03288nas a2200169 4500008004100000245006700041210006500108260001500173300001100188490000700199520278500206100002002991700001703011700001603028700001903044856005503063 2013 eng d00aOptimal entanglement-assisted one-shot classical communication0 aOptimal entanglementassisted oneshot classical communication c2013/06/03 a0623010 v873 a

The one-shot success probability of a noisy classical channel for transmitting one classical bit is the optimal probability with which the bit can be successfully sent via a single use of the channel. Prevedel et al. [Phys. Rev. Lett. 106, 110505 (2011)] recently showed that for a specific channel, this quantity can be increased if the parties using the channel share an entangled quantum state. In this paper, we characterize the optimal entanglement-assisted protocols in terms of the radius of a set of operators associated with the channel. This characterization can be used to construct optimal entanglement-assisted protocols for a given classical channel and to prove the limits of such protocols. As an example, we show that the Prevedel et al. protocol is optimal for two-qubit entanglement. We also prove some tight upper bounds on the improvement that can be obtained from quantum and nonsignaling correlations.

1 aHemenway, Brett1 aMiller, Carl1 aShi, Yaoyun1 aWootters, Mary uhttp://link.aps.org/doi/10.1103/PhysRevA.87.06230103224nas a2200205 4500008004100000022001400041245009700055210006900152260001500221300001400236490000700250520257700257653002302834653002602857653002802883100002002911700001702931700001602948856005402964 2011 eng d a1533-714600aDeciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States0 aDeciding Unitary Equivalence Between Matrix Polynomials and Sets c2001/09/01 a813–8190 v113 a

In this brief report, we consider the equivalence between two sets of m + 1 bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree m matrix polynomials are unitarily equivalent; i.e. UAiV† = Bi for 0 ≤ i ≤ m where U and V are unitary and (Ai, Bi) are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices U and V.

10amatrix polynomials10aSchwartz-Zippel lemma10aunitary transformations1 aChitambar, Eric1 aMiller, Carl1 aShi, Yaoyun uhttp://dl.acm.org/citation.cfm?id=2230936.223094208283nas a2200169 4500008004100000022001300041245005100054210005100105260001500156300001100171490000700182520779500189100002007984700001708004700001608021856007608037 2010 eng d a0022248800aMatrix pencils and entanglement classification0 aMatrix pencils and entanglement classification c2010/01/01 a0722050 v513 a

Quantum entanglement plays a central role in quantum information processing. A main objective of the theory is to classify different types of entanglement according to their interconvertibility through manipulations that do not require additional entanglement to perform. While bipartite entanglement is well understood in this framework, the classification of entanglements among three or more subsystems is inherently much more difficult. In this paper, we study pure state entanglement in systems of dimension 2mn. Two states are considered equivalent if they can be reversibly converted from one to the other with a nonzero probability using only local quantum resources and classical communication (SLOCC). We introduce a connection between entanglement manipulations in these systems and the well-studied theory of matrix pencils. All previous attempts to study general SLOCC equivalence in such systems have relied on somewhat contrived techniques which fail to reveal the elegant structure of the problem that can be seen from the matrix pencil approach. Based on this method, we report the first polynomial-time algorithm for deciding when two2mstates are SLOCC equivalent. We then proceed to present a canonical form for all 2mstates based on the matrix pencil construction such that two states are equivalent if and only if they have the same canonical form. Besides recovering the previously known 26 distinct SLOCC equivalence classes in 23systems, we also determine the hierarchy between these classes.

1 aChitambar, Eric1 aMiller, Carl1 aShi, Yaoyun uhttp://scitation.aip.org/content/aip/journal/jmp/51/7/10.1063/1.3459069