We present observable lower bounds for several bipartite entanglement measures including entanglement of formation, geometric measure of entanglement, concurrence, convex-roof extended negativity, and G-concurrence. The lower bounds facilitate estima
tes of these entanglement measures for arbitrary finite-dimensional bipartite states. Moreover, these lower bounds can be calculated analytically from the expectation value of a single observable. Based on our results, we use several real experimental measurement data to get lower bounds of entanglement measures for these experimentally realized states. In addition, we also study the relations between entanglement measures.
By incorporating the asymmetry of local protocols, i.e., some party has to start with a nontrivial measurement, into an operational method of detecting the local indistinguishability proposed by Horodecki {it et al.} [Phys.Rev.Lett. 90 047902 (2003)]
, we derive a computable criterion to efficiently detect the local indistinguishability of maximally entangled states. Locally indistinguishable sets of $d$ maximally entangled states in a $dotimes d$ system are systematically constructed for all $dge 4$ as an application. Furthermore, by exploiting the fact that local protocols are necessarily separable, we explicitly construct small sets of $k$ locally indistinguishable maximally entangled states with the ratio $k/d$ approaching 3/4. In particular, in a $dotimes d$ system with even $dge 6$, there always exist $d-1$ maximally entangled states that are locally indistinguishable by separable measurements.
We establish a quantitative relation between Hardys paradox and the breaking of uncertainty principle in the sense of measurement-disturbance relations in the conditional measurement of non-commuting operators. The analysis of the inconsistency of lo
cal realism with entanglement by Hardy is simplified if this breaking of measurement-disturbance relations is taken into account, and a much simplified experimental test of local realism is illustrated in the framework of Hardys thought experiment. The essence of Hardys model is identified as a combination of two conditional measurements, which give rise to definite eigenvalues to two non-commuting operators simultaneously in hidden-variables models. Better understanding of the intimate interplay of entanglement and measurement-disturbance is crucial in the current discussions of Hardys paradox using the idea of weak measurement, which is based on a general analysis of measurement-disturbance relations.
A kind of paradoxical effects has been demonstrated that the pigeonhole principle, i.e., if three pigeons are put in two pigeonholes then at least two pigeons must stay in the same hole, fails in certain quantum mechanical scenario. Here we shall sho
w how to associate a proof of Kochen-Specker theorem with a quantum pigeonhole effect and vise versa, e.g., from state-independent proofs of Kochen-Specker theorem some kind of state-independent quantum pigeonhole effects can be demonstrated. In particular, a state-independent version of the quantum Cheshire cat, which can be rendered as a kind of quantum pigeonhole effect about the trouble of putting two pigeons in two or more pigeonholes, arises from Peres-Mermins magic square proof of contextuality.
Fragile quantum features such as entanglement are employed to improve the precision of parameter estimation and as a consequence the quantum gain becomes vulnerable to noise. As an established tool to subdue noise, quantum error correction is unfortu
nately overprotective because the quantum enhancement can still be achieved even if the states are irrecoverably affected, provided that the quantum Fisher information, which sets the ultimate limit to the precision of metrological schemes, is preserved and attained. Here, we develop a theory of robust metrological schemes that preserve the quantum Fisher information instead of the quantum states themselves against noise. After deriving a minimal set of testable conditions on this kind of robustness, we construct a family of $2t+1$ qubits metrological schemes being immune to $t$-qubit errors after the signal sensing. In comparison at least five qubits are required for correcting arbitrary 1-qubit errors in standard quantum error correction.
Heisenbergs uncertainty relations for measurement quantify how well we can jointly measure two complementary observables and have attracted much experimental and theoretical attention recently. Here we provide an exact tradeoff between the worst-case
errors in measuring jointly two observables of a qubit, i.e., all the allowed and forbidden pairs of errors, especially asymmetric ones, are exactly pinpointed. For each pair of optimal errors we provide an optimal joint measurement that is realizable without introducing any ancilla and entanglement. Possible experimental implementations are discussed and Toronto experiment [Rozema et al., Phys. Rev. Lett. 109, 100404 (2012)] can be readily adapted to an optimal joint measurement of two orthogonal observables.
Heisenbergs uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report improved n
The Mach-Zehnder interferometric setup quantitatively characterizing the wave-particle duality implements in fact a joint measurement of two unsharp observables. We present a necessary and sufficient condition for such a pair of unsharp observables t
o be jointly measurable. The condition is shown to be equivalent to a duality inequality, which for the optimal strategy of extracting the which-path information is more stringent than the Jaeger-Shimony-Vaidman-Englert inequality.
We investigate the Bell inequalities derived from the graph states with violations detectable even with the presence of noises, which generalizes the idea of error-correcting Bell inequalities [Phys. Rev. Lett. 101, 080501 (2008)]. Firstly we constru
ct a family of valid Bell inequalities tolerating arbitrary $t$-qubit errors involving $3(t+1)$ qubits, e.g., 6 qubits suffice to tolerate single qubit errors. Secondly we construct also a single-error-tolerating Bell inequality with a violation that increases exponentially with the number of qubits. Exhaustive computer search for optimal error-tolerating Bell inequalities based on graph states on no more than 10 qubits shows that our constructions are optimal for single- and double-error tolerance.
We discuss quantitatively the complementarity of information transmitted by a quantum system prepared in a basis state in one out of several different mutually unbiased bases (MUBs). We obtain upper bounds on the information available to a receiver w
ho has no knowledge of which MUB was chosen by the sender. These upper bounds imply a complementarity of information encoded via different MUBs and ultimately ensure the security in quantum key distribution protocols.
