Quantum key distribution via pulse position modulation

A system and method for distributing a quantum key from a first party to a second party. A first node is connected to a public channel, wherein the first node includes a pulse position modulation encoder connected to a quantum channel. A second node is connected to the public channel, wherein the second node includes a pulse position modulation decoder connected to the quantum channel. The pulse position modulation encoder encodes quantum states |0> and |1>, and transmits the encoded quantum states from the first node to the second node via the quantum channel. Quantum state |1> is encoded as |1>≡(|t1>+|t2>)/√{square root over (2)}.

BACKGROUND

There have been recent proposals for implementing the quantum cryptographic protocol BB92 with quantum states based on pulse-position modulation instead of polarization. Attempts to do so to date have been flawed; they are vulnerable to eavesdropping attacks since they do not fully implement the BB92 protocol. Some such approaches are detailed in Nazarathy, “Quantum key distribution over a fiber-optic channel by means of pulse position modulation,” Optics Letters 1533, 30 (2005).

What is needed is a quantum cryptographic protocol BB92 with quantum states based on pulse-position modulation which addresses these issues, and other issues that become apparent in the discussion below.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following detailed description of example embodiments of the invention, reference is made to specific examples by way of drawings and illustrations. These examples are described in sufficient detail to enable those skilled in the art to practice the invention, and serve to illustrate how the invention may be applied to various purposes or embodiments. Other embodiments of the invention exist and are within the scope of the invention, and logical, mechanical, electrical, and other changes may be made without departing from the subject or scope of the present invention. Features or limitations of various embodiments of the invention described herein, however essential to the example embodiments in which they are incorporated, do not limit the invention as a whole, and any reference to the invention, its elements, operation, and application do not limit the invention as a whole but serve only to define these example embodiments. The following detailed description does not, therefore, limit the scope of the invention, which is defined only by the appended claims.

A system100for Quantum Key Distribution (QKD) via pulse position modulation is shown inFIG. 1. In the example embodiment shown inFIG. 1, quantum key distribution allows two parties, Alice102and Bob104, to share a common secret key via a quantum channel106. The shared secret key is then used to encrypt data transferred between Alice and Bob via public channel108.

Quantum Key Distribution, when done properly, guarantees the secrecy of the distributed key. If an eavesdropper (Eve110) tries to determine the key, she will introduce transmission errors in the distribution of the key and will be detected; the shared secret key can then be discarded before it is used to transmit compromised data. If, on the other hand, no eavesdropping is detected, the secrecy of the distributed key is guaranteed.

Pulse position modulation coding of bits0and1is illustrated inFIG. 2. In the example embodiment ofFIG. 2, the position of the pulse in an active time window of length 2Δ determines the bit: position in time bin 2 (bin122inFIG. 2) corresponds to the bit0, and position in time bin 1 (bin120inFIG. 2) corresponds to the bit1. Active windows are separated by a fixed latency time interval τ.

As shown inFIG. 3, the BB92 protocol according to the present invention is the following: Alice encodes quantum states |0> and |1> at200and sends them to Bob at202. Quantum states |0> and |1> are not orthogonal: <1|0>≠0. Quantum state |0> is how a zero is encoded as a quantum state (as detailed below). Quantum state |1> is how a one is encoded as a quantum state (as detailed below). Initially, Alice sends Bob a random string of |0>'s and |1>'s. At204, Bob measures the states he receives by randomly applying the projections on |0>⊥and |1>⊥:
P|0>⊥≡1−|0><0|
P|1>⊥≡1−|1><1|

Bob publicly announces, at206, the indices of those measurements (projections) in which he got a positive result (=1). Alice privately constructs the substring which consists of the bits she sent Bob with the same indices as those Bob just publicly announced. Alice reveals a portion of the substring at208.

Bob privately constructs the string

In the new PPM protocol, the state |0> is encoded as the state “pulse is in second bin” represented by |0>, |t2>, and the state |1> is encoded as the state “pulse is in coherent superposition of the first and second bins,” represented by |1>≡(|t1>+|t2>)/√{square root over (2)}. An example pulse position modulation encoder is shown inFIG. 4. In some embodiments, the new protocol relies on precise clock synchronization between Alice and Bob as part of the implementation of two key requirements.

The first key requirement is the efficient construction of the states:
|0>≡|t2> and |1>≡(|t1>+|t2>)/√{square root over (2)},

The construction of the state |0> is the same as the classical PPM state. The construction of the superposition state |1>, however, is more complex because, as noted above, |1>≡(|t1>+|t2>)/√{square root over (2)}. A pulse position modulation encoder for encoding |1>≡(|1>+|t2>)/√{square root over (2)} is shown inFIG. 4. In the example shown inFIG. 4, simple optical elements are used to transmit the non-classical coherent superposition state (|t2>+|t1>)/√{square root over (2)}. Schematically, as shown inFIG. 4, these simple optical elements include an initial beam splitter140and mirrors142(to delay half the beam by Δ). In one such embodiment, the split beams are combined into output channel144at the end.

The second key requirement is the construction of the projection operators P|0>⊥≡1−|0><0| and P|1>⊥≡1−|1><1|. Observe that the measurement P|0>⊥must be guaranteed to not click when the input state is |0>, and click with probability 1−|<1|0>|2when the input state is |1). Conversely, the measurement P|1>⊥must be guaranteed to not click when the input state is |1>, and click with probability 1−|<1|0>2when the input state is |0>. One example implementation of these measurement operators is illustrated in the pulse position modulation decoder ofFIG. 5.

In the example embodiment shown inFIG. 5, a mirror144receives quantum states sent by Alice102and, in time bin 1 reflects the quantum states while in time bin 2, letting the signal through. Mirrors142reflect the reflected quantum states and the delayed reflected quantum states are combined with a delayed bin 2 set of quantum states by beam splitter140before being detected by detector146. In one embodiment, detector146only detects photons that have are moving down to it.

In one example embodiment, the measurement P|0>⊥must be guaranteed to not click with input state |0>, and click with probability ½ with input state |1>. As shown inFIG. 5, implementing P|0>⊥is easy: Just do a detection in time bin 1.

Likewise, the measurement P|1>⊥must be guaranteed to not click with input state |1>, and click with probability ½ with input state |0>. Implementing P|1>⊥is hard. In one embodiment, it requires precise timekeeping and synchronization in the placement of the initial mirror (in time bin 1 only), and in controlling the phase and time delays to make sure the detector never goes off with input state |1>.

As noted above, precise clock synchronization is required between Alice102and Bob104. In one example embodiment, this is achieved, at least in part, via an ultra-stable frequency reference such as described in U.S. patent application Ser. No. 13/400,348, filed by Wilkerson et al. on Feb. 20, 2012 the description of which is incorporated herein by reference. Synchronization of distant ultra-stable clocks can be achieved via a number of methods such as the Einstein synchronization protocol using optical two-way time transfer, with either optical fiber or free-space propagation.

In some embodiments, the ultra-stable frequency reference generating system described in U.S. patent application Ser. No. 13/400,348 includes a cavity-stabilized reference laser that includes a laser source locked to a stabilized cavity. In some such embodiments, the system also includes a Rubidium (Rb) cell that may be interrogated by a stabilized laser output of the cavity-stabilized reference laser to cause at least a two-photon Rubidium transition (to an upper state) within the Rubidium cell. A detector detects fluorescence within the Rubidium cell resulting from the spontaneous decay of the upper state Rubidium transition. Other vapor cell references can be used as well.

In vapor cell embodiments, the detector provides a detector output at a wavelength of the fluorescence to lock the cavity-stabilized reference laser to generate a stabilized laser output. In some such embodiments, the laser source is locking to both the stabilized cavity and to the Rubidium transition within the Rubidium cell. The combination of a cavity stabilized laser and femtosecond frequency comb referenced to the 778 nm two-photon transition in Rubidium as a source of ultra-low phase noise optical and microwave frequencies can be used, for instance, as standards in a compact system configuration.

As noted in the patent application, such systems are useful in systems that require synchronization; they are also suitable for use in, for instance, radar systems, communication systems, signal-collection systems and difficult EMI environments.

What have been described above are new systems and methods for quantum key distribution. The systems and methods described fully implement the BB92 protocol and which thus have the same absolute unconditional security properties as the standard polarization-based QKD protocol BB84. In one embodiment, a new method of encoding a |1> simplifies construction of a quantum key encoder.