On the relation between quantum mechanical probabilities and event frequencies

The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We demonstrate that there are only two ways to resolve this problem. The first solution places emphasis on the precise use of the concept of conditional probability for successive measurements. The physically correct conditional probabilities define additive probabilities for two-time measurements. These probabilities depend explicitly on the resolution of the physical device and do not, therefore, correspond to a function of the associated projection operators. It follows that quantum theory distinguishes between physical events and propositions about events, the latter are not represented by projection operators and that the outcomes of two-time experiments cannot be described by quantum logic. The alternative explanation is rather radical: it is conceivable that the relative frequencies for two-time measurements do not converge, unless a particular consistency condition is satisfied. If this is true, a strong revision of the quantum mechanical formalism may prove necessary. We stress that it is possible to perform experiments that will distinguish the two alternatives.     

Phase-Dependent Effects in Stern-Gerlach Experiments

In the frame of quantum mechanics, we consider an ensemble of spin-1/2 neutral particles passing through a Stern-Gerlach apparatus and explore how their motions depend on the initial phase difference between two internal spin states. Assuming the particles moving along y-axis, due to the initial phase difference between spin states, they not only split along the longitudinal direction （z-axis） but also separate along the lateral direction （x-axis）. The dependence of the lateral displacement on the initial phase difference reminds one of the picture of a quantum interference. This generalized interference provides an alternative approach to measuring the initial phase difference. The experimental realization with ultracold atoms or Bose-Einstein condensates is also discussed.     

The uncertainties in radial position and radial momentum of an electron in the non-relativistic hydrogen-like atom

Similar to the case of a simple harmonic oscillator, an increase in azimuthal quantum number l will result in simultaneous decrease in both the uncertainty in radial position and the uncertainty in radial momentum for the same principal quantum number n in the non-relativistic hydrogen-like atom. Thus, in some cases of hydrogen-like atom and in the case of a simple harmonic oscillator, the more precisely the position is determined, the more precisely the momentum is known in that instant, and vice versa.     

Continuous QND measurements: no quantum noise

Monitoring an arbitrary observable is analyzed in the framework of Restricted-Path-Integral (RPI) theory of continuous quantum measurements. While in an usual (quantum-demolition) continuous measurement the measurement noise contains both classical and quantum parts, only the classical noise is shown to be present in a quantum nondemolition (QND) continuous measurement. As a result, no absolute restrictions exist on measurability of a QND observable and the measurement output satisfies the classical equation of motion. Monitoring the energy gives an example of a discrete-spectrum observable. Received: 7 April 1996 / Revised version: 7 August 1996     

State reconstruction of one-dimensional wave packets

76 , 1985 (1996)] for quantum-state reconstruction of one-dimensional non-relativistic wave packets from position observations. We illuminate the theoretical background of the technique and show how to extend the procedure to the continuous part of the spectrum. Received: 7 July 1997     

Oscillatory motion in confined potential systems with dissipation in the context of the Schrödinger-Langevin-Kostin equation

The quantum dissipative motion of wave packets in confined systems with polynomial potentials is numerically investigated in the context of the Schrödinger-Langevin-Kostin equation. Oscillatory patterns are studied in detail and they confirm the validity of the correspondence principle. The transition to the stationary state is also discussed.     

Dynamics of entanglement of bosonic modes on symmetric graphs

We investigate the dynamics of an initially disentangled Gaussian state on a general finite symmetric graph. As concrete examples we obtain properties of this dynamics on mean field graphs (also called fully connected or complete graphs) of arbitrary sizes. In the same way that chains can be used for transmitting entanglement by their natural dynamics, these graphs can be used to store entanglement. We also consider two kinds of regular polyhedron which show interesting features of entanglement sharing.     

Closing the detection loophole in the Bell test for local models based upon three hidden variables

Locality and fair sampling are proved to be contradictory assumptions in hidden variable models of the Bell test that are based upon a 3-dimensional sample space. This result makes the class of 3-dimensional hidden variable models incompatible with quantum mechanics in the ideal case, independently of detection efficiencies.     

Deterministic generation of squeezing for a cavity field with a collection of driven atoms

We propose an efficient scheme for realizing squeezing for a cavity mode. In the scheme, a collection of ladder-type three-level atoms are trapped in a cavity and driven by two classical fields. Under certain conditions, the cavity field deterministically evolves to a squeezed state. The scheme can also be used for conditional generation of superpositions of different squeezed vacuum states.     

Controlled Teleportation of Multi-Qudit Quantum Information

We present a controlled teleportation scheme for teleporting an arbitrary superposition state of an M-qudit quantum system. The scheme employs only one entangled state as quantum channel, which consists of the qudits from Alice, Bob and every agent. The quantum operations used in the teleportation process are a series of qudit Bell measurements, single-qudit projective measurements, qudit H-gates, qudit-Pauli gates and qudit phase gates. It is shown that the original state can be restored by the receiver only on the condition that all the agents collaborate. If any agent does not cooperate, the original state can not be fully recovered.     

Testing a Bell-type inequality with a micromaser

We propose a phase-sensitive micromaser setup to demonstrate experimentally a violation of a Bell-type inequality. The interaction of atoms with the cavity field produces entanglement between the atoms and the cavity photons and therefore also between the atoms. We derive a Bell-type inequality for the atom-atom correlations and show that it can be violated not only in an idealized model but also under realistic circumstances when various sources of additional randomness are accounted for. Among them are the energy dissipation in the resonator and the Poissonian arrival statistics of the atoms.Prof. F.P. Schäfer on the occasion of his 65th birthday.     

Generation of a displaced qubit and entangled displaced photon state via conditional measurement and their properties

We study optical schemes for generating both a displaced photon and a displaced qubit via conditional measurement. Combining one mode prepared in different microscopic states (one-mode qubit, single photon, vacuum state) and another mode in macroscopic states (coherent state, single photon added coherent state), a conditional state in the other output mode exhibits properties of a superposition of the displaced vacuum and a single photon. We propose to use the displaced qubit and entangled states composed of the displaced photon as components for quantum information processing. Basic states of such a qubit are distinguishable from each other with high fidelity. We show that the qubit reveals both microscopic and macroscopic properties. Entangled displaced states with a coherent phase as an additional degree of freedom are introduced. We show that additional degree of freedom enables to implement complete Bell state measurement of the entangled displaced photon states.     

Manipulation of optical fields by atomic interferometry: Quantum variations on a theme by young

We analyze the principle of a very general and conceptually simple method for manipulating optical fields by coupling them into a matter waves Young double slit apparatus. The field, non resonant with the atoms, acts as a phase-retarding medium in one of the arms of the interferometer and shifts the atomic fringe pattern. The method constitutes a simple quantum nondemolition measuring scheme of the photon number. Non classical states such as Schrödinger cats and Fock states of the field are generated in the measurement process. The analysis of the atomic interferometer with optical retarding fields provides a very simple and striking illustration of basic concepts of the quantum measurement theory and of the principle of complementarity. This scheme, which would be very difficult to implement in the optical domain, is equivalent to a more feasible and recently proposed Ramsey interference method to measure small microwave fields with beams of Rydberg atoms.Associé au Centre National de la Recherche Scientifique et à l'Université Pierre et Marie Curie     

Properties of the frequency operator do not imply the quantum probability postulate

We review the properties of the frequency operator for an infinite number of systems and disprove claims in the literature that the quantum probability postulate can be derived from these properties.     

Berry phase in a bipartite system with general subsystem–subsystem couplings

The Berry phase in a bipartite system described by the XXZ model is studied in this Letter. We calculate the Berry phase acquired by the bipartite system as well as the geometric phase gained by each subsystem. The results show that as the coupling constants tend to infinity all geometric phases go to zero, this confirms the prediction given by us previously [X.X. Yi, L.C. Wang, T.Y. Zheng, Phys. Rev. Lett. 92 (2004) 150406] for bipartite systems with a specific subsystem–subsystem coupling.     

Mean-Field Dynamics of a Two-Mode Bose-Einstein Condensate Subject to Decoherence

We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherenee （or particle loss）. Starting from the full many-body dynamics described by the master equation, an effective Gross- Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.     

A new protocol for constructing nonlocal n-qubit controlled-U gates

We present a new protocol for constructing a nonlocal n-qubit controlled-U gate. In this protocol, no prior sharing of entanglement is needed and only one ancilla qubit is sent once from one party to another. Thus, the present protocol is very efficient for performing a nonlocal multiqubit controlled-U gate, which is important to network quantum information processing and communication.     

Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schrödinger Hamiltonians

Some exactly solvable potentials in the position dependent mass background are generated whose bound states are given in terms of Laguerre- or Jacobi-type X₁ exceptional orthogonal polynomials. These potentials are shown to be shape invariant and isospectral to the potentials whose bound state solutions involve classical Laguerre or Jacobi polynomials.     

A method for demonstrating violation of local realism with a two-photon downconverter without use of Bell inequalities

We show that the recent proposal by Hardy and Jordan for a test of local realism without the use of Bell inequalities can be implemented in two-photon coincidence measurements with linear polarizers, when the photon pairs are produced by parametric downconversion. If the probabilities measured with real detectors are proportional to the corresponding probabilities determined with ideal detectors, this method does not depend on the use of detectors with high or even known quantum efficiencies.Dedicated to H. Walther on the occasion of his 60th birthday