Tomography is Necessary for Universal Entanglement Detection with Single-Copy Observables

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.

Deep learning of quantum entanglement from incomplete measurements

The quantification of the entanglement present in a physical system is of paramount importance for fundamental research and many cutting-edge applications. Now, achieving this goal requires either a priori knowledge on the system or very demanding experimental procedures such as full state tomography or collective measurements. Here, we demonstrate that, by using neural networks, we can quantify the degree of entanglement without the need to know the full description of the quantum state. Our method allows for direct quantification of the quantum correlations using an incomplete set of local measurements. Despite using undersampled measurements, we achieve a quantification error of up to an order of magnitude lower than the state-of-the-art quantum tomography. Furthermore, we achieve this result using networks trained using exclusively simulated data. Last, we derive a method based on a convolutional network input that can accept data from various measurement scenarios and perform, to some extent, independently of the measurement device.

Fundamental Limitation on the Detectability of Entanglement

Entanglement detection is essential in quantum information science and quantum many-body physics. It has been proved that entanglement exists almost surely for a random quantum state, while the realizations of effective entanglement criteria usually consume exponentially many resources with regard to system size or qubit number, and efficient criteria often perform poorly without prior knowledge. This fact implies a fundamental limitation might exist in the detectability of entanglement. In this work, we formalize this limitation as a fundamental trade-off between the efficiency and effectiveness of entanglement criteria via a systematic method to evaluate the detection capability of entanglement criteria theoretically. For a system coupled to an environment, we prove that any entanglement criterion needs exponentially many observables to detect the entanglement effectively when restricted to single-copy operations. Otherwise, the detection capability of the criterion will decay double exponentially. Furthermore, if multicopy joint measurements are allowed, the effectiveness of entanglement detection can be exponentially improved, which implies a quantum advantage in entanglement detection problems. Our results may shed light on why quantum phenomena are difficult to observe in large noisy systems.

Experimental Realization of a Quantum Refrigerator Driven by Indefinite Causal Orders

Indefinite causal order (ICO) is playing a key role in recent quantum technologies. Here, we experimentally study quantum thermodynamics driven by ICO on nuclear spins using the nuclear magnetic resonance system. We realize the ICO of two thermalizing channels to exhibit how the mechanism works, and show that the working substance can be cooled or heated albeit it undergoes thermal contacts with reservoirs of the same temperature. Moreover, we construct a single cycle of the ICO refrigerator based on the Maxwell's demon mechanism, and evaluate its performance by measuring the work consumption and the heat energy extracted from the low-temperature reservoir. Unlike classical refrigerators in which the coefficient of performance (COP) is perversely higher the closer the temperature of the high-temperature and low-temperature reservoirs are to each other, the ICO refrigerator's COP is always bounded to small values due to the nonunit success probability in projecting the ancillary qubit to the preferable subspace. To enhance the COP, we propose and experimentally demonstrate a general framework based on the density matrix exponentiation (DME) approach, as an extension to the ICO refrigeration. The COP is observed to be enhanced by more than 3 times with the DME approach. Our Letter demonstrates a new way for nonclassical heat exchange, and paves the way towards construction of quantum refrigerators on a quantum system.

Blindly verifying partially unknown entanglement

Quantum entanglement has shown distinguished features beyond any classical state. Many methods have been presented to verify unknown entanglement with the complete information about the density matrices by quantum state tomography. In this work, we aim to identify unknown entanglement with only partial information of the state space. The witness consists of a generalized Greenberger-Horne-Zeilinger-like paradox expressed by Pauli observables, and a nonlinear entanglement witness expressed by density matrix elements. First, we verify unknown bipartite entanglement and study the robustness of entanglement witnesses against the white noise. Second, we generalize such verification to partially unknown multipartite entangled states, including the Greenberger-Horne-Zeilinger-type and W-type states. Third, we give a quantum-information application related to the quantum zero-knowledge proof. It further provides a useful method in blindly verifying universal quantum computation resources. These results may be interesting in entanglement theories, quantum communication, and quantum networks.

•

A model of entanglement set verification is proposed and analyzed

•

Nonlinear entanglement witnesses for specific entanglement sets are constructed

•

Blind quantum verification scheme is built

Probing quantum state space: does one have to learn everything to learn something?

Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement set-up that reveals this property with as little effort as possible. Here, we investigate whether, in order to successfully complete a given task of this kind, one needs an informationally complete measurement, or if something less demanding would suffice. The first alternative means that in order to complete the task, one needs a measurement which fully determines the state. We formulate the task as a membership problem related to a partitioning of the quantum state space and, in doing so, connect it to the geometry of the state space. For a general membership problem, we prove various sufficient criteria that force informational completeness, and we explicitly treat several physically relevant examples. For the specific cases that do not require informational completeness, we also determine bounds on the minimal number of measurement outcomes needed to ensure success in the task.

Quantum State Tomography via Reduced Density Matrices

Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However, it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work, we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally, we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results demonstrate the advantages and possible pitfalls of quantum state tomography with local measurements.