arXiv:1006.1426 · Electronic Proceedings in Theoretical Computer Science

Classification of delocalization power of global unitary operations in terms of LOCC one-piece relocalization

Akihito Soeda, Mio Murao

Published Jun 9, 2010• 0 citations

Abstract

We study how two pieces of localized quantum information can be delocalized across a composite Hilbert space when a global unitary operation is applied. We classify the delocalization power of global unitary operations on quantum information by investigating the possibility of relocalizing one piece of the quantum information without using any global quantum resource. We show that one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent of a controlled-unitary operation. The delocalization power turns out to reveal different aspect of the non-local properties of global unitary operations characterized by their entangling power.

DOI: 10.4204/eptcs.26.11

Related papers

Delocalization power of global unitary operations on quantum information

Akihito Soeda, Mio Murao

We investigate how two pieces of localized quantum information represented by a tensor product of two unknown qudit states are delocalized by performing two-qudit global unitary operations. To characterize the delocalization power of global unitary operations on quantum information, we analyze the necessary and sufficient condition to deterministically relocalize one of the two pieces of quantum information to its original Hilbert space by using only local operation and classical communication (LOCC). We prove that this LOCC one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent to a controlled-unitary operation. The delocalization power and the entangling power characterize different non-local properties of global unitary operations.

arXiv:1004.2114New Journal of PhysicsSep 9, 201010 citations

Comparing globalness of bipartite unitary operations acting on quantum information: delocalization power, entanglement cost, and entangling power

Akihito Soeda, Mio Murao

We compare three different characterizations of the globalness of bipartite unitary operations, namely, delocalization power, entanglement cost, and entangling power, to investigate global properties of unitary operations. We show that the globalness of the same unitary operation depends on whether input states are given by unknown states representing pieces of quantum information, or a set of known states for the characterization. We extend our analysis on the delocalization power in two ways. First, we show that the delocalization power differs whether the global operation is applied on one piece or two pieces of quantum information. Second, by introducing a new task called LOCC one-piece relocation, we prove that the controlled-unitary operations do not have the delocalization power strong enough to relocate one of two pieces of quantum information by adding LOCC.

arXiv:1010.4599Oct 22, 20100 citations

Comparing the globalness of bipartite unitary operations: delocalisation power, entanglement cost and entangling power

Akihito Soeda, Mio Murao

We compare three different characterisations of the globalness of bipartite unitary operations, namely, delocalisation power, entanglement cost and entangling power, to investigate the global properties of unitary operations. We show that the globalness of the same unitary operation depends on whether input states are given by unknown states representing pieces of quantum information or a set of known states for the characterisation. We extend our analysis of delocalisation power in two ways. First we show that the delocalisation power differs according to whether the global operation is applied to one piece or two pieces of quantum information. Then we introduce a new task called LOCC one-piece relocation, and prove that the controlled-unitary operations do not have enough delocalisation power to relocate one of two pieces of quantum information by adding LOCC.

Mathematical Structures in Computer ScienceFeb 28, 20130 citations

Quantum states with the same entanglement and local unitary equivalence

Julio I. de Vicente

Local operations assisted by classical communication (LOCC) play a fundamental role in the resource-theoretic formulation of entanglement theory inducing an operationally meaningful ordering in the set of entangled states. The particular class within LOCC of local unitary (LU) transformations is obviously closed under inversion. Thus, LU-equivalent states are interconvertible by LOCC and have therefore the same entanglement. For this reason LU-equivalence has been thoroughly studied in the context of entanglement theory. However, as I note here with a simple example, the converse is not true: there exist entangled states that are interconvertible by LOCC but which are not LU-equivalent. This motivates studying under which conditions LOCC interconvertibility is characterized by LU-equivalence. I provide a sufficient condition for this to hold. When one considers multipartite states with full entanglement dimensionality (as quantified by the Schmidt number vector) LOCC interconvertibility can only hold under LU-equivalence.

quant-pharXiv:2609.21558Sep 21, 20260 citations

Discrimination of two-qubit unitaries via local operations and classical communication

Joonwoo Bae

Distinguishability is a fundamental and operational measure generally connected to information applications. In quantum information theory, from the postulates of quantum mechanics it often has an intrinsic limitation, which then dictates and also characterises capabilities of related information tasks. In this work, we consider discrimination between bipartite two-qubit unitary transformations by local operations and classical communication (LOCC) and its relations to entangling capabilities of given unitaries. We show that a pair of entangling unitaries which do not contain local parts, if they are perfectly distinguishable by global operations, can also be perfectly distinguishable by LOCC. There also exist non-entangling unitaries, e.g. local unitaries, that are perfectly discriminated by global operations but not by LOCC. The results show that capabilities of LOCC are strictly restricted than global operations in distinguishing bipartite unitaries for a finite number of repetitions, contrast to discrimination of a pair of bipartite states and also to asymptotic discrimination of unitaries.

arXiv:1601.07256Scientific ReportsDec 15, 201515 citations

Violation of Bell-CHSH Inequality Under Global Unitary Operations

Arup Roy, Some Sankar Bhattacharya, Amit Mukherjee +1 more

The action of global unitary operations can have intriguing effects on the non-local manifestations of a quantum state. States which do not violate Bell-CHSH inequality, can violate it when transformed by a global unitary. This phenomena assumes significance when one exercises to augment non-local resources(in terms of violation of Bell-CHSH inequality) from these seemingly useless states(i.e., in terms of non-local tasks). However, equally intriguing is the existence of states from which no non-local resource can be generated with a global unitary. The present work confirms the existence of such a set, pertaining to two qubit states. The set exhibits counter intuitive features by containing within it some entangled states which remain Bell-CHSH local on the action of any unitary. Furthermore through an analytic characterization of the set we lay down a generic prescription through which one can operationally identify states which can generate non-local resources under the action of a unitary on the composite system. It has also been shown that our prescription remains valid for any linear Bell inequality.

Aug 14, 20160 citations