Class Of Quantum States Research Articles

Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox

We formally link the concept of steering (a concept created by Schrodinger but only recently formalized by Wiseman, Jones and Doherty Phys. Rev. Lett. 98 140402 (2007)]) and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid Phys. Rev. A 40 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variable observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-type criteria can be rederived within this formalism, thus unifying these efforts from a modern quantum-information perspective and clarifying their conceptual and formal origin. The theory follows in close analogy with criteria for other forms of quantum nonlocality (Bell nonlocality and entanglement), and because it is a hybrid of those two, it may lead to insights into the relationship between the different forms of nonlocality and the criteria that are able to detect them.

Measuring position and momentum together

We describe an operational scheme for determining both the position and momentum distributions in a large class of quantum states, together with an experimental implementation.

Weakly entangled states are dense and robust

Motivated by the mathematical definition of entanglement we undertake a rigorous analysis of the separability and nondistillability properties in the neighborhood of those three-qubit mixed states which are entangled and completely biseparable. Our results are not only restricted to this class of quantum states, since they rest upon very general properties of mixed states and unextendible product bases for any possible number of parties. Robustness against noise of the relevant properties of these states implies the significance of their possible experimental realization, therefore being of physical---and not exclusively mathematical---interest.

A new class of quantum states generated by m -fold application of Bogoliubov's transformation

By applying higher powers of the Bogoliubov transformation operator bdagger = v*a + mu*adagger to the two-photon coherent states (or minimum uncertainty squeezed states) we construct a new type of quantum state which we call the generalized excited two-photon coherent states. Analytic expressions for the quantum statistical properties are derived, and through numerical computation the phase space quasi-probability distributions are found. These states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. For particular values of two parameters lambda and rho, these generalized states reduce to other classes of coherent states formerly reported. Our theory thus presents a much broader approach to these types of quantum states.

On quantum one-way permutations

\We discuss the question of the existence of quantum one-way permutations. First, we consider the question: if a state is difficult to prepare, is the reflection operator about that state difficult to construct? By revisiting Grover's algorithm, we present the relationship between this question and the existence of quantum one-way permutations. Next, we prove the equivalence between inverting a permutation and that of constructing polynomial size quantum networks for reflection operators about a class of quantum states. We will consider both the worst case and the average case complexity scenarios for this problem. Moreover, we compare our method to Grover's algorithm and discuss possible applications of our results.

Minimum-error discrimination between multiply symmetric states

An optimum measurement strategy is presented for a new class of quantum states. This provides discrimination among the states with the minimum probability of error.

Entangled versus classical quantum states

We discuss usefulness of the criterion of fragility with respect to a measurement-like dynamics in the description of entanglement of both pure and statistical states.

Effectively classical quantum states for open systems

Notions of robust and `classical' states for an open quantum system are introduced and discussed in the framework of the isometric-sweeping decomposition. Using the predictability sieve proposed by Zurek [Phys. Rev. D 24 (1981) 1516; 26 (1982) 1862],`quasi-classical' states are defined. A number of examples illustrating how the `quasi-classical' states correspond to classical points in phase space connected with the measuring apparatus are presented.

Quantum statistical properties of superposition of squeezed and displaced number states

In this article we introduce general class of quantum states, as a single mode vibration of electromagnetic field, sudden squeezed-plus-displaced by a collection of two displacements 180° out of phase. For such class the quantum statistical quantities, such as the second-order correlation function, quasiprobability distribution functions and the photon-number distribution function are examined analytically and numerically. Generation schemes are proposed. Regimes of strongly nonclassical behaviour of such states are demonstrated.

Statistical inference, distinguishability of quantum states, and quantum entanglement

We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described by density matrices. We extend this notion to describe the amount of entanglement between two quantum systems from a statistical point of view. Our measure is independent of the number of entangled systems and their dimensionality.

Quantum mechanical states as attractors for Nelson processes

In this paper we reconsider, in the light of the Nelson stochastic mechanics, the idea originally proposed by Bohm and Vigier that arbitrary solutions of the evolution equation for the probability densities always relax in time toward the quantum mechanical density ¦ψ¦2 derived from the Schrodinger equation. The analysis of a few general propositions and of some physical examples show that the choice of the L1 metrics and of the Nelson stochastic flux is correct for a particular class of quantum states, but cannot be adopted in general. This indicates that the question if the quantum mechanical densities attract other solution of the classical Fokker-Planck equations associated to the Schrodinger equation is physically meaningful, even if a classical probabilistic model good for every quantum stale is still not available. A few suggestion in this direction are finally discussed.

Constraints on negative-energy fluxes.

Locally negative energy due to quantum coherence effects in quantum field theory is discussed. In a previous work, it was argued that a beam carrying negative energy must satisfy an uncertainty-principle-type inequality of the form \ensuremath{\Vert}\ensuremath{\Delta}E\ensuremath{\Vert}\ensuremath{\Delta}t\ensuremath{\le}1, where \ensuremath{\Vert}\ensuremath{\Delta}E\ensuremath{\Vert} is the magnitude of the negative energy that may be transmitted in a time \ensuremath{\Delta}t. This conclusion applied only to two-dimensional spacetime, and was based on an examination of particular classes of quantum states. In the present work, we give more precise formulations of this type of inequality for a free massless scalar field in both two- and four-dimensional flat spacetime. These inequalities are proven to hold for all quantum states. The physical interpretation of these inequalities is also discussed, and it is argued that they are likely to prevent negative energy from producing such large-scale effects as violations of the second law of thermodynamics or of cosmic censorship.

Amplification of quantum states and noiseless photon amplifiers

It is shown that in principle a device exists which would duplicate a quantum system within a class of quantum states if and only if those quantum states are mutually orthogonal. The possible existence of a related noiseless photon amplifier is also established.

Microscopic nuclear collective motion studied by classical equations of motion

The time-dependent variation principle is used to obtain generally non-canonical equations of motion from any class of quantum states which are parameterized by a set of continuous complex quantities. A class of states is presented whose associated classical dynamics is described by the five collective quadrupole degrees of freedom. Information about the classical dynamics of the system can be obtained from the non-canonical equations by finding physically interesting quantities which are coordinate independent and which characterize the low-energy collective motion. Approximate collective hamiltonians, of either a Bohr-Mottelson or an IBM type, can be found by insisting that the interesting physical quantities which describe the low-energy classical behavior of the many-body system are the same as those describing the classical behavior of the system given by the collective hamiltonian. The method is applied to two simple schematic models, one vibrational and one rotational, and IBM hamiltonians are obtained.