Having the quantum correlations in a general mixed or pure bipartite state in mind, the part of information accessible by simultaneous measurement on both subsystems is shown never to exceed the part accessible by measurement on one subsystem, which, in turn is proved not to exceed the von Neumann mutual information. A particular pair of (opposite-subsystem) observables is shown to be responsible both for the amount of quasiclassical correlations and for that of the purely quantum entanglement in the pure-state case: the former via simultaneous subsystem measurements, and the latter through the entropy of coherence or of incompatibility, which is defined for the general case. The observables at issue are so-called twin observables. A general definition of the latter is given in terms of their detailed properties.
In this paper, two conjectures which were proposed in [Phys. Rev. A \textbf{82}, 052122(2010)] on the correlations in a bipartite state
ρAB are studied. If the mutual information $I\Pa{\rho^{AB}}$ between two quantum systems
A and
B before any measurement is considered as the total amount of correlations in the state
ρAB, then it can be separated into two parts: classical correlations and quantum correlations. The so-called classical correlations $C\Pa{\rho^{AB}}$ in the state
ρAB, defined by the maximizing mutual information between two quantum systems
A and
B after von Neumann measurements on system
B, we show that it is upper bounded by the von Neumann entropies of both subsystems
A and
B, this answered the conjecture on the classical correlation. If the quantum correlations $Q\Pa{\rho^{AB}}$ in the state
ρAB is defined by $Q\Pa{\rho^{AB}}= I\Pa{\rho^{AB}} - C\Pa{\rho^{AB}}$, we show also that it is upper bounded by the von Neumann entropy of subsystem
B. It is also obtained that $Q\Pa{\rho^{AB}}$ is upper bounded by the von Neumann entropy of subsystem
A for a class of states.
We analyze a family of measures of general quantum correlations for composite systems, defined in terms of the bipartite entanglement necessarily created between systems and apparatuses during local measurements. For every entanglement monotone
E, this operational correspondence provides a different measure
QE of quantum correlations. Examples of such measures are the relative entropy of quantumness, the quantum deficit, and the negativity of quantumness. In general, we prove that any so-defined quantum correlation measure is always greater than (or equal to) the corresponding entanglement between the subsystems, ${Q}_{E}\ensuremath{\ge}E$, for arbitrary states of composite quantum systems. We analyze qualitatively and quantitatively the flow of correlations in iterated measurements, showing that general quantum correlations and entanglement can never decrease along von Neumann chains, and that genuine multipartite entanglement in the initial state of the observed system always gives rise to genuine multipartite entanglement among all subsystems and all measurement apparatuses at any level in the chain. Our results provide a comprehensive framework to understand and quantify general quantum correlations in multipartite states.
The concept of physical twin observables (PTO) for bipartite quantum states, introduced and proved relevant for quantum information theory in recent work, is substantially simplified. The relation of observable and state is studied in detail from the point of view of coherence entropy. Properties of this quantity are further explored. It is shown that, besides for pure states, also for a class of mixed states, quantum discord (measure of entanglement) can be expressed through the coherence entropy of a PTO complete in relation to the state.
Twin observables are opposite subsystem observables A + and A - if they are indistinguishable in measurement in a given mixed or pure state ρ in the sense that the measurement of one amounts to the same as the measurement of the other (direct measurement and so-called distant measurement, respectively). It is pointed out that twin observables may reveal quantum correlations that give rise to the disappearance of interference in the two-slit experiment. Twin observables in general states are investigated in detail algebraically and geometrically. It is shown that there is a far-reaching correspondence between the detectable (in ρ) spectral entities of the two operators. Twin observables are state-dependently quantum-logically equivalent, and the direct subsystem measurement of one of them ipso facto gives rise to the indirect (i.e. distant) measurement of the other. Existence of nontrivial twins requires a singularity of ρ. Systems in thermodynamic equilibrium do not admit subsystem twins. These observables may enable one to simplify the matrix representing ρ.
The concept of physical twin observables (PTO) for bipartite quantum states,introduced and proved relevant for quantum information theory in recent work, is substantially simplified. The relation of observable and state is studied in detail from the point of view of coherence entropy. Properties of this quantity are further explored. It is shown that, besides for pure states, quantum discord (measure of entanglement) can be expressed through the coherence entropy of a PTO complete in relation to the state.
In relation to an observable and quantum state, the entity IC from previous work quantifies simultaneously coherence, incompatibility and quantumness. In this paper, its application to quantum correlations in bipartite states is studied. It is shown that Zurek's quantum discord can always be expressed as excess coherence information (global minus local). Strong and weak zero-discord cases are distinguished and investigated in terms of necessary and sufficient and sufficient conditions respectively. A unique string of relevant subsystem observables, each a function of the next, for "interrogating" the global state about the state of the opposite subsystem is derived with detailed entropy and information gain discussion. The apparent disappearance of discord in measurement is investigated, and it is shown that it is actually shifted from between subsystems 1 and 2 to between subsystems 1 and (2 + 3), where 3 is the measuring instrument. Finally, it is shown that the global coherence information IC(A2, ρ12) is shifted into the global coherence information [Formula: see text] in the final state [Formula: see text] of the measurement interaction.