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Register a new userMajorization relations and entanglement generation in a beam splitter
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We prove that a beam splitter, one of the most common optical components, fulfills several classes of majorization relations, which govern the amount of quantum entanglement that it can generate. First, we show that the state resulting from k photons impinging on a beam splitter majorizes the corresponding state with any larger photon number k>k, implying that the entanglement monotonically grows with k. Then, we examine parametric infinitesimal majorization relations as a function of the beam-splitter transmittance, and find that there exists a parameter region where majorization is again fulfilled, implying a monotonic increase of entanglement by moving towards a balanced beam splitter. We also identify regions with a majorization default, where the output states become incomparable. In this latter situation, we find examples where catalysis may nevertheless be used in order to recover majorization. The catalyst states can be as simple as a path-entangled single-photon state or a two-mode vacuum squeezed state.
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A beam splitter is a simple, readily available device which can act to entangle the output optical fields. We show that a necessary condition for the fields at the output of the beam splitter to be entangled is that the pure input states exhibit nonclassical behavior. We generalize this proof for arbitrary (pure or impure) Gaussian input states. Specifically, nonclassicality of the input Gaussian fields is a necessary condition for entanglement of the field modes with the help of the beam splitter. We conjecture that this is a general property of the beam splitter: Nonclassicality of the inputs is a necessary condition for entangling fields in the beam splitter.
We propose an entanglement beam splitter (EBS) using a quantum-dot spin in a double-sided optical microcavity. In contrast to the conventional optical beam splitter, the EBS can directly split a photon-spin product state into two constituent entangled states via transmission and reflection with high fidelity and high efficiency (up to 100 percent). This device is based on giant optical circular birefringence induced by a single spin as a result of cavity quantum electrodynamics and the spin selection rule of trion transition (Pauli blocking). The EBS is robust and it is immune to the fine structure splitting in a realistic quantum dot. This quantum device can be used for deterministically creating photon-spin, photon-photon and spin-spin entanglement as well as a single-shot quantum non-demolition measurement of a single spin. Therefore, the EBS can find wide applications in quantum information science and technology.
In spite of enormous theoretical and experimental progresses in quantum uncertainty relations, the experimental investigation of most current, and universal formalism of uncertainty relations, namely majorization uncertainty relations (MURs), has not been implemented yet. A significant problem is that previous studies on the classification of MURs only focus on their mathematical expressions, while the physical difference between various forms remains unknown. First, we use a guessing game formalism to study the MURs, which helps us disclosing their physical nature, and distinguishing the essential differences of physical features between diverse forms of MURs. Second, we tighter the bounds of MURs in terms of flatness processes, or equivalently, in terms of majorization lattice. Third, to benchmark our theoretical results, we experimentally verify MURs in the photonic systems.
Optical lossless beam splitters are frequently encountered in fundamental physics experiments regarding the nature of light, including which-way determination of light particles, N. Bohrs complementarity principle, or the EPR paradox and all their measurement apparatus. Although they look as common optical components at first glance, their behaviour remains somewhat mysterious since they apparently exhibit stand-alone particle-like features, and then wave-like characteristics when inserted into a Mach-Zehnder interferometer. In this communication are examined and discussed some basic properties of these beamssplitters, both from a classical optics and quantum physics point of view. Herein some convergences and contradictions are highlighted, and the results of a few emblematic experiments demonstrating photon existence are discussed. An alternative empirical model in wave optics is also proposed in order to shed light on some remaining questions
The Braess paradox encountered in classical networks is a counterintuitive phenomenon when the flow in a road network can be impeded by adding a new road or, more generally, the overall net performance can degrade after addition of an extra available choice. In this work, we discuss the possibility of a similar effect in a phase-coherent quantum transport and demonstrate it by example of a simple Y-shaped metallic fork. To reveal the Braess-like partial suppression of the charge flow in such device, it is proposed to transfer two outgoing arms into a superconducting state. We show that the differential conductance-vs-voltage spectrum of the hybrid fork structure varies considerably when the extra link between the two superconducting leads is added and it can serve as an indicator of quantum correlations which manifest themselves in the quantum Braess paradox.
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