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Register a new userQuantum frameness for Charge-Parity-Time inversion symmetry
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We develop a theory of charge-parity-time (CPT) frameness resources to circumvent CPT-superselection. We construct and quantify such resources for spin~0, $frac{1}{2}$, 1, and Majorana particles and show that quantum information processing is possible even with CPT superselection. Our method employs a unitary representation of CPT inversion by considering the aggregate action of CPT rather than the composition of separate C, P and T operations, as some of these operations involve problematic anti-unitary representations.
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We show that appropriate superpositions of motional states are a reference frame resource that enables breaking of time -reversal superselection so that two parties lacking knowledge about the others direction of time can still communicate. We identify the time-reversal reference frame resource states and determine the corresponding frameness monotone, which connects time-reversal frameness to entanglement. In contradistinction to other studies of reference frame quantum resources, this is the first analysis that involves an antiunitary rather than unitary representation.
Quantum walks (QW) are of crucial importance in the development of quantum information processing algorithms. Recently, several quantum algorithms have been proposed to implement network analysis, in particular to rank the centrality of nodes in networks represented by graphs. Employing QW in centrality ranking is advantageous comparing to certain widely used classical algorithms (e.g. PageRank) because QW approach can lift the vertex rank degeneracy in certain graphs. However, it is challenging to implement a directed graph via QW, since it corresponds to a non-Hermitian Hamiltonian and thus cannot be accomplished by conventional QW. Here we report the realizations of centrality rankings of both a three-vertex and four-vertex directed graphs with parity-time (PT) symmetric quantum walks. To achieve this, we use high-dimensional photonic quantum states, optical circuitries consisting of multiple concatenated interferometers and dimension dependent loss. Importantly, we demonstrate the advantage of QW approach experimentally by breaking the vertex rank degeneracy in a four-vertex graph. Our work shows that PT-symmetric quantum walks may be useful for realizing advanced algorithm in a quantum network.
The emergence of parity-time ($mathcal{PT}$) symmetry has greatly enriched our study of symmetry-enabled non-Hermitian physics, but the realization of quantum $mathcal{PT}$-symmetry faces an intrinsic issue of unavoidable symmetry-breaking Langevin noises. Here we construct a quantum pseudo-anti-$% mathcal{PT}$ (pseudo-$mathcal{APT}$) symmetry in a two-mode bosonic system without involving Langevin noises. We show that the pseudo-$mathcal{APT}$ phase transition across the exceptional point yields a transition between different types of quantum squeezing behaviors, textit{i.e.}, the squeezing factor increases exponentially (oscillates periodically) with time in the pseudo-$mathcal{APT}$ symmetric (broken) region. Such dramatic changes of squeezing factors and associated quantum states near the exceptional point are utilized for ultra-precision quantum sensing with divergent sensitivity. These exotic quantum phenomena and sensing applications induced by quantum pseudo-$mathcal{APT}$ symmetry can be experimentally observed in two physical systems: spontaneous wave mixing nonlinear optics and atomic Bose-Einstein condensates.
In function inversion, we are given a function $f: [N] mapsto [N]$, and want to prepare some advice of size $S$, such that we can efficiently invert any image in time $T$. This is a well studied problem with profound connections to cryptography, data structures, communication complexity, and circuit lower bounds. Investigation of this problem in the quantum setting was initiated by Nayebi, Aaronson, Belovs, and Trevisan (2015), who proved a lower bound of $ST^2 = tildeOmega(N)$ for random permutations against classical advice, leaving open an intriguing possibility that Grovers search can be sped up to time $tilde O(sqrt{N/S})$. Recent works by Hhan, Xagawa, and Yamakawa (2019), and Chung, Liao, and Qian (2019) extended the argument for random functions and quantum advice, but the lower bound remains $ST^2 = tildeOmega(N)$. In this work, we prove that even with quantum advice, $ST + T^2 = tildeOmega(N)$ is required for an algorithm to invert random functions. This demonstrates that Grovers search is optimal for $S = tilde O(sqrt{N})$, ruling out any substantial speed-up for Grovers search even with quantum advice. Further improvements to our bounds would imply new classical circuit lower bounds, as shown by Corrigan-Gibbs and Kogan (2019). To prove this result, we develop a general framework for establishing quantum time-space lower bounds. We further demonstrate the power of our framework by proving quantum time-space lower bounds for Yaos box problem and salted cryptography.
The decay of any unstable quantum state can be inhibited or enhanced by carefully tailored measurements, known as the quantum Zeno effect (QZE) or anti-Zeno effect (QAZE). To date, studies of QZE (QAZE) transitions have since expanded to various system-environment coupling, in which the time evolution can be suppressed (enhanced) not only by projective measurement but also through dissipation processes. However, a general criterion, which could extend to arbitrary dissipation strength and periodicity, is still lacking. In this letter, we show a general framework to unify QZE-QAZE effects and parity-time (PT) symmetry breaking transitions, in which the dissipative Hamiltonian associated to the measurement effect is mapped onto a PT-symmetric non- Hermitian Hamiltonian, thus applying the PT symmetry transitions to distinguish QZE (QAZE) and their crossover behavior. As a concrete example, we show that, in a two-level system periodically coupled to a dissipative environment, QZE starts at an exceptional point (EP), which separates the PT-symmetric (PTS) phase and PT-symmetry broken (PTB) phase, and ends at the resonance point (RP) of the maximum PT-symmetry breaking; while QAZE extends the rest of PTB phase and remains the whole PTS phase. Such findings reveal a hidden relation between QZE-QAZE and PTS-PTB phases in non-Hermitian quantum dynamics.
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