Study reveals existing limitations in detecting entanglement

Study reveals existing limitations in detecting entanglement

Study reveals existing limitations in detecting entanglement

An intuitive illustration of our theorem. Suppose the state we are considering has dimension d and is coupled to an environment of dimension k. We use three balls to represent the states, while the outer ball contains all the states. The maximally mixed state (blue star) is in the middle of the figure. All states with a maximum mixed-state distance less than r are separable, which is represented by the inner ball. For the mixed state, it can be shown that the distribution is concentrated in the typical set. Outside the typical set is the sparse area, where we can ignore the existence of states. The states above the satisfactory hyperplane are detectable by the entanglement indicator, which forms a large spherical cap. The ability to detect an entanglement indicator is limited by the volume ratio of the detectable set, which is exponentially small. Credit: Liu et al.

Quantum entanglement is a process by which two particles become entangled and remain connected over time, even when separated by great distances. The detection of this phenomenon is of crucial importance both for the development of quantum technology and for the study of many-body quantum physics.

Researchers from Tsinghua recently conducted a study exploring possible reasons why reliable and efficient detection of entanglement in complex and “noisy” systems has often proven to be very difficult. Their findings, published in Physical examination letterssuggest the existence of a trade-off between the effectiveness and efficiency of entanglement detection methods.

“More than 20 years ago, researchers discovered that most quantum states are entangled,” Xiongfeng Ma, one of the researchers who led the study, told

“This means that, for example, if we manage to build a system of 100 qubits, say a superconducting or ion-trap quantum computing system, this system will evolve over a period of time, during which the qubits interact intensively with each other. with others. Of course, there will be errors, so to maintain consistent good control, we reasonably isolate the system from the environment. As long as the purity (quantifying the effectiveness of our isolation effort) is not exponentially small with the number of qubits, the system is very susceptible to entanglement.”

While entanglement may theoretically seem quite simple to achieve, achieving it in experimental settings is actually very difficult. Studies have shown that this is particularly difficult in large quantum systems, such as systems composed of 18 qubits. The key goal of recent work by Ma and his colleagues was to better understand the challenges associated with detecting entanglement in large systems.

“Researchers gradually realized that while preparing the entangled state for a large system could be easy, detecting entanglement could be very difficult in practice,” Ma explained. “In our work, we establish a mathematical formulation to quantify the efficiency of an entanglement detection method. We employ an appropriate quantum state distribution, use the detectable entangled state ratio to quantify its efficiency, and also quantify the efficiency of a method of entanglement detection. by the number of observables needed for this method.”

Ma and his colleagues first looked at what is arguably the simplest entanglement detection protocol available today, known as entanglement witnesses. They showed that the ability of this protocol to detect entanglement decreases by a double exponential value as the system gets larger.

The researchers then found that this reduction in efficiency related to the size of a system also affected other entanglement detection protocols. After a series of theoretical considerations, they were able to extend their observations of the performance of the entanglement witness method to arbitrary entanglement protocols that rely on single-copy quantum state measurements.

“For a random state coupled with the environment, any entanglement detection protocol with single-copy realization is either inefficient or inefficient,” Ma said. “Inefficient means that the protocol relies on measuring a number exponential of observables and inefficient means the success rate of entanglement is doubly exponential.”

Essentially, Ma and his colleagues showed that to observe large-scale entanglement, researchers must be able to control all interactions in a system with high precision and know almost all information about them. When there is a lot of uncertainty about the system, the probability of detecting its entanglement is therefore very low, even if we are almost certain of its appearance.

“We proved that no entanglement detection protocol is both effective and efficient,” Ma explained. “This could help designing entanglement detection protocols in the future. detection of large-scale entanglement could be a good indicator for comparing different quantum computing systems. For example, when a lab team claims to have built a system of hundreds of qubits, they should detect entanglement. Otherwise, they did not control the system well enough.”

Overall, the results collected by this team of researchers highlight the existence of a trade-off between the efficiency and effectiveness of existing entanglement detection methods. Furthermore, they offer valuable insights into why detecting entanglement in large-scale and noisy quantum systems is so difficult.

“Our result does not prevent us from designing a protocol that is both efficient and effective when the system is well controlled (i.e. the coupled environment is relatively small),” Ma added. “Currently, we We only have entanglement detection protocols that work well for pure states, such as entanglement witnesses, and protocols that work for large environments at the expense of exponential cost. Entanglement detection protocol that works for moderate environment size with relatively low cost is still lacking, and now we would like to try to develop one.”

More information:
Pengyu Liu et al, Fundamental limitation of detectability of entanglement, Physical examination letters (2022). DOI: 10.1103/PhysRevLett.129.230503

Karol Życzkowski et al, Volume of the Set of Separable States, Physical examination A (2002). DOI: 10.1103/PhysRevA.58.883

Leonid Gurvits et al, The largest separable balls around the maximally mixed bipartite quantum state, Physical examination A (2002). DOI: 10.1103/PhysRevA.66.062311

Stanislaw J. Szarek, The volume of separable states is super-doubly exponentially small in the number of qubits, Physical examination A (2005). DOI: 10.1103/PhysRevA.72.032304

Xi-Lin Wang et al, Entanglement of 18 qubits with the three degrees of freedom of six photons, Physical examination letters (2018). DOI: 10.1103/PhysRevLett.120.260502

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