Superiority of entangled measurements over all local strategies for the estimation of product coherent states

Operational effects of the UNOT gate on classical and quantum correlations

The NOT gate that flips a classical bit is ubiquitous in classical information processing. However its quantum analogue, the universal NOT (UNOT) gate that flips a quantum spin in any alignment into its antipodal counterpart is strictly forbidden. Here we explore the connection between this discrepancy and how UNOT gates affect classical and quantum correlations. We show that while a UNOT gate always preserves classical correlations between two spins, it can non-locally increase or decrease their shared discord in ways that allow violation of the data processing inequality. We experimentally illustrate this using a multi-level trapped ¹⁷¹Yb⁺ ion that allows simulation of anti-unitary operations.

Determining Complementary Properties with Quantum Clones

In a classical world, simultaneous measurements of complementary properties (e.g., position and momentum) give a system's state. In quantum mechanics, measurement-induced disturbance is largest for complementary properties and, hence, limits the precision with which such properties can be determined simultaneously. It is tempting to try to sidestep this disturbance by copying the system and measuring each complementary property on a separate copy. However, perfect copying is physically impossible in quantum mechanics. Here, we investigate using the closest quantum analog to this copying strategy, optimal cloning. The coherent portion of the generated clones' state corresponds to "twins" of the input system. Like perfect copies, both twins faithfully reproduce the properties of the input system. Unlike perfect copies, the twins are entangled. As such, a measurement on both twins is equivalent to a simultaneous measurement on the input system. For complementary observables, this joint measurement gives the system's state, just as in the classical case. We demonstrate this experimentally using polarized single photons.

Inductive Supervised Quantum Learning

In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the classical setting, from a simple independence requirement with a physical interpretation of being nonsignaling. Thus, two seemingly different definitions of inductive learning happen to coincide. This follows from the properties of classical information that break down in the quantum setup. We prove a quantum de Finetti theorem for quantum channels, which shows that in the quantum case, the equivalence holds in the asymptotic setting, that is, for large numbers of test instances. This reveals a natural analogy between classical learning protocols and their quantum counterparts, justifying a similar treatment, and allowing us to inquire about standard elements in computational learning theory, such as structural risk minimization and sample complexity.

Directly Measuring the Degree of Quantum Coherence using Interference Fringes

Quantum coherence is the most distinguished feature of quantum mechanics. It lies at the heart of the quantum-information technologies as the fundamental resource and is also related to other quantum resources, including entanglement. It plays a critical role in various fields, even in biology. Nevertheless, the rigorous and systematic resource-theoretic framework of coherence has just been developed recently, and several coherence measures are proposed. Experimentally, the usual method to measure coherence is to perform state tomography and use mathematical expressions. Here, we alternatively develop a method to measure coherence directly using its most essential behavior-the interference fringes. The ancilla states are mixed into the target state with various ratios, and the minimal ratio that makes the interference fringes of the "mixed state" vanish is taken as the quantity of coherence. We also use the witness observable to witness coherence, and the optimal witness constitutes another direct method to measure coherence. For comparison, we perform tomography and calculate l_{1} norm of coherence, which coincides with the results of the other two methods in our situation. Our methods are explicit and robust, providing a nice alternative to the tomographic technique.

Fidelity criterion for quantum-domain transmission and storage of coherent states beyond the unit-gain constraint

We generalize the experimental success criterion for quantum teleportation (memory) in continuous-variable quantum systems to be suitable for a non-unit-gain condition by considering attenuation (amplification) of the coherent-state amplitude. The new criterion can be used for a nonideal quantum memory and long distance quantum communication as well as quantum devices with amplification process. It is also shown that the framework to measure the average fidelity is capable of detecting all Gaussian channels in the quantum domain.