Showing all papers from arXiv author **cosentino_a_1**

- Somshubhro Bandyopadhyay, Alessandro Cosentino, Nathaniel Johnston, Vincent Russo, John Watrous, Nengkun YuSep 01 2014 quant-ph arXiv:1408.6981v1We prove limitations on LOCC and separable measurements in bipartite state discrimination problems using techniques from convex optimization. Specific results that we prove include: an exact formula for the optimal probability of correctly discriminating any set of either three or four Bell states via LOCC or separable measurements when the parties are given an ancillary partially entangled pair of qubits; an easily checkable characterization of when an unextendable product set is perfectly discriminated by separable measurements, along with the first known example of an unextendable product set that cannot be perfectly discriminated by separable measurements; and an optimal bound on the success probability for any LOCC or separable measurement for the recently proposed state discrimination problem of Yu, Duan, and Ying.
- Jul 12 2013 quant-ph arXiv:1307.3232v2We study the problem of distinguishing quantum states using local operations and classical communication (LOCC). A question of fundamental interest is whether there exist sets of $k \leq d$ orthogonal maximally entangled states in $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$ that are not perfectly distinguishable by LOCC. A recent result by Yu, Duan, and Ying [Phys. Rev. Lett. 109 020506 (2012) -- arXiv:1107.3224 [quant-ph]] gives an affirmative answer for the case $k = d$. We give, for the first time, a proof that such sets of states indeed exist even in the case $k < d$. Our result is constructive and holds for an even wider class of operations known as positive-partial-transpose measurements (PPT). The proof uses the characterization of the PPT-distinguishability problem as a semidefinite program.
- Quantum formulas, defined by Yao [FOCS '93], are the quantum analogs of classical formulas, i.e., classical circuits in which all gates have fanout one. We show that any read-once quantum formula over a gate set that contains all single-qubit gates is equivalent to a read-once classical formula of the same size and depth over an analogous classical gate set. For example, any read-once quantum formula over Toffoli and single-qubit gates is equivalent to a read-once classical formula over Toffoli and NOT gates. We then show that the equivalence does not hold if the read-once restriction is removed. To show the power of quantum formulas without the read-once restriction, we define a new model of computation called the one-qubit model and show that it can compute all boolean functions. This model may also be of independent interest.
- May 07 2012 quant-ph arXiv:1205.1031v2We show a simple semidefinite program whose optimal value is equal to the maximum probability of perfectly distinguishing orthogonal maximally entangled states using any PPT measurement (a measurement whose operators are positive under partial transpose). When the states to be distinguished are given by the tensor product of Bell states, the semidefinite program simplifies to a linear program. In [Phys. Rev. Lett. 109, 020506 (2012) -- arXiv:1107.3224v1], Yu, Duan and Ying exhibit a set of 4 maximally entangled states in $C^4 \otimes C^4$, which is distinguishable by any PPT measurement only with probability strictly less than 1. Using semidefinite programming, we show a tight bound of 7/8 on this probability (3/4 for the case of unambiguous PPT measurements). We generalize this result by demonstrating a simple construction of a set of k states in $C^k \otimes C^k$ with the same property, for any k that is a power of 2. Finally, by running numerical experiments, we obtain some non-trivial results about the PPT-distinguishability of certain interesting sets of generalized Bell states in $C^5 \otimes C^5$ and $C^6 \otimes C^6$.
- Jun 16 2009 quant-ph arXiv:0906.2488v3We prove a connection between Schmidt-rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results concerning the weight of quadratic forms in terms of graph states properties. As a byproduct, we obtain a straightforward characterization of the weight of functions associated with pivot-minor of bipartite graphs.