Stochastic local operations and classical communication properties of the n-qubit symmetric Dicke states

Abstract

Recently, several schemes for the experimental creation of Dicke states were described. In this paper, we show that all the n-qubit symmetric Dicke states with l (2 ≤ l ≤ (n − 2)) excitations are inequivalent to the |GHZ state or the |W state under SLOCC, that the even n-qubit symmetric Dicke state with n/2 excitations is inequivalent to any even n-qubit symmetric Dicke state with l = n/2 excitations under SLOCC, and that all the n-qubit symmetric Dicke states with l (2 ≤ l ≤ (n − 2)) excitations satisfy Coffman, Kundu and Wootters' generalized monogamy inequality C

Optimal reducibility of allWstates equivalent under stochastic local operations and classical communication

“…i N and the sum varies over all permutations of (≤ N/2 ) number of 1 and N − number of 0; c i ∈ C with i |c i | 2 = 1 and c i = 0. The standard Dicke states (i.e., when all the coefficients are equal) are SLOCC inequivalent to each other for different and also inequivalent to the GHZ states [16]. In our earlier work we had shown that for < N/2 , the class of states (19) is determined by 2 -partite marginals.…”

Classification of Generaln-Qubit States under Stochastic Local Operations and Classical Communication in Terms of the Rank of Coefficient Matrix

“…. , [n/2] are SLOCC inequivalent [14,15]. These states, as demonstrated below, can also be distinguished by the rank of their coefficient matrices which depends only on the number of excitations and is independent of the number of qubits.…”

“…Considerable efforts have been undertaken over the last decade for the SLOCC entanglement classification of four-qubit states resulting in a finite number of families [3][4][5][6] or classes [7][8][9][10][11][12]. For more than four qubits, a few attempts have been made for SLOCC classification for subsets of the general n-qubit states such as the Greenberger-Horne-Zeilinger (GHZ)-type, W-type, and GHZ-W-type n-qubit states [13], symmetric n-qubit states [14][15][16], even nqubit states [17,18], and odd n-qubit states [19]. Despite these efforts, a SLOCC classification for general n-qubit states is still beyond reach.…”

Frequency thermal response and cooling performance in a microscopic system with a time-dependent perturbation

“…At the meso and nanoscale several interesting applications have been developed in molecular electronics, thermometry and thermal machinary [3,4,5]. Many models of heat pumps have been proposed based on different mechanisms such as heat ratchets that periodically adjusts two baths' temperatures while the average remains equal, brownian heat motors to shuttle heat across the system [6], heat pumps which directs heat against thermal bias in nanomechanical systems [7]. At molecular levels phonon pumps can also be induced by an external force or by mechanical switch on-off of the coupling between different parts of the system [8,9,10,11,12,13,14].…”