**TMOD TECHNOLOGY/ENGINEERING TASK**

**PROPOSAL WORKSHEET FY01**

+----------------------------------+-----------------------------------+
| **PROPOSAL TITLE: Quantum        |                                   |
| Communications, Channel          |                                   |
| Capacity, and Coding**           |                                   |
+----------------------------------+-----------------------------------+
| **PROPOSERS: V. Vilnrotter ,     | **PI CONTACT INFORMATION: Vic     |
| S. Dolinar (Co-PIs);**           | Vilnrotter; Sam Dolinar**         |
|                                  |                                   |
| **P. Arabshahi , C. Lau,         | **JPL BADGE #: 101972; 101902**   |
| F. Pollara, D. Divsalar          |                                   |
| (Co-Is)**                        |                                   |
|                                  |                                   |
| **PI ORGANIZATION:               |                                   |
| Communications Research Section, |                                   |
| 331**                            |                                   |
+----------------------------------+-----------------------------------+
| **TECHNOLOGY WORK AREA OR SSM:   | **PHONE: 4-2745; 4-7403**         |
| CSA**                            |                                   |
|                                  |                                   |
| **DATE DISCUSSED WITH WAM OR     |                                   |
| SSM: 4/04/01**                   |                                   |
+----------------------------------+-----------------------------------+
| **OTHER PARTICIPATING            | **FAX: 3-1717; 4-6825**           |
| ORGANIZATIONS:**                 |                                   |
|                                  |                                   |
| **Sections 335, 367, and UCLA**  |                                   |
+----------------------------------+-----------------------------------+
| **SUBMISSION DATE: May 23,       | **E-MAIL:**                       |
| 2001**                           | <vic@arcadia.jpl.nasa.gov>**;**   |
|                                  |                                   |
|                                  | <sam@shannon.jpl.nasa.gov>        |
+----------------------------------+-----------------------------------+

**BRIEF TECHNICAL SUMMARY *(Objectives****) **(2500 characters-max) ***

This work has three main objectives: (1) to compute the error
performance of optimal or near-optimal measurements for detecting
classical information sent over quantum channels using various
modulation and coding schemes; (2) to compare the capacity of sending
classical and quantum information via quantum channels; and (3) to
interpret existing theoretical and experimental results on quantum
communications, and relate them to our needs for future planetary
communications.

In regard to (1), we will extend previously developed techniques to
evaluate the performance of more complex modulation and coding schemes,
with particular emphasis on the quantum-limited optical channel. In
regard to (3), we will investigate the value of quantum teleportation
for space communications. In regard to (2), we will attempt to define
and contrast the concepts of classical and quantum information
transmission, construct examples to illustrate the key differences, and
compare capacities or capacity bounds where feasible. This study will be
mostly conscribed to the *interpretation* of already existing
theoretical and experimental results to put them in context with our
needs for future planetary communications.

**JUSTIFICATION AND BENEFITS *(2500 characters-max) ***

Optical receivers currently contemplated cannot improve significantly on
existing RF communications system performance primarily because the
detection techniques and receiver structures used do not approach the
theoretical limits imposed by quantum mechanics. The proposed effort
will help to define the fundamental limits of optical communications
performance, both in terms of achievable error probability and channel
capacity, leading to potential enhancement of JPL\'s deep-space
communications capabilities. The general comparisons of quantum
information capacities will help to quantify the potential improvements
that the quantum communications channel might provide in the future.

**SPECIFIC MISSIONS OR CAPABILITIES TO BENEFIT** *(750
characters-max**)***

All future missions contemplating use of optical frequencies for
high-rate or long distance communications, including Mars data-return,
Europa Orbiter and Pluto Flyby. Also, this technology may enable
interstellar missions in the far future.

**PRODUCT TO WHICH THIS CONTRIBUTES *(500 characters-max)***

Both ground-based and spaceborne receivers of a future DSN that approach
quantum-limited bounds.

**APPROACH AND PLAN *(7500 characters-max) ***

Channel capacity for two different ways of using a quantum channel will
be characterized. In the first method, the channel is used to transmit
*classical* information from the sender Alice to the receiver Bob. Alice
encodes her message into quantum states (with their corresponding
probabilities) and sends them to Bob one by one. Bob has then to perform
suitable measurements to reveal the nature of Alice's message. The
capacity of this method is given by the Holevo bound. In the second
method we use the same channel to send *quantum* information. Here Alice
prepares a quantum state, which she wants to transmit to Bob as
faithfully as possible through a decohering quantum channel. Once they
share a certain amount of entanglement, they can use a standard
teleportation protocol to reliably send a state from Alice to Bob. The
capacity in this case is governed by the *coherent information*
(Schumacher and Nielsen). We will relate and compare these two methods
in terms of mutual information, entanglement, and coherent information,
and will discuss their implications to future space communications.

Analysis techniques have already been developed for determining the
average probability of error of the optimum quantum receiver for
detecting classical information sent over a quantum channel using
modulation and coding schemes such as OOK, M-ary PPM and BPSK. Results
to date demonstrate that quantum performance limits for these schemes
have not been reached by means of conventional detection methods (such
as photon counting for the optical channel). These preliminary results
will be extended to determine the performance of more complex coding
schemes over the quantum channel, and to calculate classical capacity
for simple binary and M-ary channels of interest. Initially, the
approach for computing capacity will be similar to that used previously
for evaluating the average probability of error: capacity will be
computed for different orientations of the measurement states with
respect to the signal states within the signal subspace, until a maximum
is found. We will also explore the possibility of using generalized
probability operator measures for maximizing the classical capacity of
the quantum channel. We will also try to determine what physically
realizable quantum measurements correspond to the optimum quantum
operators, or suggest reasonable approximations to them.

After the error performance and capacity of relatively simple signal
sets have been characterized, more complex block codes will be examined.
Existing analysis tools will be expanded to add increasing numbers of
codewords within a product Hilbert space, thus enabling evaluation of
realistic codes. Error performance and capacity will then be determined
and compared with classical performance. For example, a logical next
step after block-orthogonal codes would be to examine bi-orthogonal
Reed-Muller codes by simply augmenting the product states to include the
negative of each codeword. The same techniques of optimally aligning the
resulting 2*M* measurement states to yield minimum error probability, or
maximum capacity, can then be applied to obtain a solution.

The concept of entangled quantum states will be explored, and included
in the quantum communications model. Quantum states are entangled by
using superposition to form composite states from product states, such
as those representing higher dimensional signaling (PPM). These
composite, or entangled, states will then be applied to simple
communication examples to determine the feasibility of using such exotic
quantum states for enhanced optical receiver performance and capacity.

We will also review results on *dense coding* for quantum communication
based on the non-local feature of quantum entangled states. Channel
capacity for dense coding is always higher than that of coherent-state
communication and also of squeezed-state communication.

Finally, we will consider the information transmission capability of
recent experimental results (Kimble) based on squeezed-state
entanglement, which go beyond quantum information transmission based on
*dichotomic* internal atomic states (qubits) by using *continuous*
quantum variables.

**DELIVERABLES *(1500 characters-max) ***

A clear account of the implications of recent experimental/theoretical
results on quantum information transmission for the DSN.

1)  Analysis techniques for evaluating a wide variety of quantum
    communications problems, including error probability and capacity
    calculations, relevant to optical communications.

2)  A recommendation and a roadmap for future studies in this field that
    could benefit space communications.

3)  Results will be documented in the form of a TMO Progress Report.

**PARTNERING *(500 characters-max) ***

Possible partnering with Prof. Roychaudhuri (UCLA) for clarifications of
quantum physics concepts, and with members of other JPL groups that have
expertise in quantum mechanics.

**INFUSION PLAN** *(750 characters-max)*

After feasibility and performance gains of optical communications
systems have been fully developed and demonstrated, optical receivers
with performance approaching the quantum limit will be developed and
implemented for the DSN. New capacity results will be delivered and
explained in a form usable for future mission planning.

**COMMERCIALIZATION POTENTIAL/PLAN** *(500 characters-max)*

Not in the short term.

**REPORTING PLAN** *(500 characters-max)*

Final results will be documented in a TMO Progress Report.

**RESOURCE REQUIREMENTS** *(750 characters-max)*

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                      ***Prior     ***FY01***   ***FY01        ***FY02***   ***Total at
                      Year(s)***                (midyear)***                Completion***

  **Funding (\$K)**   0            20           125            TBD          **145 +**

  **Workforce (WY)**  0            0.1          0.7            TBD          **0.8 +**

  **Co-Funding                                                              
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  **Projected Savings                                                       
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  Co-Funding Source                          Co-Funding Committed? \*  
  \*                                         Y                         

  **Old Account                              **N**                     
  Number**                                                             
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Note: \* items requiring explanation in the resource requirements text
below

# REFERENCE TO PRIOR FY01 WORK

V. Vilnrotter and C-W. Lau, \"Quantum Detection Theory for the
Free-Space Channel\", to appear in TMO Progress Report 42-146, August
15, 2001.