A few steps more towards NPT bound entanglement

We consider the problem of existence of bound entangled states with non-positive partial transpose (NPT). As one knows, existence of such states would in particular imply nonadditivity of distillable entanglement. Moreover it would rule out a simple mathematical description of the set of distillable states. Distillability is equivalent to so called n-copy distillability for some n. We consider a particular state, known to be 1-copy nondistillable, which is supposed to be bound entangled. We study the problem of its two-copy distillability, which boils down to show that maximal overlap of some projector Q with Schmidt rank two states does not exceed 1/2. Such property we call the the half-property. We first show that the maximum overlap can be attained on vectors that are not of the simple product form with respect to cut between two copies. We then attack the problem in twofold way: a) prove the half-property for some classes of Schmidt rank two states b) bound the required overlap from above for all Schmidt rank two states. We have succeeded to prove the half-property for wide classes of states, and to bound the overlap from above by c<3/4. Moreover, we translate the problem into the following matrix analysis problem: bound the sum of the squares of the two largest singular values of matrix A \otimes I + I \otimes B with A,B traceless 4x4 matrices, and Tr A^\dagger A + Tr B^\dagger B = 1/4.Comment: 15 pages, Final version for IEEE Trans. Inf. Theor

No purification in all discrete theories and the power of the complete extension

Quantum theory has an outstanding property, namely each state has its well defined purification - a state extremal in the set of states in larger Hilbert space. It is known that the classical theory and the theory of non-signaling boxes does not have purification for all of their states. These theories are examples of the so called generalized probabilistic theories (GPTs). However in any non-signaling GPT each state has a number of extensions to a larger system. We single out the most relevant among them, called a complete extension, unique up to local reversible operations on the extending system. We prove that this special, finite dimensional extension bares an analogy to quantum purification in that (i) it allows for an access to all ensembles of the extended system (ii) from complete extension one can generate any other extension. It then follows, that an access to the complete extension represents the total power of the most general non-signaling adversary. A complete extension of a maximally mixed box in two-party binary input binary output scenario is up to relabeling the famous Popescu-Rohrlich box. The latter thus emerges naturally without reference to the Bell's non-locality. However the complete extension is not a purification (a vertex) in the generic case. Moreover, we show that all convex discrete theories does not provide purification for almost all of it states. In particular the theory of contextuality does not possess purification. The complete extensions are by nature high-dimensional systems. We were able however to provide explicit structure of complete extension for the noisy Popescu-Rohrlich-boxes and the 3-cycle contextual box.Comment: 34 pages, 7 figure

Constructive counterexamples to additivity of minimum output R\'enyi entropy of quantum channels for all p>2

We present a constructive example of violation of additivity of minimum output R\'enyi entropy for each p>2. The example is provided by antisymmetric subspace of a suitable dimension. We discuss possibility of extension of the result to go beyond p>2 and obtain additivity for p=0 for a class of entanglement breaking channels.Comment: 4 pages; a reference adde

Long-distance quantum communication over noisy networks without long-time quantum memory

The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension $D$ and transmission of quantum information in a $D+1$-dimensional network. We show that it is possible to obtain long-distance entanglement in a noisy two-dimensional (2D) network, even when taking into account that encoding and decoding of a state is exposed to an error. For 3D networks we propose a simple encoding and decoding scheme based solely on syndrome measurements on 2D Kitaev topological quantum memory. Our procedure constitutes an alternative scheme of state injection that can be used for universal quantum computation on 2D Kitaev code. It is shown that the encoding scheme is equivalent to teleporting the state, from a specific node into a whole two-dimensional network, through some virtual EPR pair existing within the rest of network qubits. We present an analytic lower bound on fidelity of the encoding and decoding procedure, using as our main tool a modified metric on space-time lattice, deviating from a taxicab metric at the first and the last time slices.Comment: 15 pages, 10 figures; title modified; appendix included in main text; section IV extended; minor mistakes remove

Transcervical Extended Mediastinal Lymphadenectomy (TEMLA) for staging of non-small-cell lung cancer (NSCLC)

Wstęp: Celem pracy jest przeanalizowanie wyników nowej techniki operacyjnej &#8212; rozszerzonej limfadenektomii śródpiersia z dostępu szyjnego (TEMLA) w diagnostyce przedoperacyjnej niedrobnokomórkowego raka płuca (NDRP). Materiał i metody: Operacji dokonywano z cięcia szyjnego o długości 5-8 cm, z uniesieniem rękojeści mostka za pomocą specjalnego retraktora, z obustronnym uwidocznieniem nerwów krtaniowych wstecznych oraz błędnych i wypreparowaniem wszystkich stacji węzłowych śródpiersia, z wyjątkiem węzłów więzadła płucnego (stacja 9). Wyniki: W okresie od 1 stycznia 2004 roku do 31 stycznia 2010 roku zoperowano 698 chorych (577 mężczyzn i 121 kobiet) w średnim wieku 62,8 roku (41-79), w tym 501 raków płaskonabłonkowych, 144 raki gruczołowe, 25 raków wielokomórkowych i 28 pozostałych. Średni czas operacji wyniósł 128 minut (45-330 minut) w całej grupie, zaś w grupie ostatnich 100 pacjentów średni czas operacji wyniósł 106 minut. Śmiertelność 30-dniowa wyniosła 0,7% (z przyczyn niezwiązanych bezpośrednio z zabiegiem), zaś powikłania wystąpiły u 6,6% chorych. Średnia liczba usuniętych węzłów chłonnych wyniosła 37,9 (15-85). Przerzutowe węzły N2 i N3 stwierdzono u odpowiednio 21,8% (152/698) i 3,7% (26/698) chorych. Torakotomii poddano 445/513 (86,7%) chorych po ujemnym wyniku TEMLA. W czasie torakotomii przeoczone przerzutowe węzły chłonne N2 stwierdzono w 7/445 (1,6%) przypadkach. Czułość diagnostyczna TEMLA w wykrywaniu przerzutowych węzłów śródpiersia wyniosła 96,2%, swoistość 100%, dokładność 99,0%, negatywna wartość predykcyjna (NPV) 98,7%, a pozytywna wartość predykcyjna (PPV) 100%. Wnioski: Technika TEMLA jest nową, minimalnie inwazyjną metodą chirurgiczną, zapewniającą wyjątkową możliwość wykonania bardzo rozległej, obustronnej limfadenektomii śródpiersia i charakteryzującą się bardzo wysoką wartością diagnostyczną. Pneumonol. Alergol. Pol. 2011; 79, 3: 196-206Introduction: The aim of the study is to analyze diagnostic yield of the new surgical technique - the Transcervical Extended Mediastinal Lymphadenectomy (TEMLA) in preoperative staging of Non-Small-Cell Lung Cancer (NSCLC) Material and methods: Operative technique included 5-8 cm collar incision in the neck, elevation of the sternal manubrium with a special retractor, bilateral visualization of the laryngeal recurrent and vagus nerves and dissection of all mediastinal nodal stations except of the pulmonary ligament nodes (station 9). Results: 698 patients (577 men, 121 women), of mean age 62.8 (41-79) were operated on from 1.1.2004 to 31.1.2010, including 501 squamous-cell carcinomas, 144 adenocarcinomas, 25 large cell carcinomas and 28 others. Mean operative time was 128 min. (45 to 330 min) and 106.5 min. in the last 100 patients. 30-day mortality was 0.7 % (unrelated causes) and morbidity 6.6%. The mean number of dissected nodes during TEMLA was 37.9 (15 to 85). Metastatic N2 and N3 nodes were found in 152/698 (21.8%) and 26/698 patients (3.7%), respectively. Subsequent thoracotomy was performed in 445/513 patients (86.7%) after negative result of TEMLA. During thoracotomy, omitted N2 was found in 7/445 (1.6%) patients. Sensitivity of TEMLA in discovery of metastatic N2-3 nodes was 96.2 %, specificity was 100%, accuracy was 99,0%, Negative Predictive Value (NPV) was 98.7 % and Positive Predictive Value (PPV) was 100%. Conclusions: TEMLA is a new minimally invasive surgical procedure providing unique possibility to perform very extensive, bilateral mediastinal lymphadenectomy with very high diagnostic yield in staging of NSCLC Pneumonol. Alergol. Pol. 2011; 79, 3: 196-20

Low-dimensional quite noisy bound entanglement with cryptographic key

We provide a class of bound entangled states that have positive distillable secure key rate. The smallest state of this kind is 4 \bigotimes 4. Our class is a generalization of the class presented in [1] (IEEE Trans. Inf. Theory 54, 2621 (2008); arXiv:quant-ph/0506203). It is much wider, containing, in particular, states from the boundary of PPT entangled states (all of the states in the class in [1] were of this kind) but also states inside the set of PPT entangled states, even, approaching the separable states. This generalization comes with a price: for the wider class a positive key rate requires, in general, apart from the one-way Devetak-Winter protocol (used in [1]) also the recurrence preprocessing and thus effectively is a two-way protocol. We also analyze the amount of noise that can be admixtured to the states of our class without losing key distillability property which may be crucial for experimental realization. The wider class contains key-distillable states with higher entropy (up to 3.524, as opposed to 2.564 for the class in [1]).Comment: 10 pages, final version for J. Phys. A: Math. Theo

Transcervical Extended Mediastinal Lymphadenectomy (TEMLA) for Staging of Non-Small-Cell Lung Cancer (NSCLC)

Introduction: The aim of the study is to analyze diagnostic yield of the new surgical technique — the Transcervical Extended Mediastinal Lymphadenectomy (TEMLA) in preoperative staging of Non-Small-Cell Lung Cancer (NSCLC). Material and methods: Operative technique included 5–8 cm collar incision in the neck, elevation of the sternal manubrium with a special retractor, bilateral visualization of the laryngeal recurrent and vagus nerves and dissection of all mediastinal nodal stations except of the pulmonary ligament nodes (station 9). Results: 698 patients (577 men, 121 women), of mean age 62.8 (41–79) were operated on from 1.1.2004 to 31.1.2010, including 501 squamous-cell carcinomas, 144 adenocarcinomas, 25 large cell carcinomas and 28 others. Mean operative time was 128 min. (45 to 330 min.) and 106.5 min. in the last 100 patients. 30-day mortality was 0.7% (unrelated causes) and morbidity 6.6%. The mean number of dissected nodes during TEMLA was 37.9 (15 to 85). Metastatic N2 and N3 nodes were found in 152/698 (21.8%) and 26/698 patients (3.7%), respectively. Subsequent thoracotomy was performed in 445/ 513 patients (86.7%) after negative result of TEMLA. During thoracotomy, omitted N2 was found in 7/445 (1.6%) patients. Sensitivity of TEMLA in discovery of N2–3 nodes was 96.2%, specificity was 100%, accuracy was 99,0%, Negative Predictive Value (NPV) was 98.7% and Positive Predictive Value (PPV) was 100%. Conclusions: TEMLA is a new minimally invasive surgical procedure providing unique possibility to perform very extensive, bilateral mediastinal lymphadenectomy with very high diagnostic yield in staging of NSCLC