Quantum Information Processing, Vol. 6, No. 2, April 2007 (© 2006)
No-Cloning and No-Deleting Theorems through
the Existence of Incomparable States Under LOCC
and Debasis Sarkar
Received April 25, 2006; accepted June 24, 2006; Published online November 28, 2006
No-cloning and No-deleting theorems are veriﬁed with the constraint on local
state transformations via the existence of incomparable states. Assuming the exis-
tence of exact cloning or deleting operation deﬁned on a minimum number of two
arbitrary states, an incomparable pair of states of the joint system between two
parties can be made to compare under deterministic LOCC. We have restricted
our proof with the assumption that the machine states of the cloning or deleting
operations do not keep any information about the input states. We use the same
setting to establish the no-cloning and no-deleting theorems via incomparability
that supports the reciprocity of the two operations in their operational senses. The
work associates the impossibility of operations with the evolution of an entangled
system by LOCC.
KEY WORDS: Local operations and classical communication; quantum clon-
ing; quantum deleting; incomparability of quantum states.
PACS: 03.67.Mn; 03.67.Hk.
One of the most important task in quantum information processing is to
detect the allowable set of operations performed on quantum systems. If
someone wants to copy an arbitrary quantum information encoded in a
quantum state then no-cloning theorem
restricts one to copy arbitrary
quantum information exactly. Quite reverse to it, if we want to delete arbi-
trary quantum information then we have a similar kind of restriction.
According to the no-deletion theorem,
it is not possible to delete arbi-
trary quantum information encoded in a quantum state to a standard
one. On the other hand, manipulation of pure state entanglement provides
us some other kind of restrictions on the evolution of quantum systems.
Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata
To whom correspondence should be addressed. E-mail: firstname.lastname@example.org
1570-0755/07/0400-0093/0 © 2006 Springer Science+Business Media, Inc.