Entanglement of identical particles and reference phase uncertainty

We have recently introduced a measure of the bipartite entanglement of identical particles, E_P, based on the principle that entanglement should be accessible for use as a resource in quantum information processing. We show here that particle entanglement is limited by the lack of a reference phase shared by the two parties, and that the entanglement is constrained to reference-phase invariant subspaces. The super-additivity of E_P results from the fact that this constraint is weaker for combined systems. A shared reference phase can only be established by transferring particles between the parties, that is, with additional nonlocal resources. We show how this nonlocal operation can increase the particle entanglement.Comment: 8 pages, no figures. Invited talk given at EQIS'03, Kyoto, September, 2003. Minor typos corrected, 1 reference adde

Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules

Superselection rules (SSRs) limit the mechanical and quantum processing resources represented by quantum states. However SSRs can be violated using reference systems to break the underlying symmetry. We show that there is a duality between the ability of a system to do mechanical work and to act as a reference system. Further, for a bipartite system in a globally symmetric pure state, we find a triality between the system's ability to do local mechanical work, its ability to do ``logical work'' due to its accessible entanglement, and its ability to act as a shared reference system.Comment: 5 pages, no figures. Extended resubmitted version. Slightly modified title. Transferred to PR

The Consumption of Reference Resources

Under the operational restriction of the U(1)-superselection rule, states that contain coherences between eigenstates of particle number constitute a resource. Such resources can be used to facilitate operations upon systems that otherwise cannot be performed. However, the process of doing this consumes reference resources. We show this explicitly for an example of a unitary operation that is forbidden by the U(1)-superselection rule.Comment: 4 pages 6x9 page format, 2 figure

Particle-wave duality: a dichotomy between symmetry and asymmetry

Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by log(D) where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wave-like symmetry as a whole while exhibiting particle-like asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wave-like symmetry with respect to the group of Pauli operators.Comment: 20 pages, 3 figure

Maximally Robust Unravelings of Quantum Master Equations

The stationary solution \rho of a quantum master equation can be represented as an ensemble of pure states in a continuous infinity of ways. An ensemble which is physically realizable through monitoring the system's environment we call an `unraveling'. The survival probability S(t) of an unraveling is the average probability for each of its elements to be unchanged a time t after cessation of monitoring. The maximally robust unraveling is the one for which S(t) remains greater than the largest eigenvalue of \rho for the longest time. The optical parametric oscillator is a soluble example

The Pegg-Barnett Formalism and Covariant Phase Observables

We compare the Pegg-Barnett (PB) formalism with the covariant phase observable approach to the problem of quantum phase and show that PB-formalism gives essentially the same results as the canonical (covariant) phase observable. We also show that PB-formalism can be extended to cover all covariant phase observables including the covariant phase observable arising from the angle margin of the Husimi Q-function.Comment: 10 page