Overcoming a limitation of deterministic dense coding with a non-maximally entangled initial state

Under two-party deterministic dense-coding, Alice communicates (perfectly distinguishable) messages to Bob via a qudit from a pair of entangled qudits in pure state |Psi>. If |Psi> represents a maximally entangled state (i.e., each of its Schmidt coefficients is sqrt(1/d)), then Alice can convey to Bob one of d^2 distinct messages. If |Psi> is not maximally entangled, then Ji et al. [Phys. Rev. A 73, 034307 (2006)] have shown that under the original deterministic dense-coding protocol, in which messages are encoded by unitary operations performed on Alice's qudit, it is impossible to encode d^2-1 messages. Encoding d^2-2 is possible; see, e.g., the numerical studies by Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. Answering a question raised by Wu et al. [Phys. Rev. A 73, 042311 (2006)], we show that when |Psi> is not maximally entangled, the communications limit of d^2-2 messages persists even when the requirement that Alice encode by unitary operations on her qudit is weakened to allow encoding by more general quantum operators. We then describe a dense-coding protocol that can overcome this limitation with high probability, assuming the largest Schmidt coefficient of |Psi> is sufficiently close to sqrt(1/d). In this protocol, d^2-2 of the messages are encoded via unitary operations on Alice's qudit, and the final (d^2-1)-th message is encoded via a (non-trace-preserving) quantum operation.Comment: 18 pages, published versio

Deterministic dense coding and entanglement entropy

We present an analytical study of the standard two-party deterministic dense-coding protocol, under which communication of perfectly distinguishable messages takes place via a qudit from a pair of non-maximally entangled qudits in pure state |S>. Our results include the following: (i) We prove that it is possible for a state |S> with lower entanglement entropy to support the sending of a greater number of perfectly distinguishable messages than one with higher entanglement entropy, confirming a result suggested via numerical analysis in Mozes et al. [Phys. Rev. A 71 012311 (2005)]. (ii) By explicit construction of families of local unitary operators, we verify, for dimensions d = 3 and d=4, a conjecture of Mozes et al. about the minimum entanglement entropy that supports the sending of d + j messages, j = 2, ..., d-1; moreover, we show that the j=2 and j= d-1 cases of the conjecture are valid in all dimensions. (iii) Given that |S> allows the sending of K messages and has the square roof of c as its largest Schmidt coefficient, we show that the inequality c <= d/K, established by Wu et al. [ Phys. Rev. A 73, 042311 (2006)], must actually take the form c < d/K if K = d+1, while our constructions of local unitaries show that equality can be realized if K = d+2 or K = 2d-1.Comment: 19 pages, 2 figures. Published versio

Scotin, a novel p53-inducible proapoptotic protein located in the ER and the nuclear membrane

p53 is a transcription factor that induces growth arrest or apoptosis in response to cellular stress. To identify new p53-inducible proapoptotic genes, we compared, by differential display, the expression of genes in spleen or thymus of normal and p53 nullizygote mice after γ-irradiation of whole animals. We report the identification and characterization of human and mouse Scotin homologues, a novel gene directly transactivated by p53. The Scotin protein is localized to the ER and the nuclear membrane. Scotin can induce apoptosis in a caspase-dependent manner. Inhibition of endogenous Scotin expression increases resistance to p53-dependent apoptosis induced by DNA damage, suggesting that Scotin plays a role in p53-dependent apoptosis. The discovery of Scotin brings to light a role of the ER in p53-dependent apoptosis

Conformal dimension and random groups

We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following form, where $l$ is the relator length, going to infinity. (a) 1 + 1/C < \Cdim(\bdry G) < C l / \log(l), for the few relator model, and (b) 1 + l / (C\log(l)) < \Cdim(\bdry G) < C l, for the density model, at densities $d < 1/16$. In particular, for the density model at densities $d < 1/16$, as the relator length $l$ goes to infinity, the random groups will pass through infinitely many different quasi-isometry classes.Comment: 32 pages, 4 figures. v2: Final version. Main result improved to density < 1/16. Many minor improvements. To appear in GAF

On Convergence to the Denjoy-Wolff Point

For holomorphic selfmaps of the open unit disc U that are not elliptic automorphisms, the Schwarz Lemma and the Denjoy-Wolff Theorem combine to yield a remarkable result: each such map φ has a (necessarily unique) Denjoy-Wolff point ..

Description of \u3ci\u3eHydrosmectomorpha\u3c/i\u3e Klimaszewski and Webster, a new subgenus of \u3ci\u3eAtheta\u3c/i\u3e C. G. Thomson, with three new Canadian species (Coleoptera: Staphylinidae: Aleocharinae)

A new subgenus, Hydrosmectomorpha Klimaszewski and Webster, of the genus Atheta C. G. Thomson (Coleoptera: Staphylinidae: Aleocharinae) is erected to accommodate three new species and Atheta newfoundlandica (Klimaszewski and Langor). The new species are: Atheta (Hydrosmectomorpha) meduxnekeagensis Webster and Klimaszewski, new species; Atheta (Hydrosmectomorpha) quebecensis Webster and Klimaszewski, new species, Atheta (Hydrosmectomorpha) vincenti Webster and Klimaszewski, new species. The new species are described, illustrated, and a key is provided. Atheta newfoundlandica (Klimaszewski and Langor), was recently transferred from Hydrosmecta C.G. Thomson to an unspecified subgenus of Atheta. New habitat/collection data are presented for the treated species

The augmented message-matrix approach to deterministic dense coding theory

A method is presented for producing analytical results applicable to the standard two-party deterministic dense coding protocol, wherein communication of K perfectly distinguishable messages is attainable with the aid of K selected local unitary operations on one qudit from a pair of entangled qudits of equal dimension d in a pure state. The method utilizes the properties of a (d^2)x(d^2) unitary matrix whose initial columns represent message states of the system used for communication, augmented by sufficiently many additional orthonormal column vectors so that the resulting matrix is unitary. Using the unitarity properties of this augmented message-matrix, we produce simple proofs of previously established results including (i) an upper bound on the value of the square of the largest Schmidt coefficient, given by d/K, and (ii) the impossibility of finding a pure state that can enable transmission of K=d^2-1 messages but not d^2. Additional results obtained using the method include proofs that when K=d+1 the upper bound on the square of the largest Schmidt coefficient (i) always reduces to at least (1/2)[1+sqrt{(d-2)/(d+2)}], and (ii) reduces to (d-1)/d in the special case that the identity and shift operators are two of the selected local unitaries.Comment: 16 page

A hypercyclic finite rank perturbation of a unitary operator

A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space \H are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.Comment: published in Mathematische Annale