arXiv:1808.08246 · Physical Review A

Universal detection of entanglement in two-qubit states using only two copies

Suchetana Goswami, Sagnik Chakraborty, Sibasish Ghosh A, A. S. Majumdar

Published Jan 16, 2019• 17 citations

Abstract

We revisit the problem of detection of entanglement of an unknown two-qubit state using minimal resources. Using weak values and just two copies of an arbitrary two-qubit state, we present a protocol where a postselection measurement in the computational basis provides enough information to identify if the state is entangled or not. Our protocol enables complete state identification with a single-setting postselection measurement on two copies of the state. It follows that by restricting to pure states, the global interaction required for determining the weak values can be realized by local operations. We further show that our protocol is robust against errors arising from inappropriate global interactions applied during weak value determination.

DOI: 10.1103/physreva.99.012327

Related papers

Universal observable detecting all two-qubit entanglement and determinant-based separability tests

Remigiusz Augusiak, Maciej Demianowicz, Paweł Horodecki

We construct a single observable, measurement of whose mean value on four copies of an unknown two-qubit state is sufficient to determine unambiguously whether the state is separable or entangled. In other words, there exists a universal collective entanglement witness detecting all two-qubit entanglement. The test is directly linked to a function that characterizes the entanglement quantitatively to some extent. This function is an entanglement monotone under so-called local pure operations and classical communication which preserve local dimensions. Moreover, it provides tight upper and lower bounds for negativity and concurrence. An elementary quantum computing device estimating unknown two-qubit entanglement is designed.

arXiv:quant-ph/0604109Physical Review AMar 13, 200888 citations

Quantification of concurrence via weak measurement

Mikko Tukiainen, H. Kobayashi, Yutaka Shikano

Since entanglement is not an observable per se, measuring its value in practice is a difficult task. Here we propose a protocol for quantifying a particular entanglement measure, namely, concurrence, of an arbitrary two-qubit pure state via a single fixed measurement setup by exploiting so-called weak measurements and the associated weak values together with the properties of the Laguerre-Gaussian modes. The virtue of our technique is that it is generally applicable for all two-qubit systems and does not involve simultaneous copies of the entangled state. We also propose an explicit optical implementation of the protocol.

arXiv:1611.00149Physical Review AMay 1, 201710 citations

Experimental determination of entanglement for arbitrary pure states

Shao-Ming Fei, Ming‐Jing Zhao, Kai Chen +1 more

We present a way of experimentally determining the concurrence in terms of the expectation values of local observables for arbitrary multipartite pure states. Instead of the joint measurements on two copies of a state in the experiment for two-qubit systems [S. P. Walborn et al., Nature (London) 440, 20 (2006)], we only need one copy of the state in every measurement for any arbitrary dimensional multipartite systems, avoiding the preparation of twin states or the imperfect copy of the state.

arXiv:0909.4851Physical Review ASep 21, 200931 citations

Weak Values with Remote Postselection and Shared Entanglement

Arun Kumar Pati, Uttam Singh

We propose a new protocol for the weak measurement of any observable with remote pre and postselections. We show that if two parties share a pure entangled state, then by using local operations and classical communication they can preselect and postselect at distant locations leading to the weak value of an observable as a shift in the pointer of the apparatus at one location in the process of the weak measurement. This can be achieved with either sharing of a pure maximally or non-maximally entangled state. We generalize the protocol for realizing the weak value of any observable with remote pre and postselection of mixed states. Finally, we show how the weak value is modified in the remote pre and postselection setting if Alice and Bob share a mixed entangled state.

arXiv:1310.6002Oct 22, 20131 citation

Bell-pair distillation under imperfect operations

András Kinyó, Tamás Kiss, Orsolya Kálmán

We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.

quant-pharXiv:2610.35699Oct 27, 20260 citations

Minimal Correlation Measurements for Entanglement Detection

Toru Ohira

We propose a problem: to find the minimum number of correlation function measurements that are required to determine whether a given quantum system is entangled or separable. In particular, the case when restricted knowledge of only zero or non-zero correlations is available is examined. Through the concrete investigation on a pure state for two particles, each particle having two basis states (the 2x2 system), we show that the minimum number of measurements for entanglement detection with certainty is three. This involves four quantum observables. We next consider the comparable problem applied to the mixed density matrix. The mixed quantum state case appears to require more detailed information, which we illustrate by studying the concrete example of the Werner state.

Jul 21, 20200 citations