Quantum states with a positive partial transpose are useful for metrology

We show that multipartite quantum states that have a positive partial transpose with respect to all bipartitions of the particles can outperform separable states in linear interferometers. We introduce a powerful iterative method to find such states. We present some examples for multipartite states and examine the scaling of the precision with the particle number. Some bipartite examples are also shown that possess an entanglement very robust to noise. We also discuss the relation of metrological usefulness to Bell inequality violation. We find that quantum states that do not violate any Bell inequality can outperform separable states metrologically. We present such states with a positive partial transpose, as well as with a non-positive positive partial transpose.Comment: 6 pages including two figures + three-page supplement including two figures using revtex 4.1, with numerically obtained density matrices as text files; v2: published version; v3: published version, typo in the 4x4 bound entangled state is corrected (noticed by Peng Yin

A class of genuinely high-dimensionally entangled states with a positive partial transpose

Entangled states with a positive partial transpose (so-called PPT states) are central to many interesting problems in quantum theory. On one hand, they are considered to be weakly entangled, since no pure state entanglement can be distilled from them. On the other hand, it has been shown recently that some of these PPT states exhibit genuinely high-dimensional entanglement, i.e. they have a high Schmidt number. Here we investigate $d\times d$ dimensional PPT states for $d\ge 4$ discussed recently by Sindici and Piani, and by generalizing their methods to the calculation of Schmidt numbers we show that a linear $d/2$ scaling of its Schmidt number in the local dimension $d$ can be attained.Comment: 8 page

Dimension witnesses and quantum state discrimination

Dimension witnesses allow one to test the dimension of an unknown physical system in a device-independent manner, that is, without placing assumptions about the functioning of the devices used in the experiment. Here we present simple and general dimension witnesses for quantum systems of arbitrary Hilbert space dimension. Our approach is deeply connected to the problem of quantum state discrimination, hence establishing a strong link between these two research topics. Finally, our dimension witnesses can distinguish between classical and quantum systems of the same dimension, making them potentially useful for quantum information processing.Comment: 5 page

Qutrit witness from the Grothendieck constant of order four

In this paper, we prove that $K_G(3)<K_G(4)$, where $K_G(d)$ denotes the Grothendieck constant of order $d$. To this end, we use a branch-and-bound algorithm commonly used in the solution of NP-hard problems. It has recently been proven that $K_G(3)\le 1.4644$. Here we prove that $K_G(4)\ge 1.4841$, which has implications for device-independent witnessing dimensions greater than two. Furthermore, the algorithm with some modifications may find applications in various black-box quantum information tasks with large number of inputs and outputs.Comment: 13 pages, 2 figure

Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality

We investigate the relation between the incompatibility of quantum measurements and quantum nonlocality. We show that any set of measurements that is not jointly measurable (i.e. incompatible) can be used for demonstrating EPR steering, a form of quantum nonlocality. This implies that EPR steering and (non) joint measurability can be viewed as equivalent. Moreover, we discuss the connection between Bell nonlocality and joint measurability, and give evidence that both notions are inequivalent. Specifically, we exhibit a set of incompatible quantum measurements and show that it does not violate a large class of Bell inequalities. This suggest the existence of incompatible quantum measurements which are Bell local, similarly to certain entangled states which admit a local hidden variable model.Comment: 6 pages, 1 figure, 2 tables, title slightly changed, one reference adde

Activation of Non-Local Quantum Resources

We find two two-qubit states such that any number of copies of one state or the other cannot violate the CHSH Bell inequality. However, their tensor product can produce a CHSH violation of at least 2.023. We also identify a CHSH-local state such that two copies of it are CHSH-violating. The tools employed here can be easily adapted to find instances of non-locality activation in arbitrary Bell scenarios

Optimal randomness certification from one entangled bit

By performing local projective measurements on a two-qubit entangled state one can certify in a device-independent way up to one bit of randomness. We show here that general measurements, defined by positive-operator-valued measures, can certify up to two bits of randomness, which is the optimal amount of randomness that can be certified from an entangled bit. General measurements thus provide an advantage over projective ones for device-independent randomness certification.Comment: 7 pages, 1 figure, computational details at http://nbviewer.ipython.org/github/peterwittek/ipython-notebooks/blob/master/Optimal%20randomness%20generation%20from%20entangled%20quantum%20states.ipyn

Bounding the persistency of the nonlocality of W states

The nonlocal properties of the W states are investigated under particle loss. By removing all but two particles from an $N$-qubit W state, the resulting two-qubit state is still entangled. Hence, the W state has high persistency of entanglement. We ask an analogous question regarding the persistency of nonlocality introduced in [Phys. Rev. A 86, 042113]. Namely, we inquire what is the minimal number of particles that must be removed from the W state so that the resulting state becomes local. We bound this value in function of $N$ qubits by considering Bell nonlocality tests with two alternative settings per site. In particular, we find that this value is between $2N/5$ and $N/2$ for large $N$. We also develop a framework to establish bounds for more than two settings per site.Comment: 10 pages, 4 figure

EPR Steering inequalities with Communication Assistance

In this paper, we investigate the communication cost of reproducing Einstein-Podolsky-Rosen (EPR) steering correlations arising from bipartite quantum systems. We characterize the set of bipartite quantum states which admits a local hidden state model augmented with $c$ bits of classical communication from an untrusted party (Alice) to a trusted party (Bob). In case of one bit of information ($c=1$), we show that this set has a nontrivial intersection with the sets admitting a local hidden state and a local hidden variables model for projective measurements. On the other hand, we find that an infinite amount of classical communication is required from an untrusted Alice to a trusted Bob to simulate the EPR steering correlations produced by a two-qubit maximally entangled state. It is conjectured that a state-of-the-art quantum experiment would be able to falsify two bits of communication this way.Comment: 14 pages, 3 figures. See also arXiv:1603.05079 for related work by A.B. Sainz et a

Testing the Structure of Multipartite Entanglement with Bell Inequalities

We show that the rich structure of multipartite entanglement can be tested following a device-independent approach. Specifically we present Bell inequalities for distinguishing between different types of multipartite entanglement, without placing any assumptions on the measurement devices used in the protocol, in contrast with usual entanglement witnesses. We first address the case of three qubits and present Bell inequalities that can be violated by W states but not by GHZ states, and vice versa. Next, we devise 'sub-correlation Bell inequalities' for any number of parties, which can provably not be violated by a broad class of multipartite entangled states (generalizations of GHZ states), but for which violations can be obtained for W states. Our results give insight into the nonlocality of W states. The simplicity and robustness of our tests make them appealing for experiments.Comment: 7 page