Cheat-sensitive commitment of a classical bit coded in a block of $m$ × $n$ round-trip qubits

This paper proposes a quantum protocol for a cheat-sensitive commitment of a classical bit. Alice, the receiver of the bit, can examine dishonest Bob, who changes or postpones his choice. Bob, the sender of the bit, can examine dishonest Alice, who violates concealment. For each round-trip case, Alice sends one of two spin states |$S$±⟩ by choosing basis $S$ at random from two conjugate bases $X$ and $Y$. Bob chooses basis $C$ ∈ {$X$,$Y$} to perform a measurement and returns a resultant state |$C$±⟩. Alice then performs a measurement with the other basis $R$ (≠$S$) and obtains an outcome |$R$±⟩. In the opening phase, she can discover dishonest Bob, who unveils a wrong basis with a faked spin state, or Bob can discover dishonest Alice, who infers basis $C$ but destroys |$C$±⟩ by setting $R$ to be identical to $S$ in the commitment phase. If a classical bit is coded in a block of $m$ × $n$ qubit particles, impartial examinations and probabilistic security criteria can be achieved.

Figure 1

Legitimate arrangements for sending ($S$) and readout basis ($R$), and subsequent changes in the qubit spin state.

Figure 2

Schematic diagram showing the detection of a dishonest party. (1) Alice can detect dishonest, Bob who changes the basis ($C$) from $Y$ to $X$. (2) Dishonest Alice can find Bob's coding basis as $Y$. (3) Dishonest Alice fails to answer the spin state |$C$±〉.

Figure 3

Strategy of dishonest Bob, who tries to change his coding basis for one sequence.

Figure 4

General configuration of the whole system considering entanglement-assisted operations.

Figure 5

Probability of Alice's correct guess with respect to parameter λ.