Higher-Dimensional Quantum Cryptography

We report on a high-speed quantum cryptography system with simultaneous entanglement in polarization and “time-bins”. We use multiple degrees of freedom and multiple spots on the downconversion cone to achieve 14 Mbits/s of secure key.


I. INTRODUCTION
HE nonclassical features of single and entangled photons can be used to establish a provably secure quantum communication channelin fact, this is the secure means of encryption. There have been many proof principle quantum key distribution (QKD) experiments, and now even a few vendors of first-wave commercial systems. However, in all of these the final secret key rates are much lower than one would like for an ideal practical system, where, e.g., one might want to encode at video rates. The protocols for the commercial systems only use a single qubit, which results in generating at most a single bit of key data per detection. To optimize the data rate of these QKD systems, each photon should carry the maximum information t be detected. For instance, instead of only entangling the photons in polarization (as is the case in BB84), we can also entangle the photon in additional degrees of freedom through hyper-entanglement [1]. Using these other entangled degrees of freedom, we can encode additional bits per photon (bpp). As an example, if each photon is allowed to appear in one of 1024 time-bins or spatial 'pixels,' then a single detection eve in principle could yield log 2 1024=10 bits [ additional bit of shared entropy from the polarization degree of freedom, for up to 11 bbp. We are currently pursuing this technique to thereby realize a system with over 10 bpp and a total data rate of at least 10 9 bits per second after multiplexing many channels. B Higher-Dimensional Quantum Cryptography T speed quantum cryptography system that utilizes simultaneous entanglement in polarization and in bins". With multiple degrees of freedom contributing to the secret key, we can achieve over ten bits of random entropy per incidence. In addition, we collect from multiple spots on the downconversion cone to further amplify the data rate, allowing us achieve over 10 Mbits of secure key per second. entanglement, Quantum nonclassical features of single and entangled photons can be used to establish a provably secure quantum in fact, this is the only provably There have been many proof-ofkey distribution (QKD) experiments, and wave commercial systems. However, in all of these the final secret key rates are much lower than one would like for an ideal practical system, where, video rates. The protocols for the commercial systems only use a single qubit, which e bit of key data per . To optimize the data rate of these QKD systems, each photon should carry the maximum information that can be detected. For instance, instead of only entangling the photons in polarization (as is the case in BB84), we can also entangle the photon in additional degrees of freedom through . Using these other entangled degrees eedom, we can encode additional bits per photon (bpp). As an example, if each photon is allowed to appear in one of bins or spatial 'pixels,' then a single detection event 1024=10 bits [2], with up to an it of shared entropy from the polarization degree of freedom, for up to 11 bbp. We are currently pursuing this technique to thereby realize a system with over 10 bpp and a bits per second after multiplexing To achieve the high data rate, we need to efficiently use every photon by accessing the full parameter space. The timing DOF is used to encode the majority of the bits per photon. By using a PBS and a delay line to create addition laser pulses, we can increase the repetition rate of the pump to increase the number of available time arrive in. Each doubling of the laser pulse rate adds up to an additional bit of random information (the photon has twice as many time-bins it can appear in). However, we cannot raise the repetition rate indefinitely, since the detectors have an intrinsic timing jitter; we can thus only increase the pump until the jitter in the detectors blur which time produced in (see Fig. 1). Fig. 1 The autocorrelation of the single well the detectors can distinguish neighboring pulses. As we increase the repetition rate of the laser (120 MHz, 240 MHz, 480 MHz, 960 MHz), the pulses begin to merge together and can no longer be distinguished. There is extra broadening in these figures from taking the autocorrelation (the pulses are broadened by a factor of When two neighboring pulses cannot be distinguished, there will be no additional shared entropy between Alice and Bob for additionally increasing the repetition rate of the laser. The polarization degree of freedom adds an additional ½ bit of information (Alice and Bob must randomly choose between two measurement bases, only half of the in any shared informationone basis choice over the other [3]) and is used as a security check. Currently, we assume that there exist no quantum non , Kevin T. McCusker, Daniel J. Gauthier, Daniel Kumor, Venkat Chandar, P. G. Kwiat Dimensional Quantum Cryptography IMENSIONAL QKD To achieve the high data rate, we need to efficiently use every photon by accessing the full parameter space. The timing DOF is used to encode the majority of the bits per photon. By using a PBS and a delay line to create additional laser pulses, we can increase the repetition rate of the pump to increase the number of available time-bins that the photon can arrive in. Each doubling of the laser pulse rate adds up to an additional bit of random information (the photon has twice as bins it can appear in). However, we cannot raise the repetition rate indefinitely, since the detectors have an intrinsic timing jitter; we can thus only increase the pump until the jitter in the detectors blur which time-bin the photon was The autocorrelation of the single-photon detectors shows how well the detectors can distinguish neighboring pulses. As we increase the repetition rate of the laser (120 MHz, 240 MHz, 480 MHz, 960 o merge together and can no longer be distinguished. There is extra broadening in these figures from taking the autocorrelation (the pulses are broadened by a factor of √2). When two neighboring pulses cannot be distinguished, there will be hared entropy between Alice and Bob for additionally increasing the repetition rate of the laser.
The polarization degree of freedom adds an additional ½ bit of information (Alice and Bob must randomly choose between two measurement bases, only half of the measurements result this can be increased by biasing one basis choice over the other [3]) and is used as a security check. Currently, we assume that there exist no quantum non- demolition (QND) measurements that can detect the of the photon without disturbing the polarization. knowledge no such experimental capability exists at present; currently realized QND methods thus far only work with microwave photons in ultra-high finesse superconducting cavities, and still disturb polarization. However, to be secure against any eavesdropper without assuming technological constraints, we need to eventually be able to completely secure the timing DOF. One option, similar to the polarization implementation, is to measure in a mutually unbiased basis (MUB). One possible MUB is the Fourier Transform basis, Measuring in this basis, however, requires an extremely large array of stable interferometers if we want to check the full 10 timing bits of each photon. We are still exploring other more efficient, stable, and secure ways of detecting an eavesdropper (Eve). For instance, by measuring the coherence between different sets of time-bins (e.g., the phase between |t = 0> and |1> as well as the phase between |0> and |10>) we can infer the maximum amount of information Eve could have detected, setting an upper bound on the amount of privacy amplification necessary. Another option is to measure the spectral correlations between Alice and Bob's photons. Any measurement made that localizes the photon in time, will alter the spectral bandwidth of the photons. We are still these options to determine which will require the least amount of additional (and potentially unnecessary) privacy amplification from the inferred information taken by Eve. Finally, the spatial degree of freedom for the photons will be used to multiplex multiple channels together to maximize the data rate.

III. EXPERIMENTAL SETUP
For the experiment, we use a 4-Watt, 120 rate laser (see Fig. 2). The laser pumps two orthogonal BiBO nonlinear crystals to produce polarization entanglement downconversion photons. The long coherence time of the laser enables the temporal entanglement.
By using beamsplitters, we can increase the pulse rate of the laser to 960 MHz. Two locations on the downconversion cones are collected into independent single-mode fibers for spatial filtering. The polarization entanglement is verified by subsequently passing the photons from both channels through a polarization analysis.
A nonpolarizing beamsplitter randomly sends the photons to be measured in the D/A basis as a check for an eavesdropper. We use AR low-crosstalk Brewster angle polarizing beamsplitters (extinction ratio greater than 8700:1) to make the polarization measurement.
The photons then pass through custom interference filters that create a 20-nm transmission band before being detected by single-photon The two polarization analysis channels share the same optical components (by being spatially separated demolition (QND) measurements that can detect the time-bin of the photon without disturbing the polarization. To our knowledge no such experimental capability exists at present; currently realized QND methods thus far only work with high finesse superconducting ill disturb polarization. However, to be secure against any eavesdropper without assuming technological constraints, we need to eventually be able to completely secure the timing DOF. One option, similar to the polarization in a mutually unbiased basis (MUB). One possible MUB is the Fourier Transform basis, in this basis, however, requires an extremely large array of stable interferometers if we want to check the full 10 timing bits of each photon. We are still exploring other more efficient, stable, and secure ways of detecting an instance, by measuring the coherence bins (e.g., the phase between |t = 0> and |1> as well as the phase between |0> and |10>) we can infer the maximum amount of information Eve could have he amount of privacy amplification necessary. Another option is to measure the spectral correlations between Alice and Bob's photons. Any measurement made that localizes the photon in time, will alter the spectral bandwidth of the photons. We are still exploring these options to determine which will require the least amount of additional (and potentially unnecessary) privacy amplification from the inferred information taken by Eve.
inally, the spatial degree of freedom for the photons will be ultiplex multiple channels together to maximize the ETUP Watt, 120-MHz repetition rate laser (see Fig. 2). The laser pumps two orthogonal BiBO nonlinear crystals to produce polarization entanglement in the downconversion photons. The long coherence time of the laser enables the temporal entanglement.
By using beamsplitters, we can increase the pulse rate of the laser to the downconversion cones are mode fibers for spatial filtering. The polarization entanglement is verified by from both channels through polarization analysis.
A nonpolarizing beamsplitter randomly sends the photons to be measured in the H/V or the D/A basis as a check for an eavesdropper. We use AR-coated, crosstalk Brewster angle polarizing beamsplitters (extinction ratio greater than 8700:1) to make the polarization measurement.
The photons then pass through custom nm transmission band photon-counting modules. The two polarization analysis channels share the same optical separated), but are sent to different detectors as depicted are sent to a time-to-digital converter to measure the relative arrival time of the photons. Fig. 2 Each laser pulse (at 120 MHz) is split into 8 pulses via 3 different delay lines (roughly 1-ns, 2 each delay loop, the pulse is passed through a waveplate to keep equal amplitudes in each pulse. These delay loops increase the laser repetition rate so that more information is sent per photon. All of these pulses are within the coherence len resulting dowconversion is timespots on the same downconversion is used for both channels). Each channel shares the same beamsplitters, waveplates, and filters, detectors.

IV.
Current data is shown in coincidence rates given are the average of the count rates over all 8 channels. The bit error rate (BER) is the percent of the data where Alice and Bob measure different polarizations in the same basis, and represents The two sets of data were generated by changing the laser power to increase (or decrease) the average number of photon pairs created per second. With lower singles rate, the number of time photon could have been born is increased, thus increasing the bits photon. The entropies listed include both the data from the timing and polarization degree of freedom. Bits per coincidence is calculated in terms of shared entropy per coincidence (instead of secure entropy per coincidence). The excepted secure ent decoding the two data strings along with privacy amplification from the BER. This table is for one of the two channels, the second channel operates at approximately 80% of the capacity of the displayed channel. different detectors as depicted in Fig. 2. The detector outputs digital converter to measure the relative Each laser pulse (at 120 MHz) is split into 8 pulses via 3 ns, 2-ns, and 4-ns delay loops). After each delay loop, the pulse is passed through a waveplate to keep equal amplitudes in each pulse. These delay loops increase the laser repetition rate so that more information is sent per photon. All of these pulses are within the coherence length of the laser, so the -bin entangled. We collect from two downconversion cone (the same wavelength range both channels). Each channel shares the same beamsplitters, waveplates, and filters, but is sent to independent detectors.
IV. DATA data is shown in Table I. The singles and coincidence rates given are the average of the count rates over all 8 channels. The bit error rate (BER) is the percent of the data where Alice and Bob measure different polarizations in the same basis, and represents the fraction of information Eve were generated by changing the laser power to increase (or decrease) the average number of photon pairs created per singles rate, the number of time-bins in which each photon could have been born is increased, thus increasing the bits per The entropies listed include both the data from the timing and Bits per coincidence is calculated in terms of shared entropy per coincidence (instead of secure entropy per The excepted secure entropy is the entropy retained after decoding the two data strings along with privacy amplification from the This table is for one of the two channels, the second channel operates at approximately 80% of the capacity of the displayed channel. potentially knows, and therefore determines the amount of privacy amplification necessary. As the pump power increases, the probability of generating two uncorrelated pairs of photons also increases. If Alice and Bob detect photons from the different pairs, an uncorrelated polarization coincidence results, increasing in the bit error rate. As the pump repetition rate increase, there is less energy per pulse, and therefore the probability of generating multiple pairs per pulse is reduced (and the BER is thus decreased). Utilizing detectors with reduced jitter, we expect to be able to increase the laser repetition rate to 1.92 GHz, and potentially even to 3.84 GHz. The entropy per coincidence and entropy per second are calculated directly from the singles and coincidences. A low-density parity-check (LDPC) code is used to decode the two data strings at approximately 60% of the Shannon limit. The resultant code will be sent through privacy amplification to secure the secret key from any eavesdropper.

V. CONCLUSION
We have demonstrated a high-speed quantum cryptography system that uses hyper-entangled photons to operate at a secure key rate of 10.6 Mbits/s. By decreasing the pump power, we can also generate over 10 bits of shared entropy per coincidence. Currently the data rate is limited by detector saturation, and the bits per photon are limited by detector jitter. We are currently characterizing improved detectors to further enhance the system. Future work also includes removing the need to assume a technologically limited eavesdropper, in addition to collecting from additional locations on the downconversion cone.