Quantum secret splitting based on non-orthogonal multi-particle states
View Patent ↗Systems and methods for quantum secret splitting based on non-orthogonal multi-particle states are disclosed. The method includes preparing at a sender (“Charlie”) two qubits each of which can be in one of two non-orthogonal states and distributing the qubits to respective parties Alice and Bob. The method also includes measuring at Alice the state of the qubit she receives by a projective measurement so that the measurement result is either 0 or 1, and at Bob measuring the state of the qubit he receives such that the measurement result is either 0, 1 or f, wherein f represents a failure by Bob to properly measure the qubit state. The method also includes communicating between Alice, Bob and Charlie the outcome of their respective measurements so as to deduce the state of the qubits sent to Alice and Bob.
1. A quantum-based method of secret splitting, comprising:
preparing at a sender (“Charlie”) two qubits each of which can be in one of two non-orthogonal states;
distributing the qubits to respective parties Alice and Bob;
at Alice, measuring the state of the qubit she receives by a projective measurement so that the measurement result is either 0 or 1;
at Bob, measuring the state of the qubit he receives such that the measurement result is either 0, 1 or f wherein f represents a failure by Bob to properly measure the qubit state; and
communicating between Alice, Bob and Charlie the outcome of their respective measurements so as to deduce the state of the qubits sent to Alice and Bob.
2. The method of claim 1 , including discarding failed measurements by Bob.
3. The method of claim 2 , including Alice and Bob forming a bit string based on the outcome of their respective measurements and the remaining qubit states after the failed measurements are discarded.
4. A quantum-based method of secret splitting between two parties, comprising:
preparing two qubits each having two possible states given by:
|Ψ 0 =cos θ 0 |00 +sin θ 0 |11 ,
|Ψ 1 =cos θ 0 |00 −sin θ 0 |11 ,
where 0≦θ 0 ≦π/4;
sending the qubits to respective receivers A and B;
at receiver A, performing a measurement of the qubit sent to receiver A using POVM elements |r j r j |, for j=0, 1, with
r
0
〉
=
1
2
(
0
〉
+
1
〉
)
,
r
1
〉
=
1
2
(
0
〉
-
1
〉
)
.
so that receiver A obtains only the results 0 or 1 and never receives a failure result;
at receiver B, using POVM elements
1
2
(
1
+
tan
2
θ
0
)
s
j
〉
〈
s
j
,
for
j
=
0
,
1
,
with
s
0
〉
=
1
2
(
sin
θ
0
0
〉
-
cos
θ
0
1
〉
)
,
s
1
〉
=
1
2
(
sin
θ
0
0
〉
+
cos
θ
0
1
〉
)
,
and
(1−tan 2 θ 0 )|0 0|,
which respectively corresponding to measuring 0, 1 and a measurement failure; and
sharing between A and B the outcome of their respective measurements so as to form a common bit string.
5. A quantum-based method of secret splitting between more than two parties, comprising:
preparing two different quantum N-particle states of the form
|Ψ 0 =cos θ 0 |00 . . . 0 +sin θ 0 |11 . . . 1 ,
|Ψ 1 =cos θ 0 |00 . . . 0 −sin θ 0 |11 . . . 1 ,
where 0≦θ 0 ≦π/4, one of the states represents the bit value 0 and the other represents the bit value 1;
sending a particle to each one of the receivers, say, A 1 , . . . , A N ;
performing at each receiver A 1 through A N-1 a quantum measurement on the particle in the {r 0 , r 1 } basis, where
r
0
〉
=
1
2
(
0
〉
+
1
〉
)
,
and
r
1
〉
=
1
2
(
0
〉
-
1
〉
)
,
wherein receiver A N performs the unambiguous-state discrimination procedure between states |ψ 0N =cos θ 0 |0 +(−1) n 1 sin θ 0 |1 ψ 1N =cos θ 0 |0 −(−1) n 1 sin θ 0 |1 , where n 1 is the number of results of |r 1 obtained by receivers A 1 through A N-1 .
6. A quantum-based secret-splitting method, comprising:
generating at a sender a pair of entangled photons and providing the photons to two respective parties, Alice and Bob;
at Alice, measuring a state of the photon she receives as either a 0 or a 1;
at Bob, measuring a state of the photon he receives as either a 0, 1 or f, wherein f represents a failure to measure the proper photon state; and communicating between Alice, Bob and Charlie the outcome of their respective measurements so as to deduce the state of the qubits sent to Alice and Bob.
7. The method of claim 6 , including discarding failed measurements by Bob.
8. The method of claim 7 , including Alice and Bob forming a bit string based on the outcome of their respective measurements and the remaining qubit states after the failed measurements are discarded.