arXiv subjects

J. A. Vaccaro

Publications and source records attributed to J. A. Vaccaro.

16 recordsLinked to original sources

arXiv2020

Thermodynamics from first principles: correlations and nonextensivity

The standard formulation of thermostatistics, being based on the Boltzmann-Gibbs distribution and logarithmic Shannon entropy, describes idealized uncorrelated systems with extensive energies and short-range interactions. In this letter, we use the fundamental principles of ergodicity (via Liouville's theorem), the self-similarity of correlations, and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution for long-range-interacting systems. Significantly, our formalism provides a justification for the well-studied nonextensive thermostatistics characterized by the Tsallis distribution, which it includes as a special case. We also give the complementary maximum entropy derivation of the same distributions by constrained maximization of the Boltzmann-Gibbs-Shannon entropy. The consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics.

cond-mat.stat-mech↗

arXiv2018

Information Erasure

Information is central to thermodynamics, providing the grounds to the formulation of the theory in powerful abstract statistical terms. One must not forget, however, that, as put by Landauer, {\it information is physical}. This means that the processing of information will be unavoidably linked to the costs of manipulating the real physical systems carrying the information. Here we will focus on the particular process of erasing information, which plays a fundamental role in the description of heat engines. We will review Landauer's principle and the associated erasure energy cost. We will also show, following the recent contributions from Vaccaro and Barnett, that cost of erasing does not need to be paid with energy, but with any other conserved quantity. Finally, we will address the issue of designing heat engines based on these new concepts.

quant-ph↗

arXiv2010

Group theoretic formulation of complementarity

We generalize Bohr's complementarity principle for wave and particle properties to arbitrary quantum systems. We begin by noting that a particle-like state is represented by a spatially-localized wave function and its narrow probability density is displaced by spatial translations. In contrast a wave-like state is represented by a spatially-delocalized wave function and the corresponding broad position probability density is invariant to spatial translations. The wave-particle dichotomy can therefore be seen as a competition between displacement and invariance of the state with respect to spatial translations. We generalize this dichotomy to arbitrary quantum systems with finite dimensional Hilbert spaces as follows. We use arbitrary finite symmetry groups to represent transformations of the quantum system. The symmetry (i.e. invariance) or asymmetry (i.e. displacement) of a given state with respect to transformations of the group are identified with the generalized wave and particle nature, respectively. We adopt a measure of wave and particle properties based on the amount of information that can be encoded in the symmetric and asymmetric parts of the state.

quant-ph↗

arXiv2009

Optimal reference states for maximum accessible entanglement under the local particle number superselection rule

Global conservation laws imply superselection rules (SSR) which restrict the operations that are possible on any given state. Imposing the additional constraint of local operations and classical communication (LOCC) forbids the transfer of quantum systems between spatially separated sites. In the case of particle conservation this imposes a SSR for local particle number. That is, the coherences between subspaces of fixed particle number at each site are not accessible and any state is therefore equivalent to its projection onto these subspaces. The accessible entanglement under the SSR is less than (or equal to) that available in the absence of the SSR. An ancilla can be used as a reference system to increase the amount of accessible entanglement. We examine the relationship between local particle number uncertainty and the accessible entanglement and consider the optimal reference states for recovering entanglement from certain systems. In particular we derive the optimal ancilla state for extracting entanglement for a single shared particle and make steps towards the optimum for general systems.

quant-ph↗

arXiv2008

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.

quant-ph↗

arXiv2007

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.

quant-ph↗

arXiv2007

Quantum protocols for anonymous voting and surveying

We describe quantum protocols for voting and surveying. A key feature of our schemes is the use of entangled states to ensure that the votes are anonymous and to allow the votes to be tallied. The entanglement is distributed over separated sites; the physical inaccessibility of any one site is sufficient to guarantee the anonymity of the votes. The security of these protocols with respect to various kinds of attack is discussed. We also discuss classical schemes and show that our quantum voting protocol represents a N-fold reduction in computational complexity, where N is the number of voters.

quant-ph↗

arXiv2006

Entanglement and Symmetry: A Case Study in Superselection Rules, Reference Frames, and Beyond

This paper concentrates on a particular example of a constraint imposed by superselection rules (SSRs): that which applies when the parties (Alice and Bob) cannot distinguish among certain quantum objects they have. This arises naturally in the context of ensemble quantum information processing such as in liquid NMR. We discuss how a SSR for the symmetric group can be applied, and show how the extractable entanglement can be calculated analytically in certain cases, with a maximum bipartite entanglement in an ensemble of N Bell-state pairs scaling as log(N) as N goes to infinity . We discuss the apparent disparity with the asymptotic (N >> 1) recovery of unconstrained entanglement for other sorts of superselection rules, and show that the disparity disappears when the correct notion of applying the symmetric group SSR to multiple copies is used. Next we discuss reference frames in the context of this SSR, showing the relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502 (2004)]. The action of a reference frame can be regarded as the analog of activation in mixed-state entanglement. We also discuss the analog of distillation: there exist states such that one copy can act as an imperfect reference frame for another copy. Finally we present an example of a stronger operational constraint, that operations must be non-collective as well as symmetric. Even under this stronger constraint we nevertheless show that Bell-nonlocality (and hence entanglement) can be demonstrated for an ensemble of N Bell-state pairs no matter how large N is. This last work is a generalization of that of Mermin [Phys. Rev. D 22, 356 (1980)].

quant-ph↗

arXiv2003

Experimental demonstration of quantum source coding

We report an experimental demonstration of Schumacher's quantum noiseless coding theorem. Our experiment employs a sequence of single photons each of which represents three qubits. We initially prepare each photon in one of a set of 8 non-orthogonal codeword states corresponding to the value of a block of three binary letters. We use quantum coding to compress this quantum data into a two-qubit quantum channel and then uncompress the two-qubit channel to restore the original data with a fidelity approaching the theoretical limit.

quant-ph↗

arXiv2003

Intensity-dependent dispersion under conditions of electromagnetically induced transparency in coherently prepared multi-state atoms

Interest in lossless nonlinearities has focussed on the the dispersive properties of $Λ$ systems under conditions of electromagnetically induced transparency (EIT). We generalize the lambda system by introducing further degenerate states to realize a `Chain $ Λ$' atom where multiple coupling of the probe field significantly enhances the intensity dependent dispersion without compromising the EIT condition.

quant-ph↗

arXiv2001

Resonant and off-resonant transients in electromagnetically induced transparency: turn-on and turn-off dynamics

This paper presents a wide-ranging theoretical and experimental study of non-adiabatic transient phenomena in a $Λ$ EIT system when a strong coupling field is rapidly switched on or off. The theoretical treatment uses a Laplace transform approach to solve the time-dependent density matrix equation. The experiments are carried out in a Rb$^{87}$ MOT. The results show transient probe gain in parameter regions not previously studied, and provide insight into the transition dynamics between bare and dressed states.

quant-ph↗

arXiv2001

Remote control of restricted sets of operations: Teleportation of Angles

We study the remote implementation of a unitary transformation on a qubit. We show the existence of non-trivial protocols (i.e., using less resources than bidirectional state teleportation) which allow the perfect remote implementation of certain continuous sets of quantum operations. We prove that, up to a local change of basis, only two subsets exist that can be implemented remotely with a non-trivial protocol: Arbitrary rotations around a fixed direction $\vec{n}$ and rotations by a fixed angle around an arbitrary direction lying in a plane orthogonal to $\vec{n}$. The overall classical information and distributed entanglement cost required for the remote implementation depends on whether it is a priori known to which of the two teleportable subsets the transformation belongs to. If it is so, the optimal protocol consumes one e-bit of entanglement and one c-bit in each direction. If the subset is not known, two e-bits of entanglement need to be consumed while the classical channel becomes asymmetric, two c-bits are conveyed from Alice to Bob but only one from Bob to Alice.

quant-ph↗

arXiv2001

Observation of transient gain without population inversion in a laser-cooled rubidium lambda system

We have observed clear Rabi oscillations of a weak probe in a strongly driven three-level lambda system in laser-cooled rubidium for the first time. When the coupling field is non-adiabatically switched on using a Pockels cell, transient probe gain without population inversion is obtained in the presence of uncoupled absorptions. Our results are supported by three-state computations.

quant-ph↗

arXiv2001

Observations of a doubly driven V system probed to a fourth level in laser-cooled rubidium

Observations of a doubly driven V system probed to a fourth level in an N configuration are reported. A dressed state analysis is also presented. The expected three-peak spectrum is explored in a cold rubidium sample in a magneto-optic trap. Good agreement is found between the dressed state theory and the experimental spectra once light shifts and uncoupled absorptions in the rubidium system are taken into account.

quant-ph↗

arXiv2000

Quantum remote control: Teleportation of unitary operations

We consider the implementation of an arbitrary unitary operation U upon a distant quantum system. This teleportation of U can be viewed as a quantum remote control. We investigate protocols which achieve this using local operations, classical communication and shared entanglement (LOCCSE). Lower bounds on the necessary entanglement and classical communication are determined using causality and the linearity of quantum mechanics. We examine in particular detail the resources required if the remote control is to be implemented as a classical black box. Under these circumstances, we prove that the required resources are, necessarily, those needed for implementation by bidirectional state teleportation.

quant-ph↗

arXiv1997

Maximally Robust Unravelings of Quantum Master Equations

The stationary solution ρof 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 ρfor the longest time. The optical parametric oscillator is a soluble example.

quant-ph↗