# US 11,310,040 B2 · Quantum cipher based on phase inversion

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- Number: US 11,310,040 B2
- Document ID: US11310040B2
- Status: Granted
- Kind: B2
- Application number: 16/806,430
- Filed: 2020-03-02
- Published: 2020-09-03
- Granted: 2022-04-19
- Earliest claimed: 2019-03-01
- Assignees: Parallel Wireless, Inc.
- Applicants: Parallel Wireless, Inc.
- Inventors: Vikram Menon; Ayan Chattopadhyay
- Web page: https://patentgrep.com/patent/US11310040B2

## CPC

- H04L 9/0852: {Quantum cryptography (transmission systems employing electromagnetic waves other than radio waves, e.g. light, infrared H04B10/00; wavelength-division multiplex systems H04J14/02; WDM arrangements H04J14/03)}
- H04L 9/0858: {Details about key distillation or coding, e.g. reconciliation, error correction, privacy amplification, polarisation coding or phase coding}
- G06F 17/145: {Square transforms, e.g. Hadamard, Walsh, Haar, Hough, Slant transforms}
- H04L 9/06: the encryption apparatus using shift registers or memories for block-wise {or stream} coding, e.g. DES systems {or RC4; Hash functions; Pseudorandom sequence generators}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

Methods, systems and computer readable media are disclosed for providing a quantum cipher based on phase inversion, A shared key is established between a first party and a second party. A Hadamard transformation is applied to a message intended for a second party from the first party to produce an equal superposition state. A key phase inversion is applied to the output of the Hadamard transformation. A multiple phase inversion transformation is applied to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions. The result is sent to the second party.

## Claims

### Claim 1

A method of providing a quantum cipher based on phase inversion, the method comprising:
establishing a shared key between a first party and a second party;
applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state;
applying a key phase inversion to the output of the Hadamard transformation;
applying a multiple phase inversion transformation to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions; and
sending the result to the second party.

### Claim 2 (depends on 1)

The method of claim 1 wherein the applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state, the applying a key phase inversion to the output of the Hadamard transformation, and the applying a multiple phase inversion to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions are performed by a quantum computer.

### Claim 3 (depends on 1)

The method of claim 1 wherein the quantum cipher is used for communications between a UE and a core.

### Claim 4 (depends on 1)

The method of claim 1 wherein the Hadamard transformation is performed in accordance with the formula

ψ
m
〉
=
H
⊗
n
⁡
(

m
〉
)
=
1
N
⁢
∑
x
=
0
N
-
1
⁢
(
-
1
)
m
·
x
⁢

x
〉
.

### Claim 5 (depends on 1)

The method of claim 1 wherein the key phase inversion is performed in accordance with the formula
Λk=I−2|k><k|.

### Claim 6 (depends on 1)

The method of claim 1 wherein the multiple phase inversion transformation is performed in accordance with the formula
|ψc=γk,d|ψ′c.

### Claim 7 (depends on 1)

The method of claim 1 further comprising retrieving the message from the result, the retrieving comprising:
applying a multiple phase inversion transformation to the received message;
applying a key phase inversion to the output of the multiple phase inversion transformation; and
applying a Hadamard transformation to the result from the key phase inversion.

### Claim 8

A system comprising:
a UE including a first quantum computing element; and
a core network including a second quantum computing element;
wherein the first quantum computing element provides a quantum cipher based on phase inversion for a message sent from the UE to the core network;
wherein the second quantum computing element provides a quantum cipher based on phase inversion for a message sent from the core network to the UE, wherein the quantum cipher based on phase inversion is provided by the method comprising: establishing a shared key between a first party and a second party: applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state; applying a key phase inversion to the output of the Hadamard transformation; applying a multiple phase inversion transformation to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions; and sending the result to the second party.

### Claim 9 (depends on 8)

The system of claim 8 wherein the applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state, the applying a key phase inversion to the output of the Hadamard transformation, and the applying a multiple phase inversion to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions are performed by a quantum computer.

### Claim 10 (depends on 8)

The system of claim 8 wherein the Hadamard transformation is performed in accordance with the formula

ψ
m
〉
=
H
⊗
n
⁡
(

m
〉
)
=
1
N
⁢
∑
x
=
0
N
-
1
⁢
(
-
1
)
m
·
x
⁢

x
〉
.

### Claim 11 (depends on 8)

The system of claim 8 wherein the key phase inversion is performed in accordance with the formula
Λk=I−2|k><k|.

### Claim 12 (depends on 8)

The system of claim 8 wherein the multiple phase inversion transformation is performed in accordance with the formula
|ψc=γk,d|ψ′c.

### Claim 13 (depends on 8)

The system of claim 8 further comprising retrieving a message that has been transformed into a quantum cipher based on phase inversion, the retrieving comprising:
applying a multiple phase inversion transformation to the received message;
applying a key phase inversion to the output of the multiple phase inversion transformation; and
applying a Hadamard transformation to the result from the key phase inversion to obtain the original message.

### Claim 14

A non-transitory computer-readable medium containing instructions which,
when executed, cause a quantum computing element to perform steps comprising:
establishing a shared key between a first party and a second party;
applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state;
applying a key phase inversion to the output of the Hadamard transformation;
applying a multiple phase inversion transformation to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions; and
sending the result to the second party.

### Claim 15 (depends on 14)

The non-transitory computer-readable medium of claim 14 further comprising instructions wherein the applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state, the applying a key phase inversion to the output of the Hadamard transformation, and the applying a multiple phase inversion to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions are performed by a quantum computer.

### Claim 16 (depends on 14)

The non-transitory computer-readable medium of claim 14 further comprising instructions wherein the Hadamard transformation is performed in accordance with the formula

ψ
m
〉
=
H
⊗
n
⁡
(

m
〉
)
=
1
N
⁢
∑
x
=
0
N
-
1
⁢
(
-
1
)
m
·
x
⁢

x
〉
.

### Claim 17 (depends on 14)

The non-transitory computer-readable medium of claim 14 further comprising instructions wherein the key phase inversion is performed in accordance with the formula
Λk=I−2|k><k|.

### Claim 18 (depends on 14)

The non-transitory computer-readable medium of claim 14 further comprising instructions wherein the multiple phase inversion transformation is performed in accordance with the formula
|ψc=γk,d|ψ′c.

### Claim 19 (depends on 14)

The non-transitory computer-readable medium of claim 14 further comprising instructions for retrieving the message from the result, the retrieving comprising:
applying a multiple phase inversion transformation to the received message;
applying a key phase inversion to the output of the multiple phase inversion transformation; and
applying a Hadamard transformation to the result from the key phase inversion.