Quantum Physics

We show that the resource theory of contextuality does not admit catalysts. As a corollary, we observe that the same holds for non-locality. This adds a further example to the list of "anomalies of entanglement", showing that non-locality and entanglement behave differently as resources. We also show that catalysis remains impossible even if instead of classical randomness we allow some more powerful behaviors to be used freely in the free transformations of the resource theory.

New solutions of relativistic wave equations are obtained in a unified manner from generating functions of spinorial variables. The choice of generating functions as Gaussians leads to representations in the form of generalized fractional Fourier transforms. Wave functions satisfying the Dirac, Maxwell, and Weyl equations are constructed by simple differentiations with respect to spinorial arguments. In the simplest case, one obtains Maxwell and Dirac hopfion solutions.

We present new sum rules for 3jm coefficients, which involve, in addition to the usual weighting factor (2j+1) where j is an angular momentum, the quantity [j(j+1) ] k with k?? . The sum rules appear for instance in the statistical modeling of rotational spectra within the theory of moments, and enable one to deduce the expectation values of r k (used in the theory of Stark effect for hydrogenic ions) in parabolic coordinates from the expectation values of r k in spherical coordinates.

We investigate the interferometric scheme put forward by Tan, Walls and Collett [Phys. Rev. Lett. {\bf 66}, 256 (1991)] that aims to reveal Bell non-classicality of a single photon. By providing a local hidden variable model that reproduces their results, we decisively refute this claim. In particular, this means that the scheme cannot be used in device-independent protocols.

Noise is the defining feature of the NISQ era, but it remains unclear if noisy quantum devices are capable of quantum speedups. Quantum supremacy experiments have been a major step forward, but gaps remain between the theory behind these experiments and their actual implementations. In this work we initiate the study of the complexity of quantum random circuit sampling experiments with realistic amounts of noise. Actual quantum supremacy experiments have high levels of uncorrected noise and exponentially decaying fidelities. It is natural to ask if there is any signal of exponential complexity in these highly noisy devices. Surprisingly, we show that it remains hard to compute the output probabilities of noisy random quantum circuits without error correction. More formally, so long as the noise rate of the device is below the error detection threshold, we show it is #P-hard to compute the output probabilities of random circuits with a constant rate of noise per gate. This hardness persists even though these probabilities are exponentially close to uniform. Interestingly these hardness results also have implications for the complexity of experiments in a low-noise setting. The issue here is that prior hardness results for computing output probabilities of random circuits are not robust enough to imprecision to connect with the Stockmeyer argument for hardness of sampling from circuits with constant fidelity. We exponentially improve the robustness of prior results to imprecision, both in the cases of Random Circuit Sampling and BosonSampling. In the latter case we bring the proven hardness within a constant factor in the exponent of the robustness required for hardness of sampling for the first time. We then show that our results are in tension with one another -- the high-noise result implies the low-noise result is essentially optimal, even with generalizations of our techniques.

This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-boolean oracles. The action of a non-boolean oracle U ? on an eigenstate |x??is to apply a state-dependent phase-shift ?(x) . Unlike boolean oracles, the eigenvalues exp(i?(x)) of a non-boolean oracle are not restricted to be ±1 . Two new oracular algorithms based on such non-boolean oracles are introduced. The first is the non-boolean amplitude amplification algorithm, which preferentially amplifies the amplitudes of the eigenstates based on the value of ?(x) . Starting from a given initial superposition state | ? 0 ??, the basis states with lower values of cos(?) are amplified at the expense of the basis states with higher values of cos(?) . The second algorithm is the quantum mean estimation algorithm, which uses quantum phase estimation to estimate the expectation ??? 0 | U ? | ? 0 ??, i.e., the expected value of exp(i?(x)) for a random x sampled by making a measurement on | ? 0 ??. It is shown that the quantum mean estimation algorithm offers a quadratic speedup over the corresponding classical algorithm. Both algorithms are demonstrated using simulations for a toy example. Potential applications of the algorithms are briefly discussed.

The dynamical and topological properties of non-Hermitian systems have attracted great attention in recent years. In this work, we establish an intrinsic connection between two classes of intriguing phenomena -- topological phases and dynamical quantum phase transitions (DQPTs) -- in non-Hermitian systems. Focusing on one-dimensional models with chiral symmetry, we find DQPTs following the quench from a trivial to a non-Hermitian topological phase. Moreover, the number of critical momenta and critical time periods of the DQPTs are found to be directly related to the topological invariants of the non-Hermitian system. We further demonstrate our theory in three prototypical non-Hermitian lattice models, the lossy Kitaev chain (LKC), the LKC with next-nearest-neighbor hoppings, and the nonreciprocal Su-Schrieffer-Heeger model. Finally, we present a proposal to experimentally verify the found connection by a nitrogen-vacancy center in diamond.

Nonlocal boxes are conceptual tools that capture the essence of the phenomenon of quantum non-locality, central to modern quantum theory and quantum technologies. We introduce network nonlocal boxes tailored for quantum networks under the natural assumption that these networks connect independent sources and do not allow signaling. Hence, these boxes satisfy the No-Signaling and Independence (NSI) principle. For the case of boxes without inputs, connecting pairs of sources and producing binary outputs, we prove that there is an essentially unique network nonlocal box with local random outputs and maximal 2-box correlations: E 2 = 2 ?????? .

We show that an open quantum system in a non-Markovian environment can reach steady states that it cannot reach in a Markovian environment. As these steady states are unique for the non-Markovian regime, they could offer a simple way of detecting non-Markovianity, as no information about the system's transient dynamics is necessary. In particular, we study a driven two-level system (TLS) in a semi-infinite waveguide. Once the waveguide has been traced out, the TLS sees an environment with a distinct memory time. The memory time enters the equations as a time delay that can be varied to compare a Markovian to a non-Markovian environment. We find that some non-Markovian states show exotic behaviors such as population inversion and steady-state coherence beyond 1/ 8 ????, neither of which is possible for a driven TLS in the Markovian regime, where the time delay is neglected. Additionally, we show how the coherence of quantum interference is affected by time delays in a driven system by extracting the effective Purcell-modified decay rate of a TLS in front of a mirror.

A fundamental prediction of quantum mechanics is that there are random fluctuations everywhere in a vacuum because of the zero-point energy. Remarkably, quantum electromagnetic fluctuations can induce a measurable force between neutral objects, known as the Casimir effect, which has attracted broad interests. The Casimir effect can dominate the interaction between microstructures at small separations and has been utilized to realize nonlinear oscillation, quantum trapping, phonon transfer, and dissipation dilution. However, a non-reciprocal device based on quantum vacuum fluctuations remains an unexplored frontier. Here we report quantum vacuum mediated non-reciprocal energy transfer between two micromechanical oscillators. We modulate the Casimir interaction parametrically to realize strong coupling between two oscillators with different resonant frequencies. We engineer the system's spectrum to have an exceptional point in the parameter space and observe the asymmetric topological structure near it. By dynamically changing the parameters near the exceptional point and utilizing the non-adiabaticity of the process, we achieve non-reciprocal energy transfer with high contrast. Our work represents an important development in utilizing quantum vacuum fluctuations to regulate energy transfer at the nanoscale and build functional Casimir devices.