We investigate the task of local marking for locally implementable unitary operations. In this setting, multipartite quantum unitary channels, chosen randomly from a known set, are distributed among spatially separated parties without revealing their identities. The objective is to correctly identify (mark) the applied process using only local operations supplemented with classical communication (LOCC). While local distinguishability implies local marking, local marking does not guarantee either local or even global distinguishability of a set of unitaries. Thus the task of marking is not equivalent to the task of discrimination. We demonstrate a stronger manifestation of nonlocality without entanglement by constructing a set of globally distinguishable tripartite product unitaries that cannot be locally marked. In contrast to state marking, we find that marking a subset of product unitaries does not imply the ability to mark a larger subset. Finally, we explore the hierarchy of probes-entangled and product-in the context of local marking with respect to the standard discrimination scenario.We investigate the task of local marking for locally implementable unitary operations. In this setting, multipartite quantum unitary channels, chosen randomly from a known set, are distributed among spatially separated parties without revealing their identities. The objective is to correctly identify (mark) the applied process using only local operations supplemented with classical communication (LOCC). While local distinguishability implies local marking, local marking does not guarantee either local or even global distinguishability of a set of unitaries. Thus the task of marking is not equivalent to the task of discrimination. We demonstrate a stronger manifestation of nonlocality without entanglement by constructing a set of globally distinguishable tripartite product unitaries that cannot be locally marked. In contrast to state marking, we find that marking a subset of product unitaries does not imply the ability to mark a larger subset. Finally, we explore the hierarchy of probes-entangled and product-in the context of local marking with respect to the standard discrimination scenario.

quant-pharXiv:2604.08054Apr 10, 20260 citations

Local discrimination scheme for some unitary operations

Tian-Qing Cao, Fei Gao, Guojing Tian +2 more

Science China Physics Mechanics and AstronomyJul 25, 20165 citations

Non-classicalities via perturbing local unitary operations

Jun Zhang, Yang Zhang, Shao-xiong Wu +1 more

arXiv:1411.7452The European Physical Journal DOct 1, 20134 citations

Nonlocal and controlled unitary operators of Schmidt rank three

Lin Chen, Li Zhi Yu

Implementing nonlocal unitary operators is an important and hard question in quantum computing and cryptography. We show that any bipartite nonlocal unitary operator of Schmidt rank three on the $({d}_{A}\ifmmode\times\else\texttimes\fi{}{d}_{B})$-dimensional system is locally equivalent to a controlled unitary when ${d}_{A}$ is at most three. This operator can be locally implemented assisted by a maximally entangled state of Schmidt rank $r=\mathrm{min}{{d}_{A}^{2},{d}_{B}}$ . We further show that stochastic-equivalent nonlocal unitary operators are indeed locally equivalent, and propose a sufficient condition on which nonlocal and controlled unitary operators are locally equivalent. We also provide the solution to a special case of a conjecture on the ranks of multipartite quantum states.Implementing nonlocal unitary operators is an important and hard question in quantum computing and cryptography. We show that any bipartite nonlocal unitary operator of Schmidt rank three on the $({d}_{A}\ifmmode\times\else\texttimes\fi{}{d}_{B})$-dimensional system is locally equivalent to a controlled unitary when ${d}_{A}$ is at most three. This operator can be locally implemented assisted by a maximally entangled state of Schmidt rank $r=\mathrm{min}{{d}_{A}^{2},{d}_{B}}$. We further show that stochastic-equivalent nonlocal unitary operators are indeed locally equivalent, and propose a sufficient condition on which nonlocal and controlled unitary operators are locally equivalent. We also provide the solution to a special case of a conjecture on the ranks of multipartite quantum states.

arXiv:1403.5720Physical Review AJun 23, 201425 citations

The unitary representation operators

G. Alagar Ramanujam

International Journal of Theoretical PhysicsApr 1, 19750 citations

Nonlocal operations: Purification, storage, compression, tomography, and probabilistic implementation

Wolfgang Dür, J. I. Cirac

We provide several applications of a previously introduced isomorphism between physical operations acting on two systems and entangled states [Phys. Rev. Lett. 86, 544 (2001)]. We show (i) how to implement (weakly) nonlocal two-qubit unitary operations with a small amount of entanglement; (ii) that a known, noisy, nonlocal unitary operation as well as an unknown, noisy, local unitary operation can be purified; (iii) how to perform the tomography of arbitrary, unknown, nonlocal operations; (iv) that a set of local unitary operations as well as a set of nonlocal unitary operations can be stored and compressed; and (v) how to implement probabilistically two-qubit gates for photons. We also show how to compress a set of bipartite entangled states locally, as well as how to implement certain nonlocal measurements using a small amount of entanglement. Finally, we generalize some of our results to multiparty systems.We provide several applications of a previously introduced isomorphism between physical operations acting on two systems and entangled states [Phys. Rev. Lett. 86, 544 (2001)]. We show (i) how to implement (weakly) nonlocal two-qubit unitary operations with a small amount of entanglement; (ii) that a known, noisy, nonlocal unitary operation as well as an unknown, noisy, local unitary operation can be purified; (iii) how to perform the tomography of arbitrary, unknown, nonlocal operations; (iv) that a set of local unitary operations as well as a set of nonlocal unitary operations can be stored and compressed; and (v) how to implement probabilistically two-qubit gates for photons. We also show how to compress a set of bipartite entangled states locally, as well as how to implement certain nonlocal measurements using a small amount of entanglement. Finally, we generalize some of our results to multiparty systems.

arXiv:quant-ph/0012148Physical Review AJun 15, 200163 citations

{d}_{A}

is at most three. This operator can be locally implemented assisted by a maximally entangled state of Schmidt rank

r=\mathrm{min}{{d}_{A}^{2},{d}_{B}}

. We further show that stochastic-equivalent nonlocal unitary operators are indeed locally equivalent, and propose a sufficient condition on which nonlocal and controlled unitary operators are locally equivalent. We also provide the solution to a special case of a conjecture on the ranks of multipartite quantum states.