Experimental resources needed to implement photon number splitting attack in quantum cryptography

The analysis of the security of quantum key distribution systems with respect to an attack with nondemolishing measurement of the number of photons (photon number splitting—PNS attack) is carried out under the assumption that in the communication channel in each parcel there is a pure Fock state with a different number of photons, and the distribution of states by number of photons has Poisson statistics. In reality, in the communication channel in each parcel there are not individual Fock states, but a pure coherent state with a random phase—a superposition of Fock states with different numbers of photons. The paper analyzes the necessary experimental resources necessary to prepare individual Fock states with a certain number of photons from the superposition of Fock states for a PNS attack. Optical schemes for implementing such an attack are given, and estimates of experimental parameters at which a PNS attack is possible are made.

Hadrons as QCD Bound States

Bound state perturbation theory is well established for QED atoms. Today the hyperfine splitting of Positronium is known to 𝒪 (α7 log α). Whereas standard expansions of scattering amplitudes start from free states, bound states are expanded around eigenstates of the Hamiltonian including a binding potential. The eigenstate wave functions have all powers of α, requiring a choice in the ordering of the perturbative expansion. Temporal (A0 = 0) gauge permits an expansion starting from valence Fock states, bound by their instantaneous gauge field. This formulation is applicable in any frame and seems promising even for hadrons in QCD. The 𝒪(αs0) confining potential is determined (up to a universal scale) by a homogeneous solution of Gauss’ law.

Sequential phonon measurements of atomic motion

The motion of trapped atoms plays an essential role in quantum mechanical sensing, simulations and computing. Small disturbances of atomic vibrations are still challenging to be sensitively detected. It requires a reliable coupling between individual phonons and internal electronic levels that light can readout. As available information in a few electronic levels about the phonons is limited, the coupling needs to be sequentially repeated to further harvest the remaining information. We analyze such phonon measurements on the simplest example of the force and heating sensing using motional Fock states. We prove that two sequential measurements are sufficient to reach sensitivity to force and heating for realistic Fock states and saturate the quantum Fisher information for a small amount of force or heating. It is achieved by the conventionally available Jaynes-Cummings coupling. The achieved sensitivities are found to be better than those obtained from classical states. Further enhancements are expectable when the higher Fock state generation is improved. The result opens additional applications of sequential phonon measurements of atomic motion. This measurement scheme can also be directly applied to other bosonic systems including cavity QED and circuit QED.

Light-cone distribution amplitudes of the nucleon and ∆ baryon

We investigate the light-cone wave functions and leading-twist distribution amplitudes for the nucleon and ∆ baryon within the framework of the chiral quark-soliton model. The baryon wave function consists of the valence quark and vacuum wave functions. The vacuum wave functions generate all possible higher Fock states by expanding them. We find that it is essential to consider the five-quark component and relativistic corrections to evaluate the distribution amplitudes of the nucleon and ∆ isobar. Having taken into account them, we derive the distribution amplitudes. The results are in good agreement with the lattice data.

Toolbox for non-classical state calculations

Computational challenges associated with the use of Wigner functions to identify non-classical properties of states are addressed with the aid of generating functions. It allows the computation of the Wigner functions of photon-subtracted states for an arbitrary number of subtracted photons. Both the formal definition of photon-subtracted states in terms of ladder operators and the experimental implementation with heralded photon detections are analyzed. These techniques are demonstrated by considering photon subtraction from squeezed thermal states as well as squeezed Fock states. Generating functions are also used for the photon statistics of these states. These techniques reveal various aspects of the parameter dependences of these states.

London superconductor and time-varying mesoscopic LC circuits

In this work we study the classical and quantum dynamics of a London superconductor and of a time-dependent mesoscopic or nanoscale LC circuit by assuming that the inductance and capacitance vary exponentially with time at constant rate. Surprisingly, we find that the behavior of these two systems are equivalent, both classically and quantum mechanically, and can be mapped into a standard damped harmonic oscillator which is described by the Caldirola-Kanai Hamiltonian. With the aid of the dynamical invariant method and Fock states, we solve the time-dependent Schr\"odinger equation associated with this Hamiltonian and calculate some important physical properties of these systems such as expectation values of the charge and magnetic flux, their variances and the respective uncertainty principle.

Non-Gaussianity of Four-Photon Superpositions of Fock States

We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the known minimal value (which is lower than for the Gaussian states); they have equal dimensionless values of the second- and fouth-order moments of the coordinate and momentum for all values of parameters; they possess zero covariances for all values of parameters. Since these states are obviously non-Gaussian, we consider them as good candidates to compare several different measures of non-Gaussianity proposed by different authors for the past fifteen years. The reference Gaussian states in all examples are thermal states dependent on a single parameter (an effective temperature or the coordinate variance). We analyze the measures based on the normalized Hilbert–Schmidt distance and the relative entropy (introduced by Genoni–Paris–Banaszek), the fidelity measure (Ghiu–Marian–Marian) and its logarithmic analog (Baek–Nha), as well as the Mandilara–Karpov–Cerf “Gaussianity parameter”. These measures are compared with the kurtosis of the coordinate probability density and with the non-Gaussian behavior of the Wigner function.

Non-Gaussianity of Four-Photon Superpositions of Fock States

We compare several different measures of non-Gaussianity for two families of four-photon superpositions of the Fock states: even vacuum squeezed states and orthogonal-even coherent states.