Quantum Clock Synchronization Based on Shared Prior Entanglement

Jozsa, Richard; Abrams, Daniel M.; Dowling, Jonathan P.; Williams, Colin P.

doi:10.1103/physrevlett.85.2010

Cited by 325 publications

(294 citation statements)

References 11 publications

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“…These states do not evolve in time. This property has been exploited in the quantum clock synchronization [36].…”

Section: Model Formalism and Its Wavefunctionmentioning

confidence: 99%

A linear atomic quantum coupler

El-Orany¹,

B²

2010

J. Phys. B: At. Mol. Opt. Phys.

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In this paper, we develop the notion of the linear atomic quantum coupler. This device consists of two modes propagating into two waveguides, each of them includes a localized and/or a trapped atom. These waveguides are placed close enough to allow exchanging energy between them via evanescent waves. Each mode interacts with the atom in the same waveguide in the standard way, i.e. as the Jaynes-Cummings model (JCM), and with the atom-mode in the second waveguide via evanescent wave. We present the Hamiltonian for the system and deduce the exact form for the wavefunction. We investigate the atomic inversions and the second-order correlation function. In contrast to the conventional linear coupler, the atomic quantum coupler is able to generate nonclassical effects. The atomic inversions can exhibit long revival-collapse phenomenon as well as subsidiary revivals based on the competition among the switching mechanisms in the system. Finally, under certain conditions, the system can yield the results of the two-mode JCM.

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“…These states do not evolve in time. This property has been exploited in the quantum clock synchronization [36].…”

Section: Model Formalism and Its Wavefunctionmentioning

confidence: 99%

A linear atomic quantum coupler

El-Orany¹,

B²

2010

J. Phys. B: At. Mol. Opt. Phys.

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“…The teleportation protocol of the previous section (which is equivalent to the original QCS protocol of [1]) demonstrates that as long as x 1 and x 2 are timelike separated events in spacetime, the relative phase Φ δ (x 1 , x 2 ) can be directly observed by Alice and Bob via quantum measurements followed by classical communication of the outcomes. Conversely, since the wave function contains all knowledge that can ever be obtained about a quantum system, the only observable associated with the singlet state Ψ δ which contains any information about δ is Φ δ (x 1 , x 2 ).…”

Section: Lorentz-invariant Analysis Of Qcsmentioning

confidence: 99%

“…(11): (1) If δ = 0, i.e. under the same assumption as in the original QCS protocol [1] that the shared singlet states are pure, the time-synchronization offset τ can be immediately determined by Alice (recall that α and β are known to both parties). Hence, the synchronization result of the QCS protocol can equivalently be achieved through teleportation.…”

Section: "Impure" Singlets Qcs Algorithm and Teleportationmentioning

confidence: 99%

“…(5), we have the crux of the QCS algorithm of Ref. [1]: The dark, invariant state Ψ shared between Alice and Bob contains two clock states, one for each observer, entangled in such a way as to freeze their time evolution. As soon as Bob (or Alice) performs a measurement on Ψ in the basis {|+ , |− }, thereby destroying the entanglement, he (or she) starts these two dormant clocks "simultaneously" in both reference frames (classical communications are then necessary to sort out which party has the |+ clock and which party has |− ).…”

Section: Clock Synchronization With Shared Singletsmentioning

confidence: 99%

“…al. [1], which assumes a supply of such pure singlet states shared as a resource between the synchronizing parties Alice and Bob. Specifically, consider the unitary (Hadamard) transformation (π/2 -pulse followed by the spin operator σ z ) on H given by…”

Section: Clock Synchronization With Shared Singletsmentioning

confidence: 99%

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Lorentz-invariant look at quantum clock-synchronization protocols based on distributed entanglement

Yurtsever

Dowling

2002

Phys. Rev. A

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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 the proposed QCS scheme remains incomplete. We discuss possible directions of research in quantum information theory which may lead to a complete, working QCS protocol. Clock synchronization with shared singletsSuppose a supply of identical but distinguishable twostate systems (e.g. atoms) are available whose betweenstate transitions can be manipulated (e.g. by laser pulses). Let |1 and |0 denote, respectively, the excited and ground states (which span the internal Hilbert space H) of the prototype two-state system, and let the energy difference between the two states be Ω (we will use units in which = c = 1 throughout this letter). Without loss of generality, we can assumewhere H 0 denotes the internal Hamiltonian. Suppose pairs of these two-state systems are distributed to two spatially-separated observers Alice and Bob. The Hilbert space of each pair can be written as H A ⊗ H B , where ⊗ denotes tensor product between vector spaces. A ("pure") singlet is the specific entangled quantum state in this product Hilbert space given by[in what follows, we will omit tensor-product signs in expressions of the kind Eq. (2) unless required for clarity]. Two important properties of the singlet state Ψ are: (i) it is a "dark" state (invariant up to a multiplicative phase factor) under the time evolution U t ≡ exp(itH 0 ), i.e. (U t ⊗ U t )Ψ = e iφ Ψ where e iφ is an overall phase, and (ii) it is similarly invariant under all unitary transformations of the form U ⊗ U , where U is any arbitrary unitary map on H (not necessarily equal to U t ). Both properties are needed for the Quantum Clock Synchronization (QCS) protocol of Jozsa et. al.[1], which assumes a supply of such pure singlet states shared as a resource between the synchronizing parties Alice and Bob. Specifically, consider the unitary (Hadamard) transformation (π/2 -pulse followed by the spin operator σ z ) on H given byUnlike the states |0 and |1 , which are dark under time evolution (they only pick up an overall phase under U t ), the states |+ and |− are "clock states" (in other words, they accumulate an observable relative phase under U t ) because of the energy difference Ω as specified in Eq. (1). Such states can be used to "drive" precision clocks in the following way: Start, for example, with an ensemble of atoms in the state |+ produced by an initial Hadamard pulse at time t 0 , and apply a second Hadamard pulse at a later time t 0 + T . This leads to a final state ...

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Quantum Networking

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Quantum Clock Synchronization Based on Shared Prior Entanglement

Cited by 325 publications

References 11 publications

A linear atomic quantum coupler

A linear atomic quantum coupler

Lorentz-invariant look at quantum clock-synchronization protocols based on distributed entanglement

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