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- Péter Lévay, Metod Saniga, Péter Vrana
- 2008

Abstract The set of 63 real generalized Pauli matrices of three-qubits can be factored into two subsets of 35 symmetric and 28 antisymmetric elements. This splitting is shown to be completely embodied in the properties of the Fano plane; the elements of the former set being in a bijective correspondence with the 7 points, 7 lines and 21 flags, whereas those… (More)

- Péter Lévay, Metod Saniga, Péter Vrana, Petr Pracna
- 2009

It is shown that the E6(6) symmetric entropy formula describing black holes and black strings in D = 5 is intimately tied to the geometry of the generalized quadrangle GQ(2, 4) with automorphism group the Weyl group W (E6). The 27 charges correspond to the points and the 45 terms in the entropy formula to the lines of GQ(2, 4). Different truncations with… (More)

- Péter Vrana, Péter Lévay
- 2009

We introduce a point-line incidence geometry in which the commutation relations of the real Pauli group of multiple qubits are fully encoded. Its points are pairs of Pauli operators differing in sign and each line contains three pairwise commuting operators any of which is the product of the other two (up to sign). We study the properties of its Veldkamp… (More)

- Péter Vrana, Matthias Christandl
- ArXiv
- 2016

We study the problem of converting a product of Greenberger-HorneZeilinger (GHZ) states shared by subsets of several parties in an arbitrary way into GHZ states shared by every party. Our result is that if SLOCC transformations are allowed, then the best asymptotic rate is the minimum of bipartite log-ranks of the initial state. This generalizes a result by… (More)

- Matthias Christandl, Péter Vrana, Jeroen Zuiddam
- ArXiv
- 2016

We present an upper bound on the exponent of the asymptotic behaviour of the tensor rank of a family of tensors defined by the complete graph on k vertices. For k ≥ 4, we show that the exponent per edge is at most 0.77, outperforming the best known upper bound on the exponent per edge for matrix multiplication (k = 3), which is approximately 0.79. We raise… (More)

- Milan Saniga, Richard Green, P. Lévay, Petr Pracna, Péter Vrana
- 2009

It is shown that the Veldkamp space of the unique generalized quadrangle GQ(2,4) is isomorphic to PG(5,2). Since the GQ(2,4) features only two kinds of geometric hyperplanes, namely point’s perp-sets and GQ(2,2)s, the 63 points of PG(5,2) split into two families; 27 being represented by perp-sets and 36 by GQ(2,2)s. The 651 lines of PG(5,2) are found to… (More)

- Péter Vrana, Péter Lévay
- 2009

We consider special quantum systems containing both distinguishable and identical constituents. It is shown that for these systems the Freudenthal construction based on cubic Jordan algebras naturally defines entanglement measures invariant under the group of stochastic local operations and classical communication (SLOCC). For this type of multipartite… (More)

- Matthias Christandl, Péter Vrana, Jeroen Zuiddam
- ArXiv
- 2017

The asymptotic restriction problem for tensors is to decide, given tensors s and t, whether the nth tensor power of s can be obtained from the (n+o(n))th tensor power of t by applying linear maps to the tensor legs (this we call restriction), when n goes to infinity. In this context, Volker Strassen, striving to understand the complexity of matrix… (More)

- Péter Vrana, Péter Lévay
- 2009

We introduce a point-line incidence geometry in which the commutation relations of the real Pauli group of multiple qubits are fully encoded. Its points are pairs of Pauli operators differing in sign and each line contains three pairwise commuting operators any of which is the product of the other two (up to sign). We study the properties of its Veldkamp… (More)

- Metod Saniga, Péter Lévay, Petr Pracna, Péter Vrana
- 2009

It is shown that the Veldkamp space of the unique generalized quadrangle GQ(2,4) is isomorphic to PG(5,2). Since the GQ(2,4) features only two kinds of geometric hyperplanes, namely point’s perp-sets and GQ(2,2)s, the 63 points of PG(5,2) split into two families; 27 being represented by perp-sets and 36 by GQ(2,2)s. The 651 lines of PG(5,2) are found to… (More)