Quantum Physics

Quantum tomography is an important tool for the characterisation of quantum operations. In this paper, we present a framework of quantum tomography in fermionic systems. Compared with qubit systems, fermions obey the superselection rule, which sets constraints on states, processes and measurements in a fermionic system. As a result, we can only partly reconstruct an operation that acts on a subset of fermion modes, and the full reconstruction always requires at least one ancillary fermion mode in addition to the subset. We also report a protocol for the full reconstruction based on gates in Majorana fermion quantum computer, including a set of circuits for realising the informationally-complete state preparation and measurement.

A broad family of phase transitions in the closed as well as open quantum systems is known to be mediated by a non-Hermitian degeneracy (a.k.a. exceptional point, EP) of the Hamiltonian. In the EP limit, in general, the merger of an N??plet of the energy eigenvalues is accompanied by a parallel (though not necessarily complete) degeneracy of eigenstates (forming an EP-asociated K??plet; in mathematics, K is called the geometric multiplicity of the EP). In the literature, unfortunately, only the benchmark matrix models with K=1 can be found. In our paper the gap is filled: the EP-mediated quantum phase transitions with K>1 are called "clustered", and a family of benchmark models admitting such a clustering phenomenon is proposed and described. For the sake of maximal simplicity our attention is restricted to the real perturbed-harmonic-oscillator-type N by N matrix Hamiltonians which are exactly solvable and in which the perturbation is multiparametric (i.e., maximally variable) and antisymmetric (i.e., maximally non-Hermitian). A labeling (i.e., an exhaustive classification) of these models is provided by a specific partitioning of N.

While quantum measurement theories are built around density matrices and observables, the laws of thermodynamics are based on processes such as are used in heat engines and refrigerators. The study of quantum thermodynamics fuses these two distinct paradigms. In this article, we highlight the usage of quantum process matrices as a unified language for describing thermodynamic processes in the quantum regime. We experimentally demonstrate this in the context of a quantum Maxwell's demon, where two major quantities are commonly investigated; the average work extraction ?�W??and the efficacy γ which measures how efficiently the feedback operation uses the obtained information. Using the tool of quantum process matrices, we develop the optimal feedback protocols for these two quantities and experimentally investigate them in a superconducting circuit QED setup.

We present a preliminary theoretical and experimental study of quantum projectors implemented by integrated optical directional couplers fabricated by ion-exchange Na/K processes in soda-lime glass. Theoretical considerations about devices formed by concatenated 2x2 directional couplers are presented in order to show their capabilities for implementing N-dimensional quantum projective measurements, and concomitantly the production of 1-qudit states. Since the fundamental unit of these devices are 2x2 directional couplers, we present an experimental study for obtaining, by an optical characterization, empiric relationships between fabrication and optical parameters of such couplers. Likewise, a two-dimensional quantum projector is demonstrated in such a way that projective measurements are obtained for the states of X (diagonal) and Y (circular) bases.

We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear system that it specifies, quantum computers do not provide an asymptotic speedup over classical computation. On the other hand, we show that for some problems, such as computing the parities of rows or columns or deciding if there are two identical rows or columns, quantum computers provide exponential speedup. We demonstrate this by showing equivalence between models that provide matrix-vector products, vector-matrix products, and vector-matrix-vector products, whereas the power of these models can vary significantly for classical computation.

If quantum mechanics is taken for granted the randomness derived from it may be vacuous or even delusional, yet sufficient for many practical purposes. "Random" quantum events are intimately related to the emergence of both space-time as well as the identification of physical properties through which so-called objects are aggregated. We also present a brief review of the metaphysics of indeterminism.

The protocol of quantum reading refers to the quantum enhanced retrieval of information from an optical memory, whose generic cell stores a bit of information in two possible lossy channels. In the following we analyze the case of a particular class of optical receiver, based on photon counting measurement, since they can be particularly simple in view of real applications. We show that a quantum advantage is achievable when a transmitter based on two-mode squeezed vacuum (TMSV) states is combined with a photon counting receiver, and we experimentally confirm it. In this paper, after introducing some theoretical background, we focus on the experimental realisation, describing the data collection and the data analysis in detail.

Discrete time crystals (DTCs) are exotic many-body phases of matter in which some observables exhibit robust subharmonic response to periodic driving. By highlighting the connection between DTCs and a quantum error correction model, we devise a general and realistic scheme for building DTCs exhibiting large period observable dynamics. This is accomplished by utilizing a series of Ising spin-1/2 chains, each of which simulates a quantum repetition code at the hardware level, and devising a time-periodic Hamiltonian which simulates the fault-tolerant implementation of appropriate logical quantum gates.

Rotations of microscale rigid bodies exhibit pronounced quantum phenomena that do not exist for their center-of-mass motion. By levitating nanoparticles in ultra-high vacuum, researchers are developing a promising platform for observing and exploiting these quantum effects in an unexplored mass and size regime. Recent experimental and theoretical breakthroughs demonstrate exquisite control of nanoscale rotations, setting the stage for the first table-top tests of rotational superpositions and for the next generation of ultra-precise torque sensors. Here, we review the experimental state of the art and discuss promising routes towards macroscopic quantum rotations.

Quantum dynamics is of fundamental interest and has implications in quantum information processing. The four-point out-of-time-ordered correlator (OTOC) is traditionally used to quantify quantum information scrambling under many-body dynamics. Due to the OTOC's unusual time ordering, its measurement is challenging. We propose higher-point OTOCs to reveal early-time scrambling behavior, and present protocols to measure any higher-point OTOC using the shadow estimation method. The protocols circumvent the need for time-reversal evolution and ancillary control. They can be implemented in near-term quantum devices with single-qubit readout.