After a measurement, to observe the relative phases of macroscopically distinguishable states we have to ``undo a quantum measurement. We generalise an earlier model of Peres from two state to N-state quantum system undergoing measurement process and discuss the issue of observing relative phases of different branches. We derive an inequality which is satisfied by the relative phases of macroscopically distinguishable states and consequently any desired relative phases can not be observed in interference setups. The principle of macroscopic complementarity is invoked that might be at ease with the macroscopic world. We illustrate the idea of limit on phase observability in Stern-Gerlach measurements and the implications are discussed.
We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: the Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of superconductivity. In both cases we show that the sudden drop of the mixed state fidelity marks the line of the phase transition. We conduct a detailed analysis of the general case of systems given by mutually commuting Hamiltonians, where the non-analyticity of the fidelity is directly related to the non-analyticity of the relevant response functions (susceptibility and heat capacity), for the case of symmetry-breaking transitions. Further, on the case of BCS theory of superconductivity, given by mutually non-commuting Hamiltonians, we analyze the structure of the systems eigenvectors in the vicinity of the line of the phase transition showing that their sudden change is quantified by the emergence of a generically non-trivial Uhlmann mixed state geometric phase.
The transition from quantum to classical physics remains an intensely debated question even though it has been investigated for more than a century. Further clarifications could be obtained by preparing macroscopic objects in spatial quantum superpositions and proposals for generating such states for nano-mechanical devices either in a transient or a probabilistic fashion have been put forward. Here we introduce a method to deterministically obtain spatial superpositions of arbitrary lifetime via dissipative state preparation. In our approach, we engineer a double-well potential for the motion of the mechanical element and drive it towards the ground state, which shows the desired spatial superposition, via optomechanical sideband cooling. We propose a specific implementation based on a superconducting circuit coupled to the mechanical motion of a lithium-decorated monolayer graphene sheet, introduce a method to verify the mechanical state by coupling it to a superconducting qubit, and discuss its prospects for testing collapse models for the quantum to classical transition.
The property of superadditivity of the quantum relative entropy states that, in a bipartite system $mathcal{H}_{AB}=mathcal{H}_A otimes mathcal{H}_B$, for every density operator $rho_{AB}$ one has $ D( rho_{AB} || sigma_A otimes sigma_B ) ge D( rho_A || sigma_A ) +D( rho_B || sigma_B) $. In this work, we provide an extension of this inequality for arbitrary density operators $ sigma_{AB} $. More specifically, we prove that $ alpha (sigma_{AB})cdot D({rho_{AB}}||{sigma_{AB}}) ge D({rho_A}||{sigma_A})+D({rho_B}||{sigma_B})$ holds for all bipartite states $rho_{AB}$ and $sigma_{AB}$, where $alpha(sigma_{AB})= 1+2 || sigma_A^{-1/2} otimes sigma_B^{-1/2} , sigma_{AB} , sigma_A^{-1/2} otimes sigma_B^{-1/2} - mathbb{1}_{AB} ||_infty$.
We propose a novel protocol for the creation of macroscopic quantum superposition (MQS) states based on a measurement of a non-monotonous function of a quantum collective variable. The main advantage of this protocol is that it does not require switching on and off nonlinear interactions in the system. We predict this protocol to allow the creation of multiatom MQS by measuring the number of atoms coherently outcoupled from a two-component (spinor) Bose-Einstein condensate.
The polarization properties of macroscopic Bell states are characterized using three-dimensional quantum polarization tomography. This method utilizes three-dimensional inverse Radon transform to reconstruct the polarization quasiprobability distribution function of a state from the probability distributions measured for various Stokes observables. The reconstructed 3D distributions obtained for the macroscopic Bell states are compared with those obtained for a coherent state with the same mean photon number. The results demonstrate squeezing in one or more Stokes observables.