Photon Entanglement over the Fiber-Optic Network

Quantum mechanics with its bizarre and wonderful properties—individual particles that exist in an arbitrary combination of states, entangled particles acting in concert even when separated over long distances—is usually thought of as a world separate from everyday classical physics.

Even Einstein couldn’t quite resolve entanglement with his view of the physical world and in a 1935 paper (along with Boris Podolsky and Nathan Rosen) argued that entanglement violated the locality principle (which states one physical system should have no immediate effect on another spatially separated system). But subsequent theoretical ideas and experiments have verified the existence and nonlocal behavior of entangled particles.

And in the past 20 years, the new field quantum information science has been bridging quantum physics, computer science, optical technology, and communication engineering to harness the power of quantum properties. While the initial drive came from the desire to build a quantum computer capable of vastly outperforming today’s supercomputers, more recent efforts are venturing into more immediately practical applications.

**The power of quantum mechanics
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Rather than utilizing ordinary bits that exist in only one of two states (0 or 1), quantum information science utilizes qubits (see sidebar) that, first, exist in a superposition of their states 0 and 1 and, second, are capable of interacting with one another. In theory, a computer based on these interacting qubits is capable of doing certain calculations much faster than an ordinary computer that is limited to operating on a bit’s single state. As more qubits are combined, more simultaneous operations are theoretically possible; and for certain calculations (such as factoring), a relatively small number of qubits could conceivably outperform ordinary computers with a million processors, an extraordinary advance in computing.

(Pioneering work in quantum computational theory was done by Peter Shor who, while at AT&T Bell Labs, devised a polynomial time algorithm for factoring large numbers on a quantum computer.)

An important feature of quantum cryptopgraphic systems is that they are impervious to eavesdropping . ..

Qubits can be combined, or *entangled*, because the mathematical rules of quantum mechanics allow two or more particles—atoms, photons, and ions have all been successfully entangled—to belong to a certain single joint quantum state that is not just the combination of the individual qubit states. A typical example would be a situation in which physical conservation laws constrain two qubits to have the same value so that, when measured, either both qubits are 1 or both qubits are 0.

This is true even though neither qubit has a certain value prior to any measurements, even though the result of the first reading is completely random, and *even if the second qubit is removed to a remote location*.

Quantum computers are proving very hard to build due to the difficulty of controlling the interactions of multiple qubits and keeping the entanglement state alive long enough to perform calculations. But proposals to employ entanglement for other applications—quantum metrology, quantum lithography—may be closer to reality. Currently the most advanced and promising of these proposals is quantum cryptography.

**Harnessing entanglement for secure cryptographic schemes
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Modern cryptography depends on the exchange of public and private cryptographic keys that enable two parties to encrypt information. The Achilles' heel of these systems is the safe distribution of a key without it being intercepted by third parties. The security of public-key distribution methods relies on the *unproven* hardness of math problems such as factoring (see article that describes how ALFP Fellow Adriana Lopez's research is addressing this issue ) using conventional (not quantum) computers. And while private shared keys do offer in principle the possibility of unconditionally secure communication, the key distribution process still does not completely avoid the possibility of eavesdropping or, in the case of physical couriers, immunity to bribes.

Quantum cryptography or, more correctly, quantum key distribution, offers a protocol of creating a pair of private keys secured by the laws of physics. Quantum key distribution does not invoke the transport of a key because, by the nature of the entangled state, the key can be created at the sender and receiver simultaneously.

In quantum key distribution, the outcome of each polarization (for Bob and Alice) is arbitrary. Despite this, the outcomes are identical for Bob and Alice every cycle. Each measurement results in one bit of information they hold in common. Thus the key is being built as photons are distributed.

By repeatedly sending and measuring photon polarization states in a clocked fashion, two users gradually build up identical strings of classical bits (or 0s and 1s) that they can use for encrypting another (parallel) data-stream between them. Since quantum states cannot be known before a measurement, the key is completely random.

An important feature of quantum cryptographic systems is that they are impervious to eavesdropping since the state of entanglement is constantly monitored. Any potential eavesdroppers would unavoidably degrade the entanglement and reveal themselves.

For the past year, AT&T Research has been studying photon entanglement distribution over optical fibers.

The first commercial devices for entangled photon systems (see NuCrypt) are already being sold. Though more research instruments than real network equipment, they are a tangible step to harnessing quantum mechanics. Similar equipment from noncommercial sources (see link) is now being used in actual testbeds (one example is the Tokyo QKD Network; for more information, see the News and Views section of the January 2011 issue of Nature Photonics).

**AT&T's experiments into photon entanglement
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The vast installed global fiber-optic network, consisting of over a billion meters of optical fiber cables, opens a particularly attractive opportunity for implementing quantum communications protocols that rely on the distribution of entanglement between distant parties.

Currently two major entanglement schemes have been proposed for telecom photons: polarization and time-bin entanglement. Polarization is particularly attractive because of the ease with which the polarization can be handled with standard off-the-shelf components (as a result, equipment for creating and detecting polarization-entangled photons is now commercially available).

However, there has been a long-standing concern in the community that polarization entanglement could be significantly decohered (degraded) during fiber transmission due to two polarization effects in optical fibers: polarization mode dispersion (PMD) and polarization-dependent loss (PDL).

Answers are starting to come. For the past year, AT&T Research has been conducting experiments to find out what happens to polarization entanglement over fiber optic cables with PMD and other network conditions. The equipment for these experiments has been custom-built for AT&T by NuCrypt. This project is a joint effort with two theorists: Dr. Cristian Antonelli (UniversitÃ dell’Aquila), who collaborates under the auspices of AT&T Virtual University Research Initiative, and Prof. Mark Shtaif (Tel Aviv University), a former AT&T Labs researcher.

On the way to solutions, AT&T researchers are learning more about the fundamental physics of entanglement decoherence. . .

From the outside, the lab setup doesn’t look anything quantum; like ordinary pieces of network equipment, it is housed simply in several black boxes interconnected by strips of fiber and electrical cabling.

One box is an entangled photon source. It creates a pair of entangled photon qubits, separates the paired photons spectrally, and directs each one over a dedicated fiber to one of two single photon detector stations. This process is repeated in a clocked fashion and, as the resulting stream of photon pairs arrives at corresponding detectors, the quantum state of a two-photon state is analyzed using quantum tomography, which completely quantifies a quantum state. By introducing PMD in a controlled way and performing tomography for various levels of PMD in each fiber, researchers thus probe the PMD-induced degradations. While the tomography measurement itself goes quickly (usually a few minutes), the most time is consumed by setting and verifying certain fiber conditions, which are very sensitive to miniscule changes in temperatures as well as other hard-to-control factors.

The primary goal for these experiments is to fully investigate the engineering problems and corresponding solutions that need to be put in place should entanglement-based quantum protocols be someday implemented over AT&T networks. Recent experiments together with developed theory are yielding the first steps to understanding those issues. On the way to solutions, AT&T researchers are learning more about the fundamental physics of entanglement decoherence.

This work, for the first time, found that transmission of polarization entangled photons in optical fibers reveals interplay among several intriguing physical phenomena: entanglement sudden death, the existence of decoherence-free subspaces, and the loss of non-locality. To take the example of sudden death of entanglement: this concept, originally proposed to describe the entanglement dynamics in atomic physics, describes a situation in which the entangled state degrades abruptly and completely in contrast to gradual decay of a single particle state. Interestingly, when PMD is present in one fiber only, the degradation of the entanglement is always gradual. On the other hand, adding some PMD to another fiber could either reduce or increase decoherence depending on the relative orientation of two PMD elements. Sometimes in the latter case the entanglement disappears completely, which is a manifestation of the sudden death arising naturally during photon propagation in fibers.

Remarkably, the use of polarization entanglement in fibers has been debated at numerous conferences in recent years, and the quantum communication community remains split on the subject. AT&T’s work takes a first step towards solving this critical problem, and may have implications across subfield boundaries.

Already experiment results have been presented at various conferences throughout 2010, including the most selective post-deadline session at the Optical Fiber Communication Conference. Journal papers are to follow with more details. The first that appeared in print in 2011 are: Loss of polarization entanglement in a fiber-optic systems with polarization mode dispersion in one optical path (preprint), and Nonlocal PMD compensation in the transmission of non-stationary streams of polarization entangled photons (preprint), and Sudden Death of Entanglement induced by Polarization Mode Dispersion (preprint).

**Possible future directions**

Future research in this field should encompass the following several directions.

First, PMD in realistic fibers is frequency-dependent. This strong frequency dependence could either kill the entanglement or alternatively revive the entanglement if it is lost. Second, studies of the effect of polarization-dependent loss (PDL) are needed. While the PDL of the fibers is relatively small, a notable amount of PDL is introduced by network elements such as wavelength selective switches, optical add/drop multiplexes, and dispersion compensation devices. It would be interesting to figure out the non-trivial interplay between PDL and PMD. Finally, the other effects, such as nonlinearities from strong classical signals propagating through in the same fiber, could also play a role in entanglement decoherence.

Eventually, the potential effectiveness of, and fundamental impediments to, implementing quantum repeater technology in the fiber-optic link also will need to be explored. This technology, once available, holds the promise of truly exploiting the quantum potential of long-haul fiber optic transmission.

Quantum cryptography and communications hold great promise, but numerous effects need to be understood and various related problems are in need of solutions in the rich research area of entanglement distribution via fiber optics fibers.

**What is a qubit?**

A qubit (quantum bit) is a representation of a particle state, such as the spin direction of an electron or the polarization orientation of a photon.

A qubit is the quantum equivalent of a bit in ordinary computing.

But where a bit exists in one of two states (1 or 0), a qubit can exist in an arbitrary combination of both states. Physicists describe this as a **coherent superposition** of two states. This superposition is often represented by a point on a sphere with values 0 and 1 at the sphere poles.

Measurements play an important role in quantum physics.

Once one reads a qubit (or “performs a measurement” in quantum parlance), the qubit collapses into one of the two possible outcome states, with the probability of the particular state depending on the location of the superposition on the sphere.

The result of any *particular *qubit measurement always remains uncertain until the measurement is performed: quantum mechanics just predicts the probabilities of the outcomes.

**What is entanglement?**

Entanglement is a fundamental concept in quantum mechanics. When only two particles are entangled, a measurement performed on one is reflected in the other, even when the two are separated by large distances.

(This “spooky action at a distance” bothered Einstein who, along with Boris Pokolsky and Nathan Rose, in a 1935 paper argued that entanglement violated the locality principle, which states that changes performed on one physical system should have no immediate effect on another spatially separated system. Later experiments, however, have verified the nonlocal behavior of entangled photons.)

Researchers have learned to entangle atoms, photons, atomic ensembles, superconducting quantum interference devices, and mechanical vibrations. The majority of experiments are done with light because entangled photons are easier to create and because they preserve their entanglement better than other particles. One drawback of using photons for quantum computing is that photons fly too fast for convenient storage. However, photon speed is not a constraint but an advantage for quantum cryptography.

**About the author**

Dr. Misha Brodsky joined AT&T Labs in 2000. His contributions to fiber-optic communications focused on optical transmission systems and the physics of fiber propagation, most notably through his work on polarization effects in fiber-optic networks. More recently Misha has been working on quantum communications; single photon detection; where his prime research interest is in photon entanglement and entanglement decoherence mechanisms in optical fibers.

Dr. Brodsky has authored or co-authored over 70 journal and conference papers, a book chapter, and about two dozen patent applications. He is a topical editor for Optics Letters and has been active on numerous program committees for IEEE Photonics Society and OSA conferences. Dr. Brodsky holds a PhD in Physics from MIT.