Entangling power and operator entanglement in qudit systems

Wang, Xiaoguang; Sanders, Barry C.; Berry, Dominic W.

doi:10.1103/physreva.67.042323

Cited by 71 publications

(63 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 and 2. Lower bound 3): Using the relation between different measures of entropy established in [13,14], the following inequality can be derived (see App. C):…”

Section: B Rényi Entropy Lower Boundsmentioning

confidence: 99%

Minimum Rényi and Wehrl entropies at the output of bosonic channels

et al. 2004

View full text Add to dashboard Cite

The minimum Rényi and Wehrl output entropies are found for bosonic channels in which the signal photons are either randomly displaced by a Gaussian distribution (classical-noise channel), or in which they are coupled to a thermal environment through lossy propagation (thermal-noise channel). It is shown that the Rényi output entropies of integer orders z 2 and the output Wehrl entropy are minimized when the channel input is a coherent state.PACS numbers: 03.67. Hk,03.65.Db, A principal aim of the quantum theory of information is to determine the ultimate limits on communicating classical information, i.e., limits arising from quantum physics [1,2]. Among the various figures of merit employed in this undertaking, one of the most basic is the minimum output entropy [3]. It measures the amount of noise accumulated during the transmission, and may be used to derive important properties, such as the additivity, of other figures of merit, e.g., the channel capacity. Here we will focus on the Rényi and Wehrl output entropies for a class of Gaussian bosonic channels in which the input field undergoes a random displacement. The Rényi entropies { S z (ρ) : 0 < z < ∞, z = 1 } are a family of functions that describe the purity of a state [4]. In particular, the von Neumann entropy S(ρ) can be found from this family, because S(ρ) = lim z→1 S z (ρ). So too can the linearized entropy, because it is a monotonic function of the second-order Rényi entropy [5]. On the other hand, the Wehrl entropy characterizes the phase-space localization of a bosonic state: its minimum value is realized by coherent states, whose quadratures have minimum uncertainty product and minimum uncertainty sum. In this respect, the Wehrl output entropy can be used to quantify the channel noise by measuring the phase-space "spread" of the output state (see also [6] for a previous analysis of Wehrl output entropy). For the classicalnoise and thermal-noise channels that we will consider, we show that coherent-state inputs minimize the Rényi output entropies of integer orders z 2, and the Wehrl output entropy. The results presented in this paper are connected with the study of the von Neumann output entropies of the classical-noise and thermal-noise channels given in [7], and with the analysis of these channels' additivity properties given in [8].In Sec. I we introduce the classical-noise channel map.In Sec. II we analyze the Rényi entropy at the output * Now with NEST-INFM & Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126, Pisa, Italy. † Now with QUIT -Quantum Information Theory Group, Dipartimento di Fisica "A. Volta" Universita' di Pavia, via A. Bassi 6 I-27100, Pavia, Italy. of this channel. We first show that a coherent-state input minimizes S z (ρ) for z 2 an integer, and that it minimizes S z (ρ) for all z when the input is restricted to be a Gaussian state (Sec. II A). We then provide lower bounds, for arbitrary input states, that are consistent with coherent-state inputs minimizing Rényi output entropies of all orders (Sec. II B). In Sec. I...

show abstract

“…1 and 2. Lower bound 3): Using the relation between different measures of entropy established in [13,14], the following inequality can be derived (see App. C):…”

Section: B Rényi Entropy Lower Boundsmentioning

confidence: 99%

Minimum Rényi and Wehrl entropies at the output of bosonic channels

et al. 2004

View full text Add to dashboard Cite

show abstract

“…To see more about the entangling power, its properties, and generalizations refer to [2,14,15]. By using the above facts, one can find an analytical form for entangling power of a unitary operator as in Eq.…”

Section: Discussionmentioning

confidence: 99%

“…A fundamental relevant question here is how to characterize entangling capabilities of quantum operations. In fact, in this regard a lot of investigation have been done from many different aspects [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18].…”

Section: Introductionmentioning

confidence: 99%

Characterization of two-qubit perfect entanglers

Rezakhani

2004

Phys. Rev. A

View full text Add to dashboard Cite

Here we consider perfect entanglers from another perspective. It is shown that there are some special perfect entanglers which can maximally entangle a full product basis. We have explicitly constructed a one-parameter family of such entanglers together with the proper product basis that they maximally entangle. This special family of perfect entanglers contains some well-known operators such as CNOT and DCNOT, but not √ SWAP.In addition, it is shown that all perfect entanglers with entangling power equal to the maximal value, 2 9 , are also special perfect entanglers. It is proved that the one-parameter family is the only possible set of special perfect entanglers. Also we provide an analytic way to implement any arbitrary two-qubit gate, given a proper special perfect entangler supplemented with single-qubit gates. Such these gates are shown to provide a minimum universal gate construction in that just two of them are necessary and sufficient in implementation of a generic two-qubit gate.

show abstract

“…One such tool is entangling power, which quantifies the average entanglement produced by a gate when acting on product states [2,3]. The concept of entangling power has been studied with various motivations [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Measures of operator entanglement of two-qubit gates

Balakrishnan

Sankaranarayanan

2011

Phys. Rev. A

View full text Add to dashboard Cite

Two different measures of operator entanglement of two-qubit gates, namely, Schmidt strength and linear entropy, are studied. While these measures are shown to have one-to-one relation between them for Schmidt number 2 class of gates, no such relation exists for Schmidt number 4 class, implying that the measures are inequivalent in general.Further, we establish a simple relation between linear entropy and local invariants of two-qubit gates. The implication of the relation is discussed.

show abstract

Entangling power and operator entanglement in qudit systems

Cited by 71 publications

References 27 publications

Minimum Rényi and Wehrl entropies at the output of bosonic channels

Minimum Rényi and Wehrl entropies at the output of bosonic channels

Characterization of two-qubit perfect entanglers

Measures of operator entanglement of two-qubit gates

Contact Info

Product

Resources

About