The ability of entangled states to act as resource for teleportation is linked to a property of the fully entangled fraction. We show that the set of states with their fully entangled fraction bounded by a threshold value required for performing teleportation is both convex and compact. This feature enables for the existence of hermitian witness operators the measurement of which could distinguish unknown states useful for performing teleportation. We present an example of such a witness operator illustrating it for different classes of states.PACS numbers: 03.67.-a, 03.67.Mn A. Introduction.-Quantum information processing is now widely recognized as a powerful tool for implementing tasks that cannot be performed using classical means [1]. A large number of algorithms for various information processing tasks such as super dense coding[2], teleportation [3] and key generation [4] have been proposed and experimentally demonstrated. At the practical level information processing is implemented by manipulating states of quantum particles, and it is well known that not all quantum states can be used for such purposes. Hence, given an unknown state, one of the most relevant issues here is to determine whether it is useful for quantum information processing.The key ingredient for performing many information processing tasks is provided by quantum entanglement. The experimental detection of entanglement is facilitated by the existence of entanglement witnesses [5,6] which are hermitian operators with at least one negative eigenvalue. The existence of entanglement witnesses is a consequence of the Hahn-Banach theorem in functional analysis [7,8] providing a necessary and sufficient condition to detect entanglement. Motivated by the nature of different classes of entangled states, various methods have been suggested to construct entanglement witnesses [9][10][11][12]. Study of entanglement witnesses [13] has proceeded in directions such as the construction of optimal witnesses [9,11], Schmidt number witnesses [14], and common witnesses [15]. The possibility of experimental detection of entanglement through the measurement of expectation values of witness operators for unknown states is facilitated by the decomposition of witnesses in terms of Pauli spin matrices for qubits [16] and Gell-Mann matrices in higher dimensions [17]. For macroscopic systems the properties of thermodynamic quantities provide a useful avenue for detection of entanglement [18].Teleportation [3] is a typical information processing task where at present there is intense activity in extending the experimental frontiers [19]. However, it is well known that not all entangled states are useful for teleportation. For example, while the entangled Werner state [20] in 2 ⊗ 2 dimensions is a useful resource [21], another class of maximally entangled mixed states [22], as well as other non-maximally entangled mixed states achieve a fidelity higher than the classical limit only when their magnitude of entanglement exceeds a certain value [23]. The problem of det...

Absolutely separable states form a special subset of the set of all separable states, as they remain separable under any global unitary transformation unlike other separable states. In this work we consider the set of absolutely separable bipartite states and show that it is convex and compact in any arbitrary dimensional Hilbert space. Through a generic approach of construction of suitable hermitian operators we prove the completeness of the separation axiom for identifying any separable state that is not absolutely separable. We demonstrate the action of such witness operators in different qudit systems. Examples of mixed separable systems are provided, pointing out the utility of the witness in entanglement creation using quantum gates. Decomposition of witnesses in terms of spin operators or photon polarizations facilitates their measureability for qubit states.Comment: 5 page

Teleportation witnesses are hermitian operators which can identify useful entanglement for quantum teleportation. Here we provide a systematic method to construct teleportation witnesses from entanglement witnesses corresponding to general qudit systems. The witnesses so constructed are shown to be optimal for qubit and qutrit systems, and therefore detect the largest set of states useful for teleportation within a given class. We demonstrate the action of the witness pertaining to different classes of states in qubits and qutrits. Decomposition of the witness in terms of spin operators facilitiates experimental identification of useful resources for teleportation.

Conditional von Neumann entropy is an intriguing concept in quantum information theory. In the present work, we examine the effect of global unitary operations on the conditional entropy of the system. We start with the set containing states with non-negative conditional entropy and find that some states preserve the non-negativity under unitary operations on the composite system. We call this class of states as Absolute Conditional von Neumann entropy Non Negative class (ACVENN). We are able to characterize such states for 2 ⊗ 2 dimensional systems. On a different perspective the characterization accentuates the detection of states whose conditional entropy becomes negative after the global unitary action. Interestingly, we show that this ACVENN class of states forms a set which is convex and compact. This feature enables the existence of hermitian witness operators. With these we can distinguish the unknown states which will have negative conditional entropy after the global unitary operation. We also show that this has immediate application in super dense coding and state merging as negativity of conditional entropy plays a key role in both these information processing tasks. Some illustrations followed by analysis are also provided to probe the connection of such states with absolutely separable (AS) states and absolutely local (AL) states.

PACS 03.65.Ud -Entanglement and quantum nonlocality PACS 03.67.-a -Quantum Information Abstract -The relation between Bell-CHSH violation and factorization of Hilbert space is considered here. That is, a state which is local in the sense of the Bell-CHSH inequality under a certain factorization of the underlying Hilbert space can be Bell-CHSH non-local under a different factorization. While this question has been addressed with respect to separability , the relation of the factorization with Bell-CHSH violation has remained hitherto unexplored. We find here, that there is a set containing density matrices which do not exhibit Bell-CHSH violation under any factorization of the Hilbert space brought about by global unitary operations. Using the Cartan decomposition of SU (4),we characterize the set in terms of a necessary and sufficient criterion based on the spectrum of density matrices. Sufficient conditions are obtained to characterize such density matrices based on their bloch representations. For some classes of density matrices, necessary and sufficient conditions are derived in terms of bloch parameters. Furthermore, an estimation of the volume of such density matrices is achieved in terms of purity. The criterion is applied to some well-known class of states in two qubits.Since, both local filtering and global unitary operations influence Bell-CHSH violation of a state, a comparative study is made between the two operations. The inequivalence of the two operations(in terms of increasing Bell-CHSH violation) is exemplified through their action on some classes of states.