Quantum enigma machine: Experimentally demonstrating quantum data locking

Shannon proved in 1949 that information-theoretic-secure encryption is possible if the encryption key is used only once, is random, and is at least as long as the message itself. Notwithstanding, when information is encoded in a quantum system, the phenomenon of quantum data locking allows one to encrypt a message with a shorter key and still provide information-theoretic security. We present one of the first feasible experimental demonstrations of quantum data locking for direct communication and propose a scheme for a quantum enigma machine that encrypts 6 bits per photon (containing messages, new encryption keys, and forward error correction bits) with less than 6 bits per photon of encryption key while remaining information-theoretically secure.

Figure 1

Experimental diagram. Ultraviolet (UV) laser light passes through a nonlinear bismuth triborate (BiBO) crystal to produce down-converted signal-herald photon pairs. After separating the photons with a beam splitter (BS), Alice uses single-mode (SM) fibers to transfer the herald photon to an avalanche photodiode (APD) detector while sending the signal photon to be polarization prepped by a quarter-wave plate (QWP), a half-wave plate (HWP), and a polarizer for use with a spatial light modulator (SLM). Alice then phase modulates her signal photon with an SLM to encode and lock information. Imaging lenses map Alice's wave front to Bob's SLM, where he applies an inverse unitary phase operation to unlock the information before focusing his light onto a low-noise cryogenically cooled $8\times 8$ pixel nanowire array. Bob then uses the heralded detection event sent by Alice to herald the arrival of single photons. See the Appendix pp2 for details.

Figure 2

Joint probability distributions. The joint probability distributions presented are derived from experimental data where Alice scans through 64 messages while locking the information with $128\times 128$ pixel binary phase masks. (a) Eve randomly guesses at binary phase masks in the hopes of unlocking the information while being allowed, in a worst-case scenario, to use Bob's properly aligned detector. (b) Bob unlocks the messages with binary phase masks prescribed according to a secret key. The distribution with the highest mutual information is a normalized identity matrix with diagonal elements equal to $1/64\approx 0.016$. The comb structure seen in (b) is due to a gradient of error rates across the detector array, possibly due to a slight misalignment of a lenslet array placed above the detector array. In summary, Alice and Eve's distribution is highly uncorrelated, while Alice and Bob's distribution is highly correlated, attesting to the effectiveness of this locking method.

Figure 3

Single-photon bit allocation (for $n=63$ channel uses). The plot lists how many secret-key bits (blue squares), FEC redundancy bits (red triangles), and message bits (black diamonds) are encoded within a single 6-bit photon as a function of Reed-Solomon (63, $x$) codes. The new secret-key plot shows the necessary allocation of bits to replenish the consumed key. Any FEC redundancy requires the consumption of more of the secret key. Moving from $n=63$ channel uses to $n=126$ or higher will result in less secret-key consumption per photon and larger message-bit capacities. Message bits may be allocated to either additional key or secret messages for direct communication.

Figure 4

Reed-Solomon error correction success rates. The success rates for a Reed-Solomon (63, $x$) code are presented, where $x$ is the number of 6-bit symbols containing the new key and message and 63 is the total number of packet symbols after including redundancy. These data were obtained after transmitting packets of 63 photons 420 times. The plot also depicts the available capacity for message bits per photon as a function of $x$ and the number of channel uses $n$.

Figure 5

Secret-key consumption rate. Letting $d=64$, Eq. (A5) is used to calculate the amount of key bits per photon (assuming one photon per channel use). QDL is only possible if $\left({log}_2{K}_n\right)/n<6$; we see that QDL is possible for most values of $n$.

Figure 6

Gaussian fit to beam profile. A Gaussian function was fit to the original beam profile seen within the experiment. This fit was used to find the original beam profile on Alice's SLM for a numerical simulation.

Figure 7

Eve's average distribution. This distribution was obtained by averaging over each of the 64 scrambled messages 300 times using a different random phase pattern for each scrambling operation. The lenslet array, calculated from experimental parameters, is outlined in white.

Figure 8

Secret-key consumption rate. Letting $d=650$, Eq. (A5) is used to calculate the number of key bits per photon (assuming one photon per channel use). QDL is only possible if $\left({log}_2{K}_n\right)/n<6$; we see that QDL is possible for most values of $n$. For $n\gtrsim 50$, a key size just under 4 bits per photon is sufficient for QDL and has the potential to enable the use of error-correcting codes.

Figure 9

Single-photon bit allocation (for $n=63$ channel uses). The plot lists how many secret-key bits (blue squares), FEC redundancy bits (red triangles), and message bits (black diamonds) are encoded within a single 6-bit photon as a function of Reed-Solomon (63, $x$) codes for a channel dimension $d=650$. The new secret-key plot shows the necessary allocation of bits to replenish the consumed key. Any FEC redundancy requires the consumption of more of the secret key. Moving from $n=63$ to higher values will result in less secret-key consumption per photon and larger message-bit capacities as the key asymptotically approaches a constant. The Reed-Solomon (63, 51) code holds the largest Reed-Solomon error-correcting capability for $d=650$ and $n=63$.

Figure 10

Reed-Solomon error correction success rates. The success rates for a Reed-Solomon (63,$x$) code are presented, where $x$ is the number of 6-bit symbols containing the new key and message and 63 is the total number of packet symbols after including redundancy. These data were obtained after transmitting packets of 63 photons 420 times. The plot also depicts the available capacity for message bits per photon as a function of both $x$ and the number of channel uses $n$ after allocating the necessary bits to refresh a secret encryption key obtained from Eq. (A5) with $d=650$. From the plot, we see that less key is required for $n=126$, resulting in a higher message capacity.