Masaki Owari

Bounds on Multipartite Entangled Orthogonal State Discrimination Using Local Operations and Classical Communication

We show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally. The number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement. A similar, general condition is also shown for pure and mixed states. These results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement.

Quantum memory for entangled continuous-variable states

A quantum memory for light is a key element for the realization of future quantum information networks. Requirements for a good quantum memory are (i) versatility (allowing a wide range of inputs) and (ii) true quantum coherence (preserving quantum information). Here we demonstrate such a quantum memory for states possessing Einstein-Podolsky-Rosen (EPR) entanglement. These multi-photon states are two-mode squeezed by 6.0 dB with a variable orientation of squeezing and displaced by a few vacuum units. This range encompasses typical input alphabets for a continuous variable quantum information protocol. The memory consists of two cells, one for each mode, filled with cesium atoms at room temperature with a memory time of about 1msec. The preservation of quantum coherence is rigorously proven by showing that the experimental memory fidelity 0.52(2) significantly exceeds the benchmark of 0.45 for the best possible classical memory for a range of displacements.

Local copying and local discrimination as a study for nonlocality of a set of states

We focus on the nonlocality concerning local copying and local discrimination, especially for a set of orthogonal maximally entangled states in any prime dimensional system, as a study of nonlocality of a set of states. As a result, for such a set, we completely characterize deterministic local copiability and show that local copying is more difficult than local discrimination.

Entanglement of multiparty stabilizer, symmetric, and antisymmetric states

The storage and entanglement assisted teleportation of quantum states are two of the central primitives of Quantum Information Science. The need to certify success in their experiments, and to justity the use of the term quantum in setups such as ‘quantum memories’ and ‘quantum teleportations’, requires theoretical benchmarks which bound the performance of purely classical schemes [1–5].

Power of symmetric extensions for entanglement detection

In this paper, we present new progress on the study of the symmetric extension criterion for separability. First, we show that a perturbation of order O(1/N) is sufficient and, in general, necessary to destroy the entanglement of any state admitting an N Bose symmetric extension. On the other hand, the minimum amount of local noise necessary to induce separability on states arising from N Bose symmetric extensions with Positive Partial Transpose (PPT) decreases at least as fast as O(1/N^2). From these results, we derive upper bounds on the time and space complexity of the weak membership problem of separability when attacked via algorithms that search for PPT symmetric extensions. Finally, we show how to estimate the error we incur when we approximate the set of separable states by the set of (PPT) N -extendable quantum states in order to compute the maximum average fidelity in pure state estimation problems, the maximal output purity of quantum channels, and the geometric measure of entanglement.

Squeezing the limit: quantum benchmarks for the teleportation and storage of squeezed states

We derive fidelity benchmarks for the quantum storage and teleportation of squeezed states of continuous variable systems, for input ensembles where the degree of squeezing s is fixed, no information about its orientation in phase space is given, and the distribution of phase-space displacements is a Gaussian. In the limit where the latter becomes flat, we prove analytically that the maximal classical achievable fidelity (which is 1/2 without squeezing, for s=1) is given by , vanishing when the degree of squeezing diverges. For mixed states, as well as for general distributions of displacements, we reduce the determination of the benchmarks to the solution of a finite-dimensional semidefinite program, which yields accurate, certifiable bounds thanks to a rigorous analysis of the truncation error. This approach may be easily adapted to more general ensembles of input states.

Two-way classical communication remarkably improves local distinguishability

We analyze the difference in the local distinguishability among the following three restrictions: (i) local operations and only one-way classical communications (one-way LOCC) are permitted; (ii) local operations and two-way classical communications (two-way LOCC) are permitted; and (iii) all separable operations are permitted. We obtain two main results concerning the discrimination between a given bipartite pure state and the completely mixed state with the condition that the given state should be detected perfectly. As the first result, we derive the optimal discrimination protocol for a bipartite pure state in cases (i) and (iii). As the second result, by constructing a concrete two-way local discrimination protocol, it is proven that case (ii) is much better than case (i), i.e. two-way classical communication remarkably improves the local distinguishability in comparison with one-way classical communication at least for a low-dimensional bipartite pure state.

Complete Criterion for Separability Detection

Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of efficiently solvable semidefinite programs. We apply this method to derive arbitrarily good approximations to the optimal measure-and-prepare strategy in generic state estimation problems. Finally, we report its performance in combination with the criterion developed by Doherty, Parrilo, and Spedarlieri for the calculation of the entanglement robustness of a relevant family of quantum states whose separability properties were unknown.

From Bell Inequalities to Tsirelson's Theorem

The first part of this paper contains an introduction to Bell inequalities and Tsirelson’s theorem for the non-specialist. The next part gives an explicit optimum construction for the “hard” part of Tsirelson’s theorem. In the final part we describe how upper bounds on the maximal quantum violation of Bell inequalities can be obtained by an extension of Tsirelson’s theorem, and survey very recent results on how exact bounds may be obtained by solving an infinite series of semidefinite programs.

Secrecy and robustness for active attack in secure network coding

In the network coding, we discuss the effect by sequential error injection to information leakage. We show that there is no improvement when the network is composed of linear operations. However, when the network contains non-linear operations, we find a counterexample to improve Eves obtained information. Further, we discuss the asymptotic rate in the linear network under the secrecy and robustness conditions.