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Masud Mansuripur
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 Phys. Rev. Lett. 110, 080503 (2013) [5 pages]

Entanglement and Particle Identity: A Unifying Approach

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A. P. Balachandran1,2,*, T. R. Govindarajan1,3,†, Amilcar R. de Queiroz4,‡, and A. F. Reyes-Lega5,§ 1Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
2Physics Department, Syracuse University, Syracuse, New York 13244-1130, USA
3Chennai Mathematical Institute, H1, SIPCOT IT Park, Kelambakkam, Siruseri 603103, India
4Instituto de Fisica, Universidade de Brasilia, Caixa Postal 04455, 70919-970 Brasilia, Distrito Federal, Brazil
5Departamento de Física, Universidad de los Andes, Apartado Aéreo 4976 Bogotá, Distrito Capital, Colombia

Received 22 June 2012; revised 8 November 2012; published 22 February 2013

It has been known for some years that entanglement entropy obtained from partial trace does not provide the correct entanglement measure when applied to systems of identical particles. Several criteria have been proposed that have the drawback of being different according to whether one is dealing with fermions, bosons, or distinguishable particles. In this Letter, we give a precise and mathematically natural answer to this problem. Our approach is based on the use of the more general idea of the restriction of states to subalgebras. It leads to a novel approach to entanglement, which is suitable to be used in general quantum systems and especially in systems of identical particles. This settles some recent controversy regarding entanglement for identical particles. The prospects for applications of our criteria are wide ranging, from spin chains in condensed matter to entropy of black holes.

© 2013 American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.110.080503
DOI:
10.1103/PhysRevLett.110.080503
PACS:
03.67.Mn, 02.30.Tb, 03.65.Ud, 89.70.Cf
*bal@phy.syr.edu

†trg@imsc.res.in

‡amilcarq@unb.br

§anreyes@uniandes.edu.co

 Systems of identical particles.—In the case of identical
particles, the Hilbert space of the system is no longer of the
tensor product form. Therefore, the treatment of subsystems
using partial trace becomes problematic. In contrast,
in our approach, all that is needed to describe a subsystem
is the specification of a subalgebra that corresponds to the
subsystem. Then, the restriction of the original state to the
subalgebra provides a physically motivated generalization
of the concept of partial trace, the latter not being sensible
anymore. Applying the GNS construction to the restricted
state, we can study the entropy emerging from the restriction
and use it as a generalized measure of entanglement.

                      Phys. Rev. Lett. 110, 080501 (2013) [4 pages]

Fundamental Bound on the Reliability of Quantum Information Transmission

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Naresh Sharma* and Naqueeb Ahmad Warsi† Tata Institute of Fundamental Research (TIFR), Mumbai 400005, India

Received 17 August 2012; published 20 February 2013

Information theory tells us that if the rate of sending information across a noisy channel were above the capacity of that channel, then the transmission would necessarily be unreliable. For classical information sent over classical or quantum channels, one could, under certain conditions, make a stronger statement that the reliability of the transmission shall decay exponentially to zero with the number of channel uses, and the proof of this statement typically relies on a certain fundamental bound on the reliability of the transmission. Such a statement or the bound has never been given for sending quantum information. We give this bound and then use it to give the first example where the reliability of sending quantum information at rates above the capacity decays exponentially to zero. We also show that our framework can be used for proving generalized bounds on the reliability.

© 2013 American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.110.080501
DOI:
10.1103/PhysRevLett.110.080501
PACS:
03.67.Hk
*nsharma@tifr.res.in

†naqueeb@tifr.res.in

On Feb 22, 2013, at 10:39 AM, JACK SARFATTI <adastra1@me.com> wrote:

O Brave New World ;-)
We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Hořava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit.

<HologramPhysRevLett.110.081601.pdf>