Abstract
A pure state of a physical system can be prepared in an infinite number of ways. Quantum theory dictates that given a pure state of a physical system it is impossible to distinguish two preparation procedures. Here, we show that the impossibility of distinguishing two preparation procedures for the same pure state follows from the no-signaling principle. Extending this result for a pure bipartite entangled state entails that the impossibility of distinguishing two preparation procedures for a mixed state follows from the impossibility of distinguishing two preparations for a pure bipartite state.Quanta 2020; 9: 16–21.
Highlights
Tinguishing two preparation procedures for a mixed state follows from the impossibility of distinguishing Unlike a classical system, a quantum system needs a two preparations for a pure bipartite state
The question we address can have an infinite number of orthonormal basis sets, is whether the impossibility of distinguishing two prepawe can expand a pure state using any orthonormal ba- ration procedures for a pure state can be derived from sis
We show that the impossibility to distinguish two preparations for a pure bipartite entangled In the context of mixed states, one can have manifestly state implies the impossibility of distinguishing distinct ensemble realizations of the same mixed state
Summary
Each one of distinguishing two (or more) preparations for a pure state these possible expansions represents one possible prepa- follows from the no-signaling |ψ ∈ H N by choosing the initial state of the system as of distinguishing two preparation procedures for a mixed one of the eigenstates of the observable A, i.e., |a0 and state follows from the impossibility of distinguishing two we apply a unitary U to obtain |ψ. In this case, we preparations for a pure bipartite entangled state. Condition which is another fundamental tenet of any phys- the unitary transformation that may distinguish two ical theory
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