The action reaction principle is violated by the projection of state in some simple quantum measurements. A formulation of Quantum Mechanics in an extended phase space is proposed in order to restore the action reaction principle. All predictions of the standard theory are reproduced. Observable effects of an accompanying de Broglie wave are also predicted.
The Precise Formula in a Sine Function Form of the norm of the Amplitude and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm with Arbitrary Phase Rotations
Here we report the performance of a discrete modulated Continuous Variable Quantum Key Distribution protocol based on eight and sixteen state optimal Amplitude Phase Keying constellations with pure loss quantum channel transmission. Our constellations use the same amplitudes and state probability as in an optimal four-state unidimensional constellation model and apply amplitude/phase modulation to the quadratures of coherent states. We compare the obtained results with the performance of conventional $m$-PSK and $m$-APK constellations. The results presented show that protocols that use the pro…
We study if periodic driving of a model with a quasiperiodic potential can generate interesting Floquet phases which have no counterparts in the static model. Specifically, we consider the Aubry-André model which is a one-dimensional time-independent model with an on-site quasiperiodic potential $V_0$ and a nearest-neighbor hopping amplitude which is taken to have a staggered form. We add a uniform hopping amplitude which varies periodically in time with a frequency $ω$. Unlike the static Aubry-André model which has a simple phase diagram with only two phases (only extended or only localized s…
Dynamical phase transitions are defined through non-analyticities of the survival probability of an out-of-equilibrium time-evolving state at certain critical times. They ensue from zeros of the corresponding survival amplitude. By extending the time variable onto the complex domain, we formulate the complex-time survival amplitude. The complex zeros of this quantity near the time axis correspond, in the infinite-size limit, to non-analytical points where the survival probability abruptly vanishes. Our results are numerically exemplified in the fully-connected transverse-field Ising model, whi…
Quantum particle transmission through locally periodic potentials surrounded by symmetric exterior potentials is analyzed. Closed-form conditions for locating energy peaks of total transmission are derived. Floquet/Bloch energy band types are defined and found to affect the number of peaks in transmission bands. Modifications of band types and a band fusion phenomenon are discussed. The theoretical approaches suggested consist of several ways to express a Schrödinger wave as an amplitude function multiplying a harmonic function of a phase function. In particular, an approach containing a Floqu…
The Dirac's formalism for constrained systems is applied to the analysis of time-dependent Hamiltonians in the extended phase space. We show that the Lewis invariant is a reparametrization invariant and we calculate the Feynman propagator using the extended phase description. We show that the quantum phase of the Feynman propagator is given by the boundary term of the canonical transformation of the extended phase space.
The Loschmidt amplitude of the purified states of mixed-state density matrices is shown to have zeros when the system undergoes a quasistatic, quench, or Uhlmann process. While the Loschmidt-amplitude zero of a quench process corresponds to a dynamical quantum phase transition (DQPT) accompanied by the diverging dynamical free energy, the Loschmidt-amplitude zero of the Uhlmann process corresponds to a topological phase transition (TQPT) accompanied by a jump of the Uhlmann phase. Although the density matrix remains intact in a quasistatic process, the Loschmidt amplitude can have zeros not as…
