Separability and entanglement in superpositions of quantum states

Abstract

It is known that probabilistically mixing an arbitrary pair of pure quantum states, one of which is entangled and the other product, in any bipartite quantum system, one always obtains an entangled state, provided the entangled state of the pair appears with a nonzero probability. On the other hand, if we consider any superposition of the same pair, with a nonzero amplitude for the entangled state of the pair, the output state may not always be entangled. Motivated by this fact, in this work, we study the superpositions of a pure entangled state and a pure product state, when the amplitudes corresponding to the states appearing in any superposition are nonzero. We show, in particular, that all such superpositions produce only entangled states if the initial entangled state has Schmidt rank three or higher. Again, superposing a pure entangled state and a product state cannot lead to product states only, in any bipartite quantum system. These lead us to define conditional and unconditional inseparabilities of superpositions. These concepts in turn are useful in quantum communication protocols. We find that conditional inseparability of superpositions help in identifying strategies for conclusive local discrimination of shared quantum ensembles. We also find that the unconditional variety leads to systematic methods for spotting ensembles exhibiting the phenomenon of more nonlocality with less entanglement and two-element ensembles of conclusively and locally indistinguishable shared quantum states.

Close to published version

References in corpus (25)

• Experimental quantum teleportation
• Entanglement detection
• Multipartite Nonlocality without Entanglement in Many Dimensions
• Quantifying Entanglement with Witness Operators
• Multiparticle entanglement under the influence of decoherence
• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Distinguishability of Quantum States by Separable Operations
• Tangles of superpositions and the convex-roof extension
• Entanglement robustness and geometry in systems of identical particles
• Connecting the generalized robustness and the geometric measure of entanglement
• Bounds on Negativity of Superpositions
• Robustness of multi-qubit entanglement in the independent decoherence model
• Concurrence of superposition
• Difficulty of distinguishing product states locally
• Reexamination of entanglement of superpositions
• Bounds on the multipartite entanglement of superpositions
• Tight bounds on the concurrence of quantum superpositions
• Unextendible maximally entangled bases in ${\mathbb{C}}^d⨂{\mathbb{C}}^{d^{\prime }}$
• Unextendible entangled bases with fixed Schmidt number
• Constructing UMEB from maximally entangled basis
• Entanglement of subspaces in terms of entanglement of superpositions
• A Note on Mutually Unbiased Unextendible Maximally Entangled Bases in ${\mathbb{C}}^2⨂{\mathbb{C}}^3$
• Multipartite entanglement of superpositions
• Genuine Multipartite Entanglement of Superpositions
• Robustness of entangled states that are positive under partial transposition

Cited by in corpus (2)

• To share and not share a singlet: control qubit and nonclassicality in teleportation
• Unconditionally superposition-robust entangled state in all multiparty quantum systems