Metasurfaces are highly effective at manipulating classical light in the linear regime; however, effectively controlling the polarization of non-classical light generated from nonlinear resonant metasurfaces remains a challenge. Here, we present a solution by achieving polarization engineering of frequency-nondegenerate biphotons emitted via spontaneous parametric down-conversion (SPDC) in GaAs metasurfaces, where quasi-bound states in the continuum (qBIC) resonances were utilized for boosting the biphoton generation. By performing a comprehensive polarization tomography, we demonstrate that the polarization of the emitted photons directly reflects the qBIC mode's far-field properties. Furthermore, we show that both the type of qBIC mode and the symmetry of the meta-atoms can be tailored to control each single-photon polarization state, and that the subsequent two-photon polarization states are nearly separable, offering potential applications in the heralded generation of single photons with adjustable polarization. This work provides a significant step towards utilizing metasurfaces to not only generate quantum light but also engineer their polarization, a critical aspect for future quantum technologies.
Beyond the Purcell Effect: Controlling Pure Quantum Dephasing with Spin Noise Metasurfaces
Elmore Family School of Electrical and Computer Engineering, Purdue University（普渡大学埃尔莫电气与计算机工程学院）；Birck Nanotechnology Center, Purdue University（普渡大学伯里克纳米技术中心）
Summary. A simple derivation of finite Schmidt decomposition of pure states describing finite dimensional systems interacting with the infinite dimensional ones is presented. In particular, maximally entangled pure states in such systems are being characterized. The concept of mixed-pure states has been introduced and some criterions for checking separability and entanglement of them are presented .The notion of LOCC equivalence and LOCC semi-order on the space of pure states of systems analyzed has been adopted suitably. In particular a Nielsen -like theorem has been extended to the pure (d, …
We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the mixed states. We prove that under the equal-fidelity condition, the pure-pure state discrimination scheme is superior to the pure-mixed (mixed-mixed) one. With respect to quantum filtering, the coherence exists only in one pure state and is detrimental to the state discrimination for lower dimensional systems; while it is the opposite for the mixed-mixed case …
Violation of Bell inequalities and Quantum Tomography with Pure-states, Werner-states and Maximally Entangled Mixed States created by a Universal Quantum Entangler
Masking of quantum information means that information is hidden from a subsystem and spread over a composite system. Modi et al. proved in [Phys. Rev. Lett. 120, 230501 (2018)] that this is true for some restricted sets of nonorthogonal quantum states and it is not possible for arbitrary quantum states. In this paper, we discuss the problem of masking quantum information encoded in pure and mixed states, respectively. Based on an established necessary and sufficient condition for a set of pure states to be masked by an operator, we find that there exists a set of four states that can not be ma…
The universal quantum homogeniser can transform a qubit from any state to any other state with arbitrary accuracy, using only unitary transformations to perform this task. Here we present an implementation of a finite quantum homogeniser using nuclear magnetic resonance (NMR), with a four-qubit system. We compare the homogenisation of a mixed state to a pure state, and the reverse process. After accounting for the effects of decoherence in the system, we find the experimental results to be consistent with the theoretical symmetry in how the qubit states evolve in the two cases. We analyse the …
Local Unitary Equivalent Classes of Symmetric N-Qubit Mixed States
对称$ N $ -量子比特纯态的Majorana表示已成功地用于纠缠分类。由于在构造对称混合态的Majorana几何表示时所面临的困难，这一问题的推广一直是一个悬而未决的问题。我们已经克服了这个问题，通过开发的方法分类本地酉（LU）等价类的对称$N$ -量子比特混合态的基础上的几何多轴表示（MAR）的密度矩阵。除了基于MR的对称纯态纠缠分类所定义的两个参数，即多样度和简并构型外，我们还证明了对称混合态分类还需要引入另一个参数秩.我们的分类方案是更一般的，因为它可以适用于纯态和混合态。为了揭示MR和MAR之间的异同，我们选取了$ N $ -量子比特GHZ态进行了详细的研究。我们的结论是基于MR的纯态分类不是我们基于MAR的分类方案的特例。我们还给出了识别最一般的对称$N$ -量子比特纯可分态的方法。我们的方法的权力证明使用几个著名的对称两个量子比特纯态和混合态以及三个量子比特纯态的例子。详细研究了实验室中可以制备的单轴、双轴和三轴对称两量子比特混合态的分类。
It is known that mixed quantum states are highly entropic states of imperfect knowledge (i.e., incomplete information) about a quantum system, while pure quantum states are states of perfect knowledge (i.e., complete information) with vanishing von Neumann entropy. In this paper, we propose an information geometric theoretical construct to describe and, to a certain extent, understand the complex behavior of evolutions of quantum systems in pure and mixed states. The comparative analysis is probabilistic in nature, it uses a complexity measure that relies on a temporal averaging procedure alon…
An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state of n qubits. This approach reveals the geometrical structure of the quantum search process, which turns out to be confined to a four-dimensional subspace of the Hilbert space. This work unifies and generalizes earlier results on the time evolution of the amplitudes during the quantum search, the optimal number of iterations and the success probability. Furthermore, it enables a direct generalization to the case in which the initial state is a mixed …
Quantum information processing exploits non-local functionality that has led to significant breakthroughs in the successful deployment of quantum mechanical protocols. In this regard, we address the dynamics of entanglement and coherence for three non-interacting qubits initially prepared as maximally entangled GHZ-like state coupled with independent classical environments. Two different Gaussian noises in pure and mixed noisy situations, namely, pure power-law noise, pure fractional Gaussian noise, power-law noise maximized and fractional Gaussian noise maximized cases are assumed to characte…
We demonstrate an optical receiver that achieves the quantum Chernoff bound for discriminating coherent states from thermal states in the multi-copy scenario. In contrast, we find that repeated use of the receiver approaching the Helstrom bound for single-copy measurement is sub-optimal in this multi-copy case. Furthermore, for a large class of multi-copy discrimination tasks between a pure and a mixed state, we prove that any Helstrom-bound achieving single-copy receiver is suboptimal by a factor of at least two in error-probability exponent compared to the multi-copy quantum Chernoff bound. …
General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial state, and does not require that the initial state be localized in position or momentum. This general dephasing representation is special in that, counterintuitively, all of fidelity decay is due to dephasing and none due to the decay of classical overlaps. Surprising accuracy of the approximation is justified by invoking the shadowing theorem: twice--both for ph…
We present a review on the notion of pure states and mixtures as mathematical concepts that apply for both classical and quantum physical theories, as well as for any other theory depending on statistical description. Here, states will be presented as expectation values on suitable algebras of observables, in a manner intended for the non-specialist reader; accordingly, basic literature on the subject will be provided. Examples will be exposed together with a discussion on their meanings and implications. An example will be shown where a pure quantum state converges to a classical mixture of p…
Quantum states transformation under free operations plays a central role in the resource theory of coherence. In this paper, we investigate the transformation from a mixed coherent state into a pure one by using both incoherent operations and stochastic incoherent operations. We show that contrary to the strictly incoherent operations and the stochastic strictly incoherent operations, both the incoherent operations and the stochastic incoherent operations can increase the dimension of the maximal pure coherent subspace of a state. This means that the incoherent operations are generally stronge…
Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter
Perimeter Institute for Theoretical Physics（Perimeter理论物理研究所）；Department of Physics and Astronomy, University of Waterloo（滑铁卢大学物理与天文系）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
