of the QCS protocol which shows that asynchronous entanglement purification is not possible, and, therefore, that t…
We demonstrate a point-to-point clock synchronization protocol based on bidirectionally exchanging photons produced in spontaneous parametric down conversion (SPDC). The technique exploits tight timing correlations between photon pairs to achieve a precision of 51ps in 100s with count rates of order 200s$^{-1}$. The protocol is distance independent, secure against symmetric delay attacks and provides a natural complement to techniques based on Global Navigation Satellite Systems (GNSS). The protocol works with mobile parties and can be augmented to provide authentication of the timing signal v…
A method is proposed to employ entangled and squeezed light for determining the position of a party and for synchronizing distant clocks. An accuracy gain over analogous protocols that employ classical resources is demonstrated and a quantum-cryptographic positioning application is given, which allows only trusted parties to learn the position of whatever must be localized. The presence of a lossy channel and imperfect photodetection is considered. The advantages in using partially entangled states is discussed.
The quantum clock synchronization (QCS) is to measure the time difference among the spatially separated clocks with the principle of quantum mechanics. The first QCS algorithm proposed by Chuang and Jozsa is merely based on two parties, which is further extended and generalized to the multiparty situation by Krco and Paul. They present a multiparty QCS protocol based upon W states that utilizes shared prior entanglement and broadcast of classical information to synchronize spatially separated clocks. Shortly afterwards, Ben-Av and Exman came up with an optimized multiparty QCS using Z state. I…
We propose a quantum method to judge whether two spatially separated clocks have been synchronized within a specific accuracy $σ$. If the measurement result of the experiment is obviously a nonzero value, the time difference between two clocks is smaller than $σ$; otherwise the difference is beyond $σ$. On sharing the 2$N$-qubit bipartite maximally entangled state in this scheme, the accuracy of judgement can be enhanced to $σ\simπ/{(ω(N+1))}$. This criterion is consistent with Heisenberg scaling that can be considered as beating standard quantum limit, moreover, the unbiased estimation condit…
We demonstrated ultra fast BB84 quantum key distribution (QKD) transmission at 625 MHz clock rate through a 97 km field-installed fiber using practical clock synchronization based on wavelength-division multiplexing (WDM). We succeeded in over-one-hour stable key generation at a high sifted key rate of 2.4 kbps and a low quantum bit error rate (QBER) of 2.9%. The asymptotic secure key rate was estimated to be 0.78-0.82 kbps from the transmission data with the decoy method of average photon numbers 0, 0.15, and 0.4 photons/pulse.
It is shown how possible corrections to ordinary quantum mechanics described by the Lindblad equation might be detected by exploiting the great precision of atomic clocks.
A wide variety of positioning and ranging procedures are based on repeatedly sending electromagnetic pulses through space and measuring their time of arrival. This paper shows that quantum entanglement and squeezing can be employed to overcome the classical power/bandwidth limits on these procedures, enhancing their accuracy. Frequency entangled pulses could be used to construct quantum positioning systems (QPS), to perform clock synchronization, or to do ranging (quantum radar): all of these techniques exhibit a similar enhancement compared with analogous protocols that use classical light. Q…
A clock steps a computer through a cycle of phases. For the propagation of logical symbols from one computer to another, each computer must mesh its phases with arrivals of symbols from other computers. Even the best atomic clocks drift unforeseeably in frequency and phase; feedback steers them toward aiming points that depend on a chosen wave function and on hypotheses about signal propagation. A wave function, always under-determined by evidence, requires a guess. Guessed wave functions are coded into computers that steer atomic clocks in frequency and position---clocks that step computers t…
We have demonstrated the exchange of sifted quantum cryptographic key over a 730 meter free-space link at rates of up to 1.0 Mbps, two orders of magnitude faster than previously reported results. A classical channel at 1550 nm operates in parallel with a quantum channel at 845 nm. Clock recovery techniques on the classical channel at 1.25 Gbps enable quantum transmission at up to the clock rate. System performance is currently limited by the timing resolution of our silicon avalanche photodiode detectors. With improved detector resolution, our technique will yield another order of magnitude in…
It has recently been reported [\textit{PNAS} \textbf{114}, 2303 (2017)] that, under an operational definition of time, quantum clocks would get entangled through gravitational effects. Here we study an alternative scenario: the clocks have different masses and energy gaps, which would produce time difference via gravitational interaction. The proposal of quantum clock synchronization for the gravity-induced time difference is discussed. We illustrate how the stability of measurement probability in the quantum clock synchronization proposal is influenced by the gravitational interaction induced…
The clock synchronization problem is to determine the time difference T between two spatially separated parties. We improve on I. Chuang's quantum clock synchronization algorithm and show that it is possible to obtain T to n bits of accuracy while communicating only one qubit in one direction and using an O(2^n) frequency range. We also prove a quantum lower bound of Ω(2^n) for the product of the transmitted qubits and the range of frequencies, thus showing that our algorithm is optimal.
A major outstanding problem for many quantum clock synchronization protocols is the hidden assumption of the availability of synchronized clocks within the protocol. In general, quantum operations between two parties do not have consistent phase definitions of quantum states, which introduce an unknown systematic phase error. We show that despite prior arguments to the contrary, it is possible to remove this unknown phase via entanglement purification. This closes the loophole for entanglement based quantum clock synchronization protocols, which are most compatible with current photon based lo…
Event synchronisation is a ubiquitous task, with applications ranging from 5G technology to industrial automation and smart power grids. The emergence of quantum communication networks will further increase the demand for precise synchronization in the optical and electronic domains, which implies significant resource overhead, such as the requirement for ultrastable clocks or additional synchronization lasers. Here we show how temporal correlations of energy-time entangled photons may be harnessed for synchronisation in quantum networks. We achieve stable synchronisation jitter <68 ps with as…
Entangled states of light exhibit measurable correlations between light detections at separated locations. These correlations are exploited in entangled-state quantum key distribution. To do so involves setting up and maintaining a rhythm of communication among clocks at separated locations. Here, we try to disentangle our thinking about clocks as used in actual experiments from theories of time, such as special relativity or general relativity, which already differ between each other. Special relativity intertwines the concept of time with a particular definition of the synchronization of clo…
Measuring velocities requires the synchronization of spatially-separated clocks. Because this synchronization must precede the determination of velocities, no system of clock synchronization--such as that based on Einstein's presumption of light-speed isotropy--can ever be founded on an experimentally-validated velocity. I argue that this very old observation, which lingers in the philosophical literature under the heading ``Conventionality of Synchronization,'' suggests an explanation of why ``spooky'' quantum correlations can transfer no information at any speed, superluminal or otherwise. T…
Optical lattice clocks can now resolve the height difference below 1 mm within an atomic ensemble by means of gravitational redshift with integration over sufficient amount of time. Further improvement in the stability enables the clocks to resolve the height difference of subsystems within an atomic ensemble that is conventionally interrogated as a single coherent spin state in a single Ramsey sequence, resulting in the dephasing of the coherent spin state. This effect is observable with a clock of a stability of $\lesssim 10^{-21}$ by introducing a single-layer-resolved imaging system for a …
Despite the importance of isotopically purified samples in current experiments, there have been few corresponding studies of spin qubit decoherence using full quantum bath calculations. Isotopic purification eliminates the well-studied nuclear spin baths which usually dominate decoherence. We model the coherence of electronic spin qubits in silicon near so called Clock Transitions (CT) where experiments have electronic $T_{2e}$ times of seconds. Despite the apparent simplicity of the residual decoherence mechanism, this regime is not well understood: the state mixing which underpins CTs allows…
The Conditional Probability Interpretation of Quantum Mechanics replaces the abstract notion of time used in standard Quantum Mechanics by the time that can be read off from a physical clock. The use of physical clocks leads to apparent non-unitary and decoherence. Here we show that a close approximation to standard Quantum Mechanics can be recovered from conditional Quantum Mechanics for semi-classical clocks, and we use these clocks to compute the minimum decoherence predicted by the Conditional Probability Interpretation.
A protocol for synchronizing distant clocks is proposed that does not rely on the arrival times of the signals which are exchanged, and an optical implementation based on coherent-state pulses is described. This protocol is not limited by any dispersion that may be present in the propagation medium through which the light signals are exchanged. Possible improvements deriving from the use of quantum-mechanical effects are also addressed.
The notion of time is given a different footing in Quantum Mechanics and General Relativity, treated as a parameter in the former and being an observer dependent property in the later. From a operational point of view time is simply the correlation between a system and a clock, where an idealized clock can be modelled as a two level systems. We investigate the dynamics of clocks interacting gravitationally by treating the gravitational interaction as a classical information channel. In particular, we focus on the decoherence rates and temporal resolution of arrays of $N$ clocks showing how the…
Clock synchronization between the ground and satellites is a fundamental issue in future quantum telecommunication, navigation, and global positioning systems. Here, we propose a scheme of near-Earth orbit satellite-based quantum clock synchronization with atmospheric dispersion cancellation by taking into account the spacetime background of the Earth. Two frequency entangled pulses are employed to synchronize two clocks, one at a ground station and the other at a satellite. The time discrepancy of the two clocks is introduced into the pulses by moving mirrors and is extracted by measuring the…
