The orbital angular momentum (OAM) of photons has shown the ability to generate high-dimensional entanglement. Here, we examine a novel kind of entanglement degradation caused by the Unruh effect. By paraxially quantizing the light field, we derive the mode functions in both inertial and noninertial reference frames and demonstrate that, from the perspective of an accelerating observer, empty inertial space may seem to be full of OAM particles. They may inundate the high-dimensional entangled OAM photons and cause them to decay. Additionally, we investigate high-dimensional entanglement in the vicinity of a Schwarzschild black hole. Our results suggest that higher-dimensional entanglement will suffer from greater adverse impacts in both instances.
The orbital angular momentum (OAM) of photons has shown the ability to generate high-dimensional entanglement. Here, we examine a novel kind of entanglement degradation caused by the Unruh effect. By paraxially quantizing the light field, we derive the mode functions in both inertial and noninertial reference frames and demonstrate that, from the perspective of an accelerating observer, empty inertial space may seem to be full of OAM particles. They may inundate the high-dimensional entangled OAM photons and cause them to decay. Additionally, we investigate high-dimensional entanglement in the vicinity of a Schwarzschild black hole. Our results suggest that higher-dimensional entanglement will suffer from greater adverse impacts in both instances.
In this study, we report on the evolution of photonic orbital angular momentum (OAM) entanglement in inertial reference frames under a Lorentz boost, covering the general cases of zero and non-zero relative motion between observers of the entangled state. We find that entanglement undergoes significant changes that are observer dependent, asymptotically approaching a minimum at very large velocities close to the light cone from the viewpoint of the stationary observers in the rest frame, and degrading completely from the viewpoint of the moving observer. Our results, as demonstrated through entanglement metrics such as entanglement entropy and purity, show that OAM and OAM entanglement are observer dependent, raising pertinent questions on the invariance of such entangled states to spacetime transformations.
Introduction In this chapter, we will be concerned with entangled states of light. Historically, quantum states of light, i.e., photons, have played a dominant role in the experimental study of quantum entanglement. For instance, the first Bell tests and the first realizations of quantum teleportation were performed using two-dimensional polarization-entangled twophoton states [3]. From an experimental point of view these states are readily prepared and manipulated using conventional polarization optics. Recently, however, both theoretical and experimental efforts have shifted towards entanglement in more than two modes , which is often referred to as high-dimensional entanglement. This is much richer than two-dimensional entanglement, as is, for instance, reflected in stronger violations of various measures of nonlocality which reveal the complexity of high-dimensional Hilbert spaces [4–7]. Also, from an applications perspective, it promises a larger channel capacity [8, 9] and improved security for quantum communication [10, 11]. There are several ways to implement high-dimensional two-photon entanglement. One can exploit the temporal [12], frequency [13], or spatial [14–18] degrees of freedom of the optical field. A promising way to implement high-dimensional two-photon entanglement is to use the orbital-angular-momentum (OAM) degree of freedom of light. Light beams that carry OAM have a helical wavefront that spirals around the optical axis during propagation [19]. The winding number m , which characterizes the OAM eigenmodes, can adopt any integer value between −∞ and ∞; since all coaxial OAM modes are orthogonal they can thus span a very high-dimensional Hilbert space.
Orbital angular momentum (OAM) as both classical and quantum states of light has proven essential in numerous applications, from high-capacity information transfer to enhanced precision and accuracy in metrology. Here, we extend OAM metrology to relativistic scenarios to determine the Lorentz factor of a moving reference frame, exploiting the fact that OAM is not Lorentz invariant. We show that the joint OAM spectrum from entangled states is modified by length contraction when measured by two observers moving relative to the entanglement source. This relative motion rescales the spatial dimensions, thus breaking the orthogonality of the OAM measurement process and resulting in a broadening of the joint OAM spectrum that can precisely determine the Lorentz factor. We experimentally simulate velocities up to 0.99c, confirm the predicted broadening, and use the measurement outcomes to extract the Lorentz factor. Our work provides a pathway for novel measurement techniques suitable for relativistic conditions that leverage OAM structured light as a resource.
Two observers determine the entanglement between two free bosonic modes by each detecting one of the modes and observing the correlations between their measurements. We show that a state which is maximally entangled in an inertial frame becomes less entangled if the observers are relatively accelerated. This phenomenon, which is a consequence of the Unruh effect, shows that entanglement is an observer-dependent quantity in noninertial frames. In the high acceleration limit, our results can be applied to a nonaccelerated observer falling into a black hole while the accelerated one barely escapes. If the observer escapes with infinite acceleration, the state's distillable entanglement vanishes.
We study the properties of quantum entanglement and teleportation in the background of stationary and rotating curved spacetimes with extra dimensions. We show that a maximally entangled Bell state in an inertial frame becomes less entangled in curved space due to the well-known Hawking–Unruh effect. The degree of entanglement is found to be degraded with the increase in the extra dimensions. For a finite black hole surface gravity, the observer may choose a higher frequency mode to keep high level entanglement. The fidelity of quantum teleportation is also reduced because of the Hawking–Unruh effect. We discuss the fidelity as a function of extra dimensions, mode frequency, black hole mass and black hole angular momentum parameter for both bosonic and fermionic resources.
Orbital angular momentum (OAM) is one of the most recently discovered properties of light, and it is only in the past decade its quantum properties have been the subject of experimental investigations and have found applications. Unlike polarization, which is only bidimensional, orbital angular momentum provides, with relative ease, unprecedented access to a theoretically unbounded discrete state space. The process of spontaneous parametric down-conversion has long been used as a source of two-photon states that can be entangled in several degrees of freedom, including OAM. In this thesis, the properties of the natural OAM spectrum associated with the entangled states produced by parametric down-conversion were investigated. Chapters 2 and 3 describe the production and detection of tunable high-dimensional OAM entanglement in a down-conversion system. By tuning the phase-matching conditions and improving the detection stage, a substantial increase in the half-width of the OAM correlation spectrum was observed. The conjugate variable of OAM, angular position, was also considered when examining high-dimensional states entangled in OAM. In order to efficiently determine their dimension, high-dimensional entangled states were probed by implementing a technique based on phase masks composed of multiple angular sectors, as opposed to narrow single-sector analysers. Presented in chapter 4, this technique allows the measurements of tight angular correlations while maintaining high optical throughput. The states so produced were then used for a number of applications centred around the concept of mutually unbiased bases. One can define sets of mutually unbiased bases for arbitrary subspaces of the OAM state space. Two bases are mutually unbiased if the measurement of a state in one basis provides no information about the state as described in the other basis. Complete measurements in mutually unbiased bases of high-dimensional OAM spaces are presented in chapter 5. Measurements in sets of mutually unbiased bases are integral to quantum science and can be used in a variety of protocols that fully exploit the large size of the OAM state space; we describe their use in efficient quantum state tomography, quantum key distribution and entanglement detection. Caution is however necessary when dealing with state spaces embedded in higher-dimensional spaces, such as that provided by OAM. Experimental tests of Bell-type inequalities allow us to rule out local hidden variable theories in the description of quantum correlations. Correlations inconsistent with the states observed, or even with quantum mechanics, known as super-quantum correlations, have however been recorded previously in experiments that fail to comply with the fair-sampling conditions. Chapter 6 describes an experiment that uses a particular choice of transverse spatial modes for which super-quantum correlations persist even if the detection is made perfectly efficient. The sets of modes carrying OAM allow a complete description of the transverse field. The ability to control and combine additional degrees of freedom provides the possibility for richer varieties of entanglement and can make quantum protocols more powerful and versatile. One such property of light, associated with transverse modes possessing radial nodes in the field distribution, can be accessed within the same type of experimental apparatus used for OAM. In chapter 7, the radial degree of freedom is explored, together with OAM, in the context of Hong-Ou-Mandel interference.