Robust Quantum Communication Using a Polarization-Entangled Photon Pair

Boileau, Jean-Christian; Laflamme, Raymond; Laforest, Martin; Myers, Casey R.

doi:10.1103/physrevlett.93.220501

Cited by 70 publications

(78 citation statements)

References 19 publications

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“…One can circumvent the need for a SRF encoding logical qubits in multiqubit states with appropriate symmetry properties, so that the states are rotationally invariant. This results in a considerable reduction in overhead due to initial alignment stages; but, since all the available protocols exploiting multi-qubit states of photons require the use of two [2,3,4], three [5], or four photons [5,6,7,8] to encode one single logical qubit, this increases the amount of resources as well as the sensitivity of the protocol to photon losses.…”

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confidence: 99%

Quantum Communication without Alignment using Multiple-Qubit Single-Photon States

2007

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We propose a scheme for encoding logical qubits in a subspace protected against collective rotations around the propagation axis using the polarization and transverse spatial degrees of freedom of single photons. This encoding allows for quantum key distribution without the need of a shared reference frame. We present methods to generate entangled states of two logical qubits using present day down-conversion sources and linear optics, and show that the application of these entangled logical states to quantum information schemes allows for alignment-free tests of Bell's inequalities, quantum dense coding and quantum teleportation. The most common implementations of quantum communication schemes involve two or more parties that, in order to encode and decode information, must share a common spatial reference frame. Nevertheless, it has been pointed out that a shared reference frame (SRF) is a resource that should not be taken for granted, since establishing a perfect SRF requires the transmission of an infinite amount of information [1]. One can circumvent the need for a SRF encoding logical qubits in multiqubit states with appropriate symmetry properties, so that the states are rotationally invariant. This results in a considerable reduction in overhead due to initial alignment stages; but, since all the available protocols exploiting multi-qubit states of photons require the use of two [2,3,4], three [5], or four photons [5,6,7,8] to encode one single logical qubit, this increases the amount of resources as well as the sensitivity of the protocol to photon losses.The lack of alignment between two users of a protocol is equivalent to a collective random rotation of the qubits during the transmission process, which can be considered as a special type of collective noise. Rotationally invariant states, in turn, span a decoherence-free subspace (DFS) protected against such noise. A DFS protected against collective noise is a subspace of the total Hilbert space of a system that is immune to decoherence, provided that it acts identically and simultaneously on each member of the system [9]. For example, two ions of the same species closely spaced in a Paul trap, or photons propagating close together in the same optical fiber, are exposed approximately to the same fluctuations. Thus, through the use of DFSs, their respective coherence properties can be enhanced considerably [4,10]. Nevertheless, the assumption of collective noise is in practice fulfilled only approximately, as two different particles are never actually subject to exactly the same noise.Photons are a natural candidate for quantum communication due to the ease with which they can be transmitted. Using spontaneous parametric down-conversion (SPDC), one can create triggered single photons or entangled photon pairs [11,12]. Also, there has been a great deal of recent work exploiting the fact that one can encode multiple qubits into multiple degrees of freedom (DOF) of photons [12,13]. But as different DOF are not necessarily affected in the same way by the ...

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confidence: 99%

Quantum Communication without Alignment using Multiple-Qubit Single-Photon States

2007

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“…This noise arises from the fluctuation of the birefringence of the optical fiber which alters the polarisation state of the photons. When this fluctuation is slow in time, its effect can be described with a unitary operation [43,44]. For simplicity, we shall consider that U B (θ) is parametrised only with one real parameter θ.…”

Section: Discussionmentioning

confidence: 99%

“…We include the operator U B (θ) in Eq. (34) to model the collective noise (or correlated noise) introduced by the quantum channel (e.g., optical fiber) [43,44]. This noise arises from the fluctuation of the birefringence of the optical fiber which alters the polarisation state of the photons.…”

Section: Discussionmentioning

confidence: 99%

Single-photon quantum key distribution in the presence of loss

Curty

Moroder

2007

Phys. Rev. A

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We investigate two-way and one-way single-photon quantum key distribution (QKD) protocols in the presence of loss introduced by the quantum channel. Our analysis is based on a simple precondition for secure QKD in each case. In particular, the legitimate users need to prove that there exists no separable state (in the case of two-way QKD), or that there exists no quantum state having a symmetric extension (one-way QKD), that is compatible with the available measurements results. We show that both criteria can be formulated as a convex optimisation problem known as a semidefinite program, which can be efficiently solved. Moreover, we prove that the solution to the dual optimisation corresponds to the evaluation of an optimal witness operator that belongs to the minimal verification set of them for the given two-way (or one-way) QKD protocol. A positive expectation value of this optimal witness operator states that no secret key can be distilled from the available measurements results. We apply such analysis to several well-known single-photon QKD protocols under losses.

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“…Such a tight balance provides a new understanding of reference frames as a communication resource. Note that the above protocols do not need the two parties to possess the shared secret bits beforehand: They can obtain them using quantum key distribution, which does not necessarily require a prior shared reference [7,8]. This suggests that protocols that do not use prior classical randomness can be implemented.…”

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confidence: 99%