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arXiv:quant-ph/0104036 · Physical Review Letters

Quantum State of an Ideal Propagating Laser Field

S. J. van Enk, Christopher A. Fuchs

Published Dec 26, 2001• 92 citations
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Abstract

We give a quantum information-theoretic description of an ideal propagating cw laser field and reinterpret typical quantum-optical experiments in light of this. In particular, we show that, contrary to recent claims [T. Rudolph and B. C. Sanders, Phys. Rev. Lett. 87, 077903 (2001)], a conventional laser can be used for quantum teleportation with continuous variables and for generating continuous-variable entanglement. Optical coherence is not required, but phase coherence is. We also show that coherent states play a privileged role in the description of laser light.

DOI
10.1103/physrevlett.88.027902

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arXiv:quant-ph/0303116•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 16, 2003•7 citations
We give a quantum information-theoretic description of an ideal propagating cw laser field and reinterpret typical quantum-optical experiments in light of this. In particular, we show that, contrary to recent claims [T. Rudolph and B. C. Sanders, Phys. Rev. Lett. 87, 077903 (2001)], a conventional laser can be used for quantum teleportation with continuous variables and for generating continuous-variable entanglement. Optical coherence is not required, but phase coherence is. We also show that coherent states play a privileged role in the description of laser light.
Optical implementations of quantum communication protocols typically involve laser fields. However, the standard description of the quantum state of a laser field is surprisingly insufficient to understand the quantum nature of such implementations. In this paper, we give a quantum information-theoretic description of a propagating continuous-wave laser field and reinterpret various quantum-optical experiments in light of this. A timely example is found in a recent controversy about the quantum teleportation of continuous variables. We show that contrary to the claims of T. Rudolph and B. C. Sanders [Phys. Rev. Lett. 87, 077903 (2001)], a conventional laser can be used for quantum teleportation with continuous variables and for generating continuous-variable quantum entanglement. Furthermore, we show that optical coherent states do play a privileged role in the description of propagating laser fields even though they cannot be ascribed such a role for the intracavity field.
Optical implementations of quantum communication protocols typically involve laser fields. However, the standard description of the quantum state of a laser field is surprisingly insufficient to understand the quantum nature of such implementations. In this paper, we give a quantum information-theoretic description of a propagating continuous-wave laser field and reinterpret various quantum-optical experiments in light of this. A timely example is found in a recent controversy about the quantum teleportation of continuous variables. We show that contrary to the claims of T. Rudolph and B.C. Sanders [Phys. Rev. Lett. {\bf 87}, 077903 (2001)], a conventional laser can be used for quantum teleportation with continuous variables and for generating continuous-variable quantum entanglement. Furthermore, we show that optical coherent states do play a privileged role in the description of propagating laser fields even though they cannot be ascribed such a role for the intracavity field.
It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. {\\bf 87}, 077903 (2001)] that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not `truly coherent'. Van Enk, and Fuchs [Phys. Rev. Lett, {\\bf 88}, 027902 (2002)], while arguing against Rudolph and Sanders, also accept that an `absolute phase' is achievable, even if it has not been achieved yet. I will argue to the contrary that `true coherence' or `absolute phase' is always illusory, as the concept of absolute time (at least for frequencies beyond direct human experience) is meaningless. All we can ever do is to use an agreed time standard. In this context, a laser beam is fundamentally as good a `clock' as any other. I explain in detail why this claim is true, and defend my argument against various objections. In the process I discuss super-selection rules, quantum channels, and the ultimate limits to the performance of a laser as a clock. For this last topic I use some earlier work by myself [Phys. Rev. A {\\bf 60}, 4083 (1999)] and Berry and myself [Phys. Rev. A {\\bf 65}, 043803 (2002)] to show that a Heisenberg-limited laser with a mean photon number mu\\mumu can synchronize MMM independent clocks each with a mean-square error of sqrtM/4mu\\sqrt{M}/4\\musqrtM/4mu radians2^22.
Summary form only given. Quantum teleportation, first proposed as a method for teleporting an unknown spin-1/2 quantum state from a sender, "Alice", to a receiver, "Bob", has been extended to continuous-variable quantum teleportation (CVQT). In this variant of quantum teleportation, Bob and Alice share a nonlocal entangled two-mode field which, ideally, should have perfect correlations between in-phase quadrature ('position' x) and out-of-phase quadrature ('momentum' p), although the requirement of perfect correlations can be relaxed somewhat. The experimental success of CVQT has recently been reported, with two-mode squeezed light providing the nonlocal, entangled source shared between Alice and Bob. The objective here is to consider whether CVQT has indeed been achieved, or could ever be achieved, in optical experiments employing conventional laser sources. In particular we show that, in the context of this experiment, Alice and Bob may not employ independent laser sources for their operations if the state is to be teleported, yet this requires them to share more than just the Einstein-Podolsky-Rosen (EPR) resource.
It has been argued [T.Rudolph and B.C. Sanders, Phys.Rev. Lett.87, 077903 (2001)] that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not 'truly coherent'.Here I show that 'true coherence' is always illusory, as the concept of absolute time on a scale beyond direct human experience is meaningless.A laser is as good a clock as any other, even in principle, and this objection to teleportation experiments is baseless.
It has been argued that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used was not 'truly coherent'. While arguing against Rudolph and Sanders, also accept that an 'absolute phase' is achievable, even if it has not been achieved yet. I will argue to the contrary that 'true coherence' or 'absolute phase' is always illusory, as the concept of absolute time on a scale beyond direct human experience is meaningless. All we can ever do is to use an agreed time standard. in this context, laser beam is fundamentally as good a 'clock' as any other. I explain in detail why this claim is true, and defend my argument against various objections. In the process I discuss super-selection rules, quantum work by myself and Berry and myself to show that a Heisenberg-limited laser with a mean photon number μ can synchronize M independent clocks each with a mean-square error of square root M/4μ radians2.