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Coherent and compatible information: a basis to information analysis of quantum systems
Boris A. Grishanin and Victor N. Zadkov Faculty of Physics and International Laser Center, M. V. Lomonosov Moscow State University
Moscow 119899, Russia

ABSTRACT
Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantuminformation are based on compatibility/incompatibility of the quantumstates ofa quantumsystem, resulting in the coherent information and introduced here the compatible information measures, respectively. A sketch of an information optimization of a quantumexperimental setup is proposed.

Keywords : Quantum information, coherent information, compatible information

1. INTRODUCTION
The field of quantum information wasborn at the same time the basic laws of quantumphysics hadbeenestablished and since that time it plays an important role in physics. One could even say that quantuminformation theory was established prior the classical Shannon informationtheory. In favourofthis, Bloch interpretationofthe wavefunction or information meaning of the quantum collapse postulate could be mentioned.1 Moreover, any quantumeffect, i.e., essentially microscopicprocess of atom's spontaneous emission or macroscopic superconductivity transition, is associated with the corresponding process of quantum information transmission. Although importance of the quantuminformation concept wasrecognizedlong ago, not much attentionhas been paid to its practical importance until now, when modern experiments in quantumoptics provide detailed control over quantum states of quantum systems. This allow us not only to think about quantuminformation as of an abstract concept, but apply it to real quantumsystems andreal experiments. Sometimes it is expostulated that in physics one should necessarily deal with physical values, and if dealing only with physical states it is not physics but mathematics. Yet it is not true--whenever the states are specified as the states of a physical model, they provide physically meaning information. As an example, let us discuss an operatorA in Hubert space H as a representation of a physical variable. Then, writingA as a spectraldecomposition we represent it with two types of mathematical objects: A,-, the possible A= A ) physicalvalues,and In), the correspondingphysical states. The latter contain the most general type ofphysical information on physical events regardless of the values The most general concept of classical information is the information theory introduced by Shannon.2'3 This very elegant theory is based on the specific property of classical ensembles, which follows from the basic principles of quantumphysics. This property is the reproducibilityof classical events: statisticallythere is no difference either you have at input and output physically the same system or its informationally equivalent copies. The latter case is impossiblein quantumworld, which gives a rise to a discussionwhether the Shannon approachcan be applicable to the quantum systems or not.46 As we will show, the traditional Shannon entropy and information measures can be successfullyused for analysis of quantum systems, if correctly applied with clear understanding of the basic differences between the classical and quantumstates ensembles. Let us discuss, for example, two atoms in the same state (Fig. la). Term the "same" needs to be refined for the case of quantum systems, by contrast with its classical meaning. In the classical case, we take into account only two basis states of each atom. Then, we are free to suppose that either these basic states correspond to two different atoms or to one and the same atom. Important is that there is only one non-zero probability state in a combined system of two atoms--ifa state of one of the two considered atoms is given, another atom has a non-zero probability state. In quantumcase, two atoms have additional states with non-zero probability due to the internalquantum

I (I

Send correspondenceto B A.G.: grishan©comsiml .phys.msu.su
ICONO 2001: Quantum and Atomic Optics, High-Precision Measurements in Optics, and Optical Information Processing, S. N. Bagayev, et al., Eds., SPIE Vol. 4750 (2002) © 2002 SPIE · 0277-786X/02/$15.00

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(a)

AtomA

AtomB

(b)
Ii)

Basis states

<'1i1'

Basis states

All states

All states

Figure 1.

a) Equivalenceof compatiblebasis-states ensemblesand inequivalenceofincompatible all-states ensembles of two two-levelatoms. b) Vacuum fluctuations as a result of incompatibility: eigen states of & haveequal non-zero fluctuations. probabilities p± = 1/2 at the eigen atomic state 1), thus providingnonzero

uncertainty(Fig. ib). It is well known that this uncertainty resultsfor a harmonic oscillator in vacuum fluctuation energy Fiw/2. In our case of two-level atoms it takes the form of the non-zero values & = & = I, where Pauli matrices are treated as cosine and sine amplitudes of the atomic oscillator. The corresponding fluctuations are different for these two atoms, notwithstanding the latter are in the "same" state, which belongs to different atoms possessing individual internal incompatible ensembles of quantum states. Indeed, the average squared differences -- &j)2 (&A a)2 are both different from zero due to the non-commutativity of their operators with the population operators , the latter yield certainly zero difference -- What we can learn from the considered above example is that when ensembles of quantum system states are incompatible, i.e., non-orthogonal states of eachatom (eigen states of the corresponding non-commuting operators) are involved, the states of two different atoms are always different with respect to all their ever coexisting internal quantumstates allowedby the quantumuncertainty. This statementcan be expressed in a quantitativeform as strict positivity ofthe average operatorof the squared difference between the ortho-projectors onto the corresponding wave functions of the two atoms:

(a

Á

Á

e= f(ia

(aI®IB

-IA®

I) aI)2

=

110))

((OII+Ifk))

((ku

Ic) with the volume differential dVa sin t9dt9dÃo/(2rr) and the total volume Va=D=2. This bipartite operator has two eigen subspaces composed of a singlet and triplet Bell states Ilk) ), corresponding to the eigen squared difference values Ek = 1, 1/3, the singlet one being three times
where integration is made over the Bloch sphere of the states bigger.

At this point, one can concludethat the key difference between classical and quantuminformation lies in cornpatibility or incompatibilityofthe states associated with the information of interest. The one-time states of different systems are always compatible. Therefore, they cannot copy one another if states of each system include internally incompatible states. Conversely,two-time states ofthe deterministically transformed systemare alwaysincompatible. Two-time states of different systems can be either compatible or not. In thispaper, we will classifyquantuminformationin connection with the compatibility propertydescribed above. In this vein, we can distinguish four main types of information listed below:

·

Classicalinformation--allthe states are compatible and in original form ofinformation theoryquantumsystems are not discussed.2'3 Note that classical information can be well transmitted through the quantumchannels and also can be of interest in Quantum Physics.

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.

Semiclassicalinformation--allthe input information is given by classical states A andthe output states include internalincompatibility in the form of all states of a Hubertspace H, which are automatically compatible with the input states. The quantum channel is generally described via a classical parameter dependent on the ensemble of mixed states ,A78 S Coherent information--both input and output are spaces composed of internally incompatible states, plus thesespaces are also incompatible andconnected via a channel superoperator N transforming the input density matrix into the output one: PB = .NPA.9"° It is a "flow" of quantum incompatibility from one system to

another.

.

Compatible information--both input and output are composed

of internally incompatible states, which are

mutuallycompatible.
While three first types of information where thoroughly discussed in the literature,3'7'9 including the recently introduced coherent information measure, the compatible information is introducedhere for the first time. This new type of quantum information is defined for a compound bipartite quantum system with the compatible input and output, which include internalquantumincompatibility. In our view, the coherent and compatible information exhaust all possible qualitatively different types of information in quantumchannels. Presented in the paper feasibility analysis of usingthese two measures of information for infornation analysis of real experimental schemes shows that only compatible information turns to be suitable for information effectiveness analysis of an experimental scheme (in the followingwe will simply call an experimental scheme an "experimental setup").

2. COHERENT INFORMATION 2.1. Physical meaning

of coherent information

The coherent information quantitatively represents an amount of incompatible information, which is transferred from one space to another. A case of one and the same space can be considered, as well. A trivial case of the coherent information exchange is a dynamic evolution represented with the unitary time evolution operator U, PB UI3AU'. Then, all pure states b allowedby the initial density matrix jiA are transformed with no distortion, and the transmitted coherent information coincides with its initial amount. The latter is measured, by definition,
with the von Neumann entropy, which reads
IC

=

S[,5B1

=

S[I3AJ

TPA

log ÒA.

(1)

This definition yet demands additional justifying in terms revealing an operational meaning of the density matrix, which is given in a self-consistentquantumtheory as a result of averaging of a pure statein a compound system over the auxiliary variables. Then, Eq. (1) describes an entanglement of the input system A with a reference system R, whichcorresponds to a properpure state'PAR, TrR IAR) ( IARI = ofacombined A+R system. Thusquantitative measuring of the coherent information is done in terms of the mutually compatible states of two different systems, A and R, while information transfers from input A to the output B, which differs from A here only with a unitary transformation. To complete the general structureof the information system, an information channel with the attachednoisy environment E should be added (Fig. 2a).1' The definition of the coherent information for a general type of channel reads as11

A

\f

I

= S[i5I

--

S[(.iV®I) NAR) ('I'ARI],

(2)

where is the identical superoperator applied to the variables ofthe referencesystem. The second term is the entropy exchange, which is non-zerodue to the exchangebetween the subsystems A+R and E, which is when N I. Channel superoperator N transforms the states of input A according to the equation
PB

I

=

NPA

=

TrR(N®I) IAR) (ARI

(3)

56

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b)
5..
S. S.

.5

S.

I,A I
S.

S.

i__i

7;,

{

AR R

S.

'..

__

A

B

Figure 2. a) The most general scheme of quantum information system, composed of input A, reference system R, channel with noisy environment E, and output B. b) An example of physical implementation of a quantum information system: an input A anda reference system R are the ground states of two entangled atomic A-systems, information channel .N' is provided with the laser excitation of an input system to the radiativeupper level, the two photon field states corresponding to the emitted photons togetherwith the vacuum state provide an output B, and all other field states together with the excited atomic state form the environment E. to the states ofoutput B, whichis againcompatible with the referencesystem R because of no entanglement between them at thistransformation. A physical meaning of Eq. (2) is switchedthen from an incompatibility flow to a specific measure for a preserved entanglement between the compatible systems R and B, which is left after transmission through the channel. In a general case, output B may be physically different from A and even represented with a
Hubert space of different structure,HB

/

in Fig.

HA,12,13 as shown for a specific example of a physical information system

2b.

Now we will try to answer a question how the coherent information measurecan be used in physics? Quantum theoryis usually applied to the calculation of some average values (A) = A (n)(n), where and ri) denote the eigen values and eigen vectors of an operatorA. This expansion represents averaging of physical variablesin terms of = ofquantumstates In). As far as there is an innumerable set of all possible variables and probabilities much richer than the set of all quantum states, description of the correspondences between the physical states, it is apart of physical values, provides a more general information on the physical correspondences the most economical way. Laws for coherent information exchange follow the most basic laws of quantumphysics, as they show the most general features of interaction between two systems of interest chosen as input and output and connected with a one-to-one transformation of the input states. In fact, the dependencies of the coherent information on the system parameters are even more basic than those of specific physical values. Let us consider, for example, a Dicke problem for which an information exchange shows the same oscillation type of dynamics as the energy exchange between the two atoms, assisted with the radiation damping.'2 This oscillatory evolution is characteristic not only for the energy,but also for many other variables. Therefore, there is a point in consideringevolution of the coherent information insteadof working with manyother variables. One should also keep in mind the physical meaning of the coherent information as a preserved entanglement. The latter, in its turn, is a characteristic of an internalincompatibility exchange between the mutually compatible sets of states for the reference and input systems, HR and HA. Among other types of quantuminformation the coherent information distinguishes between two types ofinformation, corresponding to the exchange via classical information and quantum entanglement. The coherent information is nonzero only for the latter case. Thus, it is adequate to discuss how well the given information transmission channel preserves the capability of using the output as an equivalent ofthe input to realize a task, when quantum properties of a signal are essential. This problem received much attention in the literature (see Ref. 14 and references therein). One can also be interested in applying the coherent information concept to an analysis of a specific model of a quantumchannel. One of the examples is discussed in Sec. 2.3.

P

(I)(I)

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2.2. One-time coherent information
A first step towards information characterization of a two-side quantum channel could be undertaken by formal quantumgeneralization of the classical Shannon mutual information = SA + SB -- SAB:

I

I

=

S[,5A]

+

S[,3B1

_

S[i5AB],

(4)

which is valid if the joint density matrix jiAB is given and treated as a strict analogue of classical joint probability distribution PAB 15 Evidently, to apply this formula to quantumsystems we should suppose that A and B states are mutually compatible, which is valid for the one-time states of the corresponding physical systems, unless they belong to the same system, both as input and output. Note at this point that physical meaning of still remains unclear.'6"7 It could be clarified by taking into account striking difference between the classical and quantum information channels. Generally, as it follows from Eq. (3), quantuminput andoutput are incompatible, being taken for a single system at two time instants. Thus, A and B cannot be treated as input and output, and their further specificationmust be made for the quantumcase. Let us then specify A as the reference system and B as the output for a given joint density matrix fiAB as it is shown in Fig. 3. The input B0 and the channel .,V are not introduced explicitly but through their action, resulting in the given densitymatrix PAB.

I

a)

PAB

A°
(_)

)
YAB0

T

If

Figure 3. Reconstruction of the quantuminformation system corresponding to the given joint density matrix PAB: mathematical description of a channel providing one-time coherent information (a) and correspondence with the Schumacher's treatment'1 (b). The pure state
'1AB0

of the

input--reference system and the channel superoperator .iV should obey the equation
PAB

(I®.A/)IWABo)('ABoI.

(5)

This automatically provides the coincidenceof the partial density matrix of the reference state
PA

TtB0

IABo)('I'ABoI

with the partial densitymatrix fA = TrBpAB calculated by averaging of the given A+B state, as far as trace over B0 of Eq. (5) is invariant on .N'. Then, the corresponding one-time coherent information can be defined as
IC

=

S[i5BI

_

S[I5AB],

(6)

which by contrast with the quantity (4) lacks the term S[,òAI. Term "one-time"heremay not have in general case a strict meaning, because any two compatible quantumsystems A and B, even related to different time instants,can be treated as related to the one time instant after the corresponding transformation of states. Additional property of one-time coherent information is that definition (6) lacks symmetry by contrast with (4). Moreover,the coherent information can be negative. The latter is evident for the density matrices PAB corresponding to the pdrely classical information exchange via orthogonal bases, PAB = II P3 Ii) Ii) (ii (ii. Then, the entropies reduce to the classical entropies S[I5ABI=SAB= -- P23 log S[/3B]=SB= -- P3 log P3 and SAB>SB. Negainformation means that the entropy exchange prevails information transmission, so it is tive value of the coherent reasonable to set = 0 in this case.

I

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2.3. Coherent information exchange rate

in the A-system

Information system presented in Fig. 2b plays a special role in new applications based on nonclassicalproperties of quantuminformation,e.g., quantum cryptography andquantumcomputations. Keyelements in such applications are atomic A-systems,whichthoughtto be promising elements (qubits) to store quantuminformation and are convenient to manipulate with the help oflaserradiation.'4"8 Forour system (Fig. 2b) treatingsecond A-system as a reference systemhas a reasonable justification, as the entanglement of two correspondingqubits has a clear physical meaning of the initially provided quantum information. Discussion of the radiationchannel is also interesting, because the transformation of the initial qubit into the photon field enables a wide choice of subsequent transformations. A particular question that can be raised here is how rapidly could the information be recycled after a single use of a qubit--photon field channel? Details of the calculations of the coherent information exchange for this channel are given in Ref. 13. The dependence of the coherent information on time and laser field action angle for a symmetric A-system is shown in Fig. 4a for a maximum entropy qubit state ,òä = 1/2, when information doesnot depend on the individual field intensities of the two applied laser fields.

(a) 0
50

(b)

010
0.25
i;J

rate/7

(qubit)

ooo

in a symmetric A-system as a function of dimensionlesstime yt and action 9 = }i- for the maximum entropy input state; y is the decay rate, 1 is the effective Rabi frequency and 'r angle is the exciting pulse duration.12 b) Dependence of the information rate on the cycle duration t and action angle 9=
Figure 4. a) The coherent information

can be easily seen from Fig. 4a that there is an optimum value for the information rate R = I/t, t = if we introduce a periodic use of the information channel with a cycle duration so that after each cycle the initial state is instantaneously renewed. The calculation results for the rate R for a symmetric A-system with the partial decay rates 71 '72'Y are shown in Fig. 4b.'9 The total optimum rate is R0 = O.178'y. Thus, the process of atom-- photon field information exchange sets the corresponding rate limit on using the coherent information stored in the A-systems. The order of its magnitude is given by the decay rate of the excited state, while an exact value depends on the partial decay rates 'Y1,2 of the A-system transitions. At the limit of a two-level radiativesystem, yi = 0 or 72 = 0, the optimum rate is equal to 0.3167.

It

r,

r,

3. COMPATIBLE INFORMATION
For one-time average values, one can restrict representation of quantum internal incompatibility in an equivalent form of classical probability distribution on the quantumstates of interest. Then, for the probability measure P(do) =
(cVI

PA

a)

dVa

(7)

on the space of all quantum states the average value of an operator A = > (iii can be written as (A) = = ri). Here dVa is the volume differential in the space ofphysically different states of AndP/dVa(an), where Ian)

I)

Proc. SPIE Vol. 4750

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the D-dimensional Hubert space HA (f dVa D), which, for example, for a qubit system with D = 2 is the Bloch sphere (see Sec. 2.1). Eq. (7) is an average of the projective measure

E(d) =

Icr)

(cVI

dVa,

(8)

which is a specific case of non-orthogonal decompositionof unit,20 or positive operator-valued measure (POVM).2' POVMs represent some physical measurement procedures made in a compound space HA®Ha with an appropriate additional space Ha and joint density matrix fiA®fia, which gives no additionalinformation about A beyond the information given by ,òA. Let us assume that two Hilbert spaces, HA and HB, of the corresponding quantum systems A and B and the joint density matrix jfAB in HA®HB are given. Specifically, they can correspond to the subsystems of a compound system A+B, given at the same time instant t, or be defined as input and output of an abstract quantum channel of a real physical system. Described above subsystems A and B are compatible. Therefore, a joint measurement represented with the two POVMs as EA ® EB gives no extra correlations between output and input measurements andthe respective joint input--output probability distributiontakes the form:

P(dc,df3) = Tr [EA(da) ®EB(d/3)],òAB.

(9)

The correspondingShannon information = S[P(dc)] + S{P(d/9)] -- S[P(da,df3)] defines then the compatible information measure.22 The physical meaning of the compatible information depends on the specific choice of the measurement and represents the quantuminformation oninput obtainable from the outputvia the POVMs, which select the information of interest in the classical form of the corresponding c and 3 variables, the information carriers. Let us consider the case when c and fi enumerate all the quantum states of HA and HB, in accordance with Eq. (8). In this case, compatible information is distributedover all quantumstates and associated with the internal quantumuncertainty, which is takenintoaccount in the distribution (7). Specifically, quantumcorrelations due to the possible entanglement between A andB are takeninto account in the joint probability (9). Moreover,the compatible information in this case yields the operational invariance property,23 which is when all the non-commuting physical variables are taken into account equivalently. Such classical representation of the quantum information can be associated with the representations of quantummechanics in terms of classical variables.24

I

4. AMOUNT OF INFORMATION ATTAINABLE BY AN EXPERIMENTAL SETUP Our previous discussion of the generalized measurements encourages us to introduce in this section a likelihood mathematical concept of information attainableby an experimental setup, which certainlyis one of the key goals of the Quantum Information Theory. It is difficult to define the information model corresponding to the experimental setup under consideration in general form. Therefore, one has first to specify the input and output information of
interest (which is actually the most difficult point here). We propose here a solution illustratedby the block scheme
shown in Fig. 5. This block scheme corresponds to a typical mathematical structure of a density matrix of a complex system including two transformations, A and B, representing control and measurement interactions, correspondingly:
iOU

BNA3.

(10)

j5 and i3out are the initialandfinal density matrices for the degreesoffreedom, chosen in a mathematical model of the experimental setup. Superoperators A, B, and N are associated with the preparationof the information, the measurement, and the transmission ofthe information to the output, correspondingly. This markovian-type structure is not the most general one--forsimplicity we assume that the reservoirs corresponding to each transformation are independent and their density matrices can be separated from f5iri· Only under this simplification we can get a separated combination of the three superoperators and the input density matrix and, as a result, get a relatively simple mathematical representation of the information structurein terms of the corresponding decompositionsof A and 13. Still, we haveto keep in mind that a proper generalization of Eq. (10) may be necessary in a general case.
Here
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environment

object measurement control

state control

Figure 5. Information structure of a quantum experimental setup. An object accompanied with the noise environment undergoes the state control interactions, produces the input information ensemble, depending on either the object dynamical parameters or quantumstates of interest. Then, after the channel superoperator transformation .N the output information is measured. A and B denote transformations provided with the controlling interactions, EB stays for the measurement procedure in the form of the corresponding POVM.
Preparationof the information always involves some interactions, resultingin the corresponding transformations, which are unitary only if all the involved degrees of freedom are taken into account. We have to include also interaction with the reservoir represented with a non-unitary superoperator. We will discuss here the recepies for two possible choicesof a physical information of interest: (i) the system dynamic parameters a, (ii) the system dynamic states a). Forthe choice (i), the requiredinformationgoalcanbe achieved with the use ofthe dynamical evolution operators UA(a), which in its turn may depend on the controlling parameters c. A priory information on a is included in a proper chosen probability measure ,a(da). Corresponding superoperator A is then can be written as A = Aa(da)
with

f

Aa

(UA(a)

U1(a))E,

(11)

where symbol denotes the place to substitutewith the transformed densitymatrix and brackets denote averaging over the noise environment. Forthe choice (ii) the required information goalcan be achieved with the use of the measurement superoperator transformation composed of superoperators
Aa

0

(Ia)(aI®Ia)(aI)E.

(12)

The corresponding A = > Aa 5 the measurement superoperator represented with an averaged standard decomsum position >: A At of the completely positive trace-preserving superoperator25 with a properlyspecifiedoperators A = At a) (al. Keeping in mind that a can represent a continuous variable, we have to use a generalized representation A = Aaj(da) in the integration form with a proper measure j(da), providing a corresponding decompositionof unit (POVM) a) (aJ jt(da) = I. In most general form, the superoperator sets (11), (12) are represented with an arbitrary positive superoperator measure (PSM) A(da) = Aa(da), which is a decomposition of a completely positive trace-preserving superoperator. PSM satisfies the conditions of complete positivity, A(da)5 0, and normalization, Tr fA(da),Ò= 1. The latter can be expressed in an equivalent form of preservation of the unit operator A*(da)I = by the conjugate PSM A*. It is worth to discuss here a special case when the POVMs are represented by Eq. (8) with all the states of the Hilbert spaces HA and HB correspondingto A and B, again. This definition of the POVMs restricts the information

-

f

f

f

I

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attainable by an experimental setup due to the basic physical limitations underlying the chosen mechanism of obtaining quantuminformation. The latter is represented here in a "solid" classical form enabling its copying and free use. This propertymay as wellbe assigned by defaultto the meaning of the term "information", by contrastto the opposing meaning ofthe coherent information discussed in Secs. 2.1--2.3. Repeating the above argumentation for the measurement superoperator B = B(db) = J3bV(db) with /3b in the form of Eq. (12), we can implement the input and output information in the form of classical variables a and b for both choices, (i) and (ii), of the information of interest. The corresponding joint probability distribution is then

f

f

given by

P(da, db)

=

TrB(db).N'A(da) 3hi.

(13)

This distribution is always positive and normalized to 1. It gives an experimenter the statistical correspondence between the states of interest and output information attainable by the experimental setup. The corresponding information capacity ofthe setup can be expressed in the quantitativeform as the responding Shannon information, which then can be used for optimization of the setup parameters. It is importantto note that mutual compatibility of the a) and Ib) states for (i) choiceis not declared here and, in general case, the states can correspond to the non-commuting projectors. In a trivial extreme, they could be the same states and all the information is sent with zero error probability. If the states belong to the different physical subsystems, they may carry on quantumcorrelations due to the correspondingstructureof the channel superoperator with UAB being the entangling unitary transformation. N. A simplest example could be given by Al = UAB D The control parameters c may be either fixed or be set of used values c e C. For their optimization one can use the Shannon information measure. The unknown probability distribution 1a(da) of the dynamical parameters a for the case (i) can be calculated in terms of the classical decision theory26and no quantummechanics is necessary. As for the specification of the action 13b ofthemeasurement system in the form (11), it may be generalizedin the form of a general type PSM. Two PSMs A(da) and B(db) cover a wide range of state control and measurement systems implemented into the model of the experimental setup.

U

5. CONCLUSIONS In the paper we classified the quantuminformation into the classical, semiclassical, coherent, and compatible information based on the compatibility property. This list exhausts all basically different types of quantuminformation. Physical meaning ofthe coherent information is an amount of the internal incompatibility exchangedbetween two systems and measured as an entanglement preserved between the output and the reference system. Introduced here

one-time coherent information sets a correct correspondence between the Schumacher's and modified Stratonovich's approaches. We calculated the coherent information exchange rate of a A-system via photon field that does not exceed O.178'y for a symmetric A-system and O.316'y, otherwise. We introduce herefor the first time the compatible information, which is an adequatecharacteristic ofthe quantum information exchangebetween compatible systems. The compatible information can be expressed in terms of classical information despite internalincompatibility, by contrastwith the coherent information, which is basically irreducible to the classical terms. It is shownthat internalcompatibilityofthe input and outputquantuminformation seems an adequate restriction for a physical information in an experimental setup. It makes possible quantitativecharacterization of the available information capacity of the experimental setup. Then, information exchange between the subsystem, preparing information, and the measuring device is formulated as a probabilistic correspondence between the classical variables determining the corresponding dynamical evolution and the measured output values. A general mathematical representation of the information generation and its readout is presented in the form of two PSMs. This representation of physical information exchange in an experimental setup seems to be promising in direct application of Quantum Information Theory to the demands of experimental physics.

ACKNOWLEDGMENTS This work was partiallysupportedby RFBR grant no. 01--02--16311,the State Science-TechnicalPrograms of the Russian Federation "Fundamental Metrology" and "Nano-technology",and INTAS grant no. 00--479.
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