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Relativistically invariant photonic wave packets

Published Jan 1, 2010• 10 citations
OpenAlex

Abstract

We present a photonic wave packet construction that is immune to the decoherence effects induced by the action of the Lorentz group. The amplitudes of a pure quantum state representing the wave packet remain invariant, irrespective of the reference frame into which the wave packet has been transformed. Transmitted information is encoded in the helicity degrees of freedom of two correlated momentum modes. The helicity encoding is considered to be particularly suitable for free-space communication. The integral part of the story is information retrieval on the receiver's side. We employed probably the simplest possible helicity (polarization) projection measurement originally studied by Peres and Terno. Remarkably, the same conditions ensuring the invariance of the wave packet also guarantee perfect distinguishability in the process of measuring the helicity.

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We present a photonic wave packet construction that is immune to the decoherence effects induced by the action of the Lorentz group. The amplitudes of a pure quantum state representing the wave packet remain invariant, irrespective of the reference frame into which the wave packet has been transformed. Transmitted information is encoded in the helicity degrees of freedom of two correlated momentum modes. The helicity encoding is considered to be particularly suitable for free-space communication. The integral part of the story is information retrieval on the receiver's side. We employed probably the simplest possible helicity (polarization) projection measurement originally studied by Peres and Terno. Remarkably, the same conditions ensuring the invariance of the wave packet also guarantee perfect distinguishability in the process of measuring the helicity.
We present a photonic wave packet construction that is immune to the decoherence effects induced by the action of the Lorentz group. The amplitudes of a pure quantum state representing the wave packet remain invariant, irrespective of the reference frame into which the wave packet has been transformed. Transmitted information is encoded in the helicity degrees of freedom of two correlated momentum modes. The helicity encoding is considered to be particularly suitable for free-space communication. The integral part of the story is information retrieval on the receiver’s side. We employed probably the simplest possible helicity (polarization) projection measurement originally studied by Peres and Terno. Remarkably, the same conditions ensuring the invariance of the wave packet also guarantee perfect distinguishability in the process of measuring the helicity.
We calculate the entanglement between a pair of polarization-entangled photon beams as a function of the reference frame, in a fully relativistic framework. We find the transformation law for helicity basis states and show that, while it is frequency independent, a Lorentz transformation on a momentum-helicity eigenstate produces a momentum-dependent phase. This phase leads to changes in the reduced polarization density matrix, such that entanglement is either decreased or increased, depending on the boost direction, the rapidity, and the spread of the beam.
We propose a free-space quantum secure direct communication protocol by using hyper-encoded single photons. The communication parties can securely exchange private information in a deterministic way. In this protocol, single photons are encoded simultaneously by both the polarization and spatial-mode degrees of freedom that constitute a decoherence-free space. The detrimental effect introduced by either reference-frame misalignment or practical channel rotational noise is passively suppressed. Finally, the security of our protocol against classical individual attacks is proved by quantum mutual information.
The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light always remains the same. Consequently, a wave packet of light exhibits different frequencies, wavelengths, and amplitudes. In this paper, we present a local approach to the relativistic Doppler effect based on relativity, spatial and time translational symmetries, and energy conservation. Afterwards, we investigate the implications of the relativistic Doppler effect for the quantum state transformations of wave packets of light and show that a local photon is a local photon at the same point in the spacetime diagram in all inertial frames.